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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:48.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:17.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:20.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:17.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5442
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:42.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:36.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:34.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4457
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:55.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:02.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:02.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:54.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:04:00.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:52.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    2.22
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:11.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:33.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.43
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.81
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.49
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.37
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.83
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.82
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.44
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  399.31
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:50.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1455.02
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:02.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6978.67
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.99
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.36
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:02.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.77
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.31
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:36.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5001.00
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:17.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45785
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869785
  j =  1                              :        399908434
  j =  2                              :            45777
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46001
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870001
  j =  1                              :        399907998
  j =  2                              :            46001
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:14.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:29.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:18.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:44.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:00.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:53.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 2.91e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:22.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 7.12e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.092
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:36.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:37.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.09
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.57
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.48
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.52
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.30
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.13
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:43.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.18
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.85
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:31.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.50
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.87
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17107.51
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:55.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.22
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   17.33
p-value of test                       :    0.9946


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.64
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.21
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.90
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.39
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.77
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.10
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.27
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.43
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.53
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.70
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.92
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.81
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:46.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.45
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.95
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.41
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.36
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.65
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.61
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.21
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.12
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.19
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.33
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.07
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  328.84
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5113.08
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.24
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.12
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.73
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :   -1.33
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:20.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.20
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:14.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.033
p-value of test                       :    0.49

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:14.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.87e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 7.06e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 3.46e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.50
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.53
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.09
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:11.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.05
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:09.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10012.53
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10055.55
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:58.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    4.94
p-value of test                       :  3.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4630.17
p-value of test                       :    0.9962

-----------------------------------------------
CPU time used                    :  00:01:48.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4914.60
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:49.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.08
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.52
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11864.08
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11956.06
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:30.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.84
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999991931

Normal statistic for number of bits   :  -0.064
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.99
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999962612

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   0.091
p-value of test                       :    0.46

Sample variance                       :    1.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.61
p-value of test                       :    0.95

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:18:31.32

 All tests were passed




Server wird beendet - Lösche Semaphor 589838.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5426
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:44.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:37.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:35.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:55.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:00.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7499
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:01.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:54.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:59.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:46.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:13.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:41.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.17
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.83
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.96
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.06
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.70
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.64
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  194.48
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.59
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:45.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1412.15
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:02.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7058.72
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:43.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:01.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.50
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.63
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:34.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5200.15
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:07.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45867
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869867
  j =  1                              :        399908269
  j =  2                              :            45861
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46045
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870045
  j =  1                              :        399907912
  j =  2                              :            46041
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:30.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:18.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:59.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:53.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.067
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:34.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.83
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.66
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.18
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.79
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.46
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:40.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.16
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.11
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.63
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.21
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:30.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17533.49
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.89
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.04
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.26
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.98
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.02
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.92
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.48
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.55
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.58
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.26
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.44
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.37
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.93
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.67
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.18
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  544.57
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.40
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.42
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.47
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.87
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.42
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.09
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.90
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  442.93
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.28
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4938.30
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.15
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.52
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.93
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:26.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.76
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :    1.15
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:21.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.33e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 3.65e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.98
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.75
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.70
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:10.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.32
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:10.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9889.13
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  3.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    3.44
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9723.77
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:56.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4842.16
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4793.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:49.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.68
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3942.41
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11597.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11859.51
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:28.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.64
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999936452

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.41
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000097948

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.19
p-value of test                       :    0.12

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    2.54
p-value of test                       :  6.5e-3

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.80
p-value of test                       :    0.96

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    2.65
p-value of test                       :  4.6e-3

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:18.00

 All tests were passed




Server wird beendet - Lösche Semaphor 1638414.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5653
p-value of test                       :  8.9e-4    *****


-----------------------------------------------
CPU time used                    :  00:03:44.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:38.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:36.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:55.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4168
p-value of test                       :    0.9949


-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7506
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:02.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:02.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:53.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:59.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.03
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:46.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.14
p-value of test                       :    0.9992    *****


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:16.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     172
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:44.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.87
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.04
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.34
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:55.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.97
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.14
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.04
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:18.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.19
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.31
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  192.73
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.01
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:42.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1535.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7071.00
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:44.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.77
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   85.43
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:58.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.12
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.27
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:34.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5223.69
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:05.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45775
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869775
  j =  1                              :        399908455
  j =  2                              :            45765
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45565
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869565
  j =  1                              :        399908874
  j =  2                              :            45557
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:31.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  6.5e-3

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:18.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:45.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:59.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:34.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.35
p-value of test                       :  9.3e-3

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:32.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.30
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:32.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  106.75
p-value of test                       :  1.5e-3

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.03
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.42
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.01
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.73
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.73
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.57
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:40.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.20
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.37
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.39
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9962

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.35
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17321.26
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:55.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.44
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.59
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.46
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.66
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.00
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.21
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   55.48
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.86
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.90
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.81
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.21
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.12
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.49
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.67
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.72
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.27
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.10
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.92
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.37
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.79
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:43.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.14
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.20
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.24
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.68
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.56
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:34.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.01
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.80
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4908.80
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.82
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.62
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:34.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.89
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :   -1.13
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:23.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.01
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:26.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 6.95e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.84e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 7.18e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.55
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.20
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.95
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:08.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.19
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:09.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9927.13
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10026.18
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:43.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4850.34
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:48.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4979.96
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:50.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.62
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4268.11
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11808.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11642.76
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:29.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.94
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000027160

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.73
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999949577

Normal statistic for number of bits   :   -0.40
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :  -0.053
p-value of test                       :    0.52

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.079
p-value of test                       :    0.47

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:15.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 13  BirthdaySpacings, t = 2         8.9e-4
 24  ClosePairs NP, t = 9            0.9992 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2555918.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:50.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5393
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:47.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:37.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:36.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:55.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:54.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:00.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:00.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7479
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:52.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:57.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.57
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     952
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:46.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.43
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:11.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.82
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:46.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.98
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.24
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.39
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.06
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.74
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.13
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.85
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.70
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  387.32
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:43.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1488.27
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:02.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7309.64
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:45.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.33
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.31
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:05.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.61
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.25
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:29.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5034.27
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:01.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46085
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870085
  j =  1                              :        399907834
  j =  2                              :            46077
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45676
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869676
  j =  1                              :        399908653
  j =  2                              :            45666
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:30.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:20.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :  3.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:45.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 8.65e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:59.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:55.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:34.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.01e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 2.63e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:22.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:33.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.90
p-value of test                       :    0.9982

-----------------------------------------------
CPU time used                    :  00:01:37.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.14
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.60
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:51.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.58
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.72
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.13
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:12.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.02
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.07
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.11
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  169.97
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17354.51
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.82
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.58
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.32
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.58
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.11
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:39.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.12
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.82
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.89
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.28
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.96
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.21
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.23
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.89
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.08
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.57
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.95
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.49
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.62
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.80
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.58
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.57
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.28
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4843.96
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  430.80
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.68
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.58
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.40
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4982.43
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.79
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.51
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.84
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:23.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.23
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:23.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.80e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 8.37e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:46.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.78e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 6.91e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.86
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.87
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:04.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.87
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:06.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 6.20e-3
p-value of test                       :    0.9934

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9683.39
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:56.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9694.57
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.022
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.87
p-value of test                       :  2.1e-3

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:46.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4916.81
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:48.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4960.64
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:50.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4197.81
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.81
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11799.34
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11595.14
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:29.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.44
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999819650

Normal statistic for number of bits   :   -1.43
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.50
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999905594

Normal statistic for number of bits   :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   0.082
p-value of test                       :    0.47

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :  -0.035
p-value of test                       :    0.51

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:42.34

 All tests were passed




Server wird beendet - Lösche Semaphor 3473422.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5420
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:52.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:38.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:55.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:01.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:02.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:54.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:59.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:11.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:39.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.01
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.46
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.90
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.31
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.84
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.34
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.02
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:43.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1475.10
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:01.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7068.31
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:42.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.02
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.4e-3

Anderson-Darling statistic = A2       :    3.29
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   85.37
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:04.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.23
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.40
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:35.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4927.12
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:00.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46192
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870192
  j =  1                              :        399907617
  j =  2                              :            46190
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45809
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869809
  j =  1                              :        399908383
  j =  2                              :            45807
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:30.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:18.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:45.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:01.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:57.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:34.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.16e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.55e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:34.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:33.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.80
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.58
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.42
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:48.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.96
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.39
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.48
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:37.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.83
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.32
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.42
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17691.39
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:52.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.87
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.53
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.10
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.80
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.00
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.55
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.95
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.97
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.43
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.98
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.34
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.29
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.82
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.80
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.94
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  107.75
p-value of test                       :    0.9925


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.98
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.82
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.18
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.41
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.15
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.71
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5099.76
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.27
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  239.30
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.05
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.30
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4810.13
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.32
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.34
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.84
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    1.98
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:25.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.94
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:24.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.08e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 7.22e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.05
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:30.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.62
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:28.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.14
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:07.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.54
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:05.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9911.46
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9944.75
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:44.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.26
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4959.61
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:50.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4232.69
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4201.80
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12039.50
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11750.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.43
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  8000114919

Normal statistic for number of bits   :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.95
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000011212

Normal statistic for number of bits   :   0.089
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :  -0.042
p-value of test                       :    0.52

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:35.34

 All tests were passed




Server wird beendet - Lösche Semaphor 4423694.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5390
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:53.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:41.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:40.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:55.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4188
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7193
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:02.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:02.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:54.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:58.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.17
p-value of test                       :    0.9966


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:46.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.17
p-value of test                       :    0.9959

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    3.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:12.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.88
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.15
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   36.32
p-value of test                       :  6.4e-3

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.82
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.88
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.00
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.95
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.91
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.90
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  385.08
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:43.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1486.57
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:03.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6944.79
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:43.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.60
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:03.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.90
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:47.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.44
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:36.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4953.26
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:59.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45816
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869816
  j =  1                              :        399908371
  j =  2                              :            45810
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46143
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870143
  j =  1                              :        399907722
  j =  2                              :            46127
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 6.86e-3
p-value of test                       :    0.9910

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :  5.2e-3

Anderson-Darling statistic = A2       :    4.55
p-value of test                       :  4.8e-3


-----------------------------------------------
CPU time used                    :  00:02:29.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:17.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:46.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:00.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 6.64e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.62e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.047
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:35.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:34.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.03
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.19
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.23
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.12
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   71.84
p-value of test                       :  5.2e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   11.44
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.11
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17423.18
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.75
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.29
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.76
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.53
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.61
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.46
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.95
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.08
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.11
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.81
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.95
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.05
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.40
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.83
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.44
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.55
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.98
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.94
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.10
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.95
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.81
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.26
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5014.43
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.26
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.02
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.15
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.65
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5097.29
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.16
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.21
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.00
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :    1.79
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:23.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.92
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:24.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.48e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 6.33e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 3.36e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    0.96
p-value of test                       :    0.9985

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.00
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.66
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:07.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.80
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:05.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9963.20
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10180.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:04:10.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5077.76
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:48.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.39
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4208.42
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11808.69
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11870.71
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.04
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999740468

Normal statistic for number of bits   :   -2.05
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.53
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000092455

Normal statistic for number of bits   :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    2.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:55.60
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 64  WeightDistrib, r = 26           5.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5406734.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5673
p-value of test                       :  3.5e-4    *****


-----------------------------------------------
CPU time used                    :  00:03:57.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:42.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:41.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4444
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:03.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:04.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:53.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:58.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.57
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.64
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.59
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.64
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.98
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:14.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.83
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:42.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.62
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.70
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.19
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.75
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.46
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.78
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.01
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.84
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:43.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.07
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:01.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6884.20
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:42.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:03.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.09
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.92
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:33.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5036.89
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:00.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45966
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869966
  j =  1                              :        399908074
  j =  2                              :            45954
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45512
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869512
  j =  1                              :        399908979
  j =  2                              :            45506
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  9.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:29.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:18.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 7.48e-3
p-value of test                       :    0.9914

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:44.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:58.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  8.9e-3

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:36.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.25e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:21.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:33.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:33.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.70
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.78
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:51.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.55
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.33
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.48
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.51
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:37.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.56
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.95
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.40
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.22
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.11
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17103.39
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.46
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.22
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.21
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.69
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.68
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.46
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.19
p-value of test                       :    0.9915


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.40
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.50
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.15
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.49
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.75
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.22
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.03
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.45
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.17
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.93
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.88
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.11
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.48
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.96
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.78
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4961.09
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.19
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.97
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.83
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.74
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.22
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.85
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.86
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.25
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:21.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.84
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :    2.44
p-value of test                       :  7.3e-3



-----------------------------------------------
CPU time used                    :  00:02:22.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.63
p-value of test                       :  1.1e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    6.64
p-value of test                       :  5.4e-4    *****

Tests on the sum of all N observations
Standardized normal statistic         :   -3.22
p-value of test                       :    0.9994    *****

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.85e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.04
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.42
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.77
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:05.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  160.45
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:04.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9932.62
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9877.71
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:42.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.09
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4936.05
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:49.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4317.53
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3934.58
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11605.65
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11828.23
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.84
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000048508

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.23
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999761411

Normal statistic for number of bits   :   -1.89
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    2.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:56.77
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 13  BirthdaySpacings, t = 2         3.5e-4
 82  LempelZiv, r = 0                0.9994 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6488078.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:38.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997309
  j =  2                              :             1344
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5432
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:57.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4206
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:43.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:59.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:05.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:05.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:54.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:59.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    2.59
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     253
p-value of test                       :    0.9970

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:14.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:40.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.27
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.34
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.79
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.55
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.77
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.33
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.46
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.81
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.33
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.04
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:43.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1574.37
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:02:03.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7223.02
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:43.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.74
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:16.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.80
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:03.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.01
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:46.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.34
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:32.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4871.46
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:59.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46006
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870006
  j =  1                              :        399907993
  j =  2                              :            45996
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45894
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869894
  j =  1                              :        399908219
  j =  2                              :            45880
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:28.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    5.05
p-value of test                       :  2.8e-3


-----------------------------------------------
CPU time used                    :  00:02:18.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:44.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:59.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.84
p-value of test                       :  3.5e-3

-----------------------------------------------
CPU time used                    :  00:01:57.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:37.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.15
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:35.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:34.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.21
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.39
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.72
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:49.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.24
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.87
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.06
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:42.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.46
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.41
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.98
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17460.31
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.64
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.29
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.63
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.05
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.73
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.11
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.08
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.21
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.12
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.54
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.82
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.78
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.35
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.25
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.69
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.82
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.86
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.78
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.99
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.97
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.06
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.50
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4755.53
p-value of test                       :    0.9934


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.41
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.41
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.19
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.10
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4959.52
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.98
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.39
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.22
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:22.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.36
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:22.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.48
p-value of test                       :    0.07

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :  9.1e-3

Kolmogorov-Smirnov- statistic = D-    : 8.60e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 5.27e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.30
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.17
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.92
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:05.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.26
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:06.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10011.10
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9860.13
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:49.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4791.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4756.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.52
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4240.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12102.03
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11785.28
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:29.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.61
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999926600

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.86
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000001765

Normal statistic for number of bits   :   0.014
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    2.63
p-value of test                       :  4.9e-3

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    1.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:25.13

 All tests were passed




Server wird beendet - Lösche Semaphor 7536654.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1501
p-value of test                       :  1.4e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334621
  j =  1                              :        599996998
  j =  2                              :             1501
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5590
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:04:00.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:44.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:44.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:58.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:59.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7181
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:05.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:07.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:56.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:04:00.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:46.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.86
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    2.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:12.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.64
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:40.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.97
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.50
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.75
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.78
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.02
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.97
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.17
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.37
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.26
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.57
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:47.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1478.70
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:04.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6853.43
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:42.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.67
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:03.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.53
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.60
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5081.82
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:53.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45949
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869949
  j =  1                              :        399908109
  j =  2                              :            45935
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45682
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869682
  j =  1                              :        399908639
  j =  2                              :            45676
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:27.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 5.20e-3
p-value of test                       :    0.9940

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.46
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  4.9e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:18.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  6.1e-3

Kolmogorov-Smirnov- statistic = D-    : 8.19e-4
p-value of test                       :    0.9992    *****

Anderson-Darling statistic = A2       :    4.96
p-value of test                       :  3.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9994    *****


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:45.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:58.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9935

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 3.77e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.01
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:21.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:37.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:34.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.51
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.26
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.56
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.20
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.73
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:41.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.01e-3
p-value of test                       :    0.9914

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   61.52
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.87
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.82
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.87
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  102.18
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:39.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17052.85
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.62
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.18
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.96
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.60
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.24
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.94
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.52
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.88
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.63
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.88
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.83
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.50
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.84
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.93
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.30
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.82
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.69
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.24
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.15
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.13
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.29
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.04
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.46
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.39
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.83
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:34.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.32
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.17
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.47
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.67
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.86
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:34.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.70
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:22.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.79
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :   -1.72
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:21.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.65
p-value of test                       :    0.05

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.29e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 8.31e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.74e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.89
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.19
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:04.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.85
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:05.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9705.90
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9976.96
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.30
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:03:46.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4858.93
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:49.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5019.51
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:49.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.26
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4040.12
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11612.23
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11774.98
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:29.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.80
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000092509

Normal statistic for number of bits   :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.27
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  7999989549

Normal statistic for number of bits   :  -0.083
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:12.19
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           1.4e-4
 48  MaxOft, t = 24                  0.9994 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8585230.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5373
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:00.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:43.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:44.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:58.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:59.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:07.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:06.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:58.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:59.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    2.56
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     854
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    3.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:51.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    3.73
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     651
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    3.25
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:17.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:45.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.46
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.06
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.89
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.77
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.00
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  271.10
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.40
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:43.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:03.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7114.61
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:44.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.24
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.65
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:04.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.54
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.51
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:33.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4943.55
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:11.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:59.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45826
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869826
  j =  1                              :        399908352
  j =  2                              :            45818
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45823
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869823
  j =  1                              :        399908358
  j =  2                              :            45815
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:26.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:18.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:46.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:00.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:55.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:32.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 9.67e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 9.19e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.027
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:21.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:32.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.20
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.66
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.37
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.94
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.47
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.11
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.64
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:41.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.44
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.63
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.17
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.93
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.00e-4
p-value of test                       :    0.9992    *****

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  172.39
p-value of test                       :  7.6e-3

-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17569.97
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:52.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.13
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.35
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.41
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   46.54
p-value of test                       :  3.8e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.24
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.17
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.64
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.92
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.55
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.97
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.07
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.03
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.96
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.23
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.70
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.16
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.10
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  435.15
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.00
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.25
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.02
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.51
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.15
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.31
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.43
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.92
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.88
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5076.11
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  325.74
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.94
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.06
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:23.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.89
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :   -0.86
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:21.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 5.15e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 5.45e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.02
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.57
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.68
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:04.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  156.61
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:05.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10065.30
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9752.75
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.092
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:43.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.26
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:47.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:49.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3891.36
p-value of test                       :    0.9942

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4033.09
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11563.61
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11671.59
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:28.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.96
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999933743

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.94
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  8000000679

Normal statistic for number of bits   : 5.37e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :  -0.069
p-value of test                       :    0.53

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   0.065
p-value of test                       :    0.47

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:14.78

 All tests were passed




Server wird beendet - Lösche Semaphor 9633806.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1484
p-value of test                       :  7.2e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334604
  j =  1                              :        599997032
  j =  2                              :             1484
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5461
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:04:02.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:45.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7170
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:47.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4427
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:00.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:02.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:11.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:08.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:04:11.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:50.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.16
p-value of test                       :    0.9972


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.79
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     325
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:17.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    3.00
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:47.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.41
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.65
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.35
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.02
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.96
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.01
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.54
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.49
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.00
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:47.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1521.21
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:05.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7127.77
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.79
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.61
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:06.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.76
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.86
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4929.70
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:10.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45780
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869780
  j =  1                              :        399908443
  j =  2                              :            45774
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45737
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869737
  j =  1                              :        399908528
  j =  2                              :            45733
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:30.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :  1.6e-3

Anderson-Darling statistic = A2       :    5.82
p-value of test                       :  1.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  8.8e-4    *****


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:18.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:46.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:02.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9988

-----------------------------------------------
CPU time used                    :  00:01:55.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.068
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:41.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:43.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.64
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:48.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.63
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:55.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.46
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:48.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.11
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.16
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.15
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:45.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.36
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9973

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.97
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.79
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.37
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.67
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17486.88
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.20
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.40
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.43
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.70
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.27
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.80
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.69
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.32
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.35
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.78
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.60
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.49
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.62
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.90
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.55
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.92
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.36
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.62
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.64
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.15
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:43.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.50
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  451.39
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4991.96
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.90
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.91
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.27
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.84
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.08
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.89
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.91
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.80
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:22.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.87
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:23.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :  -0.060
p-value of test                       :    0.52

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 7.95e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.82e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 7.74e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.13
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.63
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.58
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:05.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.99
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:04.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.26
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10120.74
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:04:20.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4764.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:51.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5011.00
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:53.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.48
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4022.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11755.27
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:31.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11938.03
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.65
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000041185

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.04
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000076630

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.82
p-value of test                       :    0.03

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:38.25
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  7  CollisionOver, t = 7            7.2e-4
 47  MaxOft, t = 16                  8.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10616846.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1461
p-value of test                       :  4.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334581
  j =  1                              :        599997078
  j =  2                              :             1461
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5470
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:04:00.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:42.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:42.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4229
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:58.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:58.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:09.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:06.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:57.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7505
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:04:01.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     863
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.76
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    2.52
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:17.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:50.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.19
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.23
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.71
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.17
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.17
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.12
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.34
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.93
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  382.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:43.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1534.41
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:02.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6951.90
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:43.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.87
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.15
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:04.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.22
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.32
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:29.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4746.84
p-value of test                       :    0.9985


-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:01.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45947
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869947
  j =  1                              :        399908107
  j =  2                              :            45945
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45670
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869670
  j =  1                              :        399908666
  j =  2                              :            45658
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:27.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:19.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:46.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:01.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:55.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:33.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 7.37e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:22.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.01e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:21.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:48.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.97
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.89
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.59
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.52
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.02
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.85
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.80
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.39
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.13
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.04
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17355.89
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.13
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.43
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.34
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.11
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.85
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.42
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.02
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.29
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.15
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.89
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.35
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  430.95
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.67
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.56
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.16
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.80
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.85
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.87
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.25
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.91
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.66
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5101.18
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  310.49
p-value of test                       :    0.9953


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.92
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.78
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.04
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.37
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.36
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.28
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.80
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:23.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    2.99
p-value of test                       :    0.9956


-----------------------------------------------
Normal statistic for number of jumps  :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:23.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.74
p-value of test                       :    0.96

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.99e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 8.57e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.65e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 7.01e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.19
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.85
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.83
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:04.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.03
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:05.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10261.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10364.98
p-value of test                       :  5.3e-3

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:41.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.36
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:49.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4927.96
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:50.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4090.32
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.99
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11868.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11846.52
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:29.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.91
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999883883

Normal statistic for number of bits   :   -0.92
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.36
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000121885

Normal statistic for number of bits   :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.43

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:53.88

 All tests were passed




Server wird beendet - Lösche Semaphor 11763726.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5551
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:58.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:43.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:42.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:58.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:00.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:08.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:09.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:56.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:01.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.47
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:49.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:15.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    2.28
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:47.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.19
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.62
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.45
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.02
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.60
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.82
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.14
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.31
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  374.38
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.60
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:03.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7128.82
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:42.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.24
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.35
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:03.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.78
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.92
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5105.87
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:00.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46426
p-value of test                       :  5.5e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870426
  j =  1                              :        399907151
  j =  2                              :            46420
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45975
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869975
  j =  1                              :        399908053
  j =  2                              :            45969
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:26.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:18.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:46.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:00.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:34.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:22.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:34.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:35.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.17
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.85
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.19
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.25
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.40
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.49
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.59
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:37.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.59
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.33
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.23
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.07
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17267.69
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.89
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.03
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.79
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.63
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.46
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.72
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.82
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.67
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.62
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.44
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.34
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.40
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  450.58
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.68
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.43
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.98
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.03
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.76
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.13
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.05
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.16
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.80
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4907.80
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.80
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.79
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.32
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.87
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5069.03
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.26
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.56
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.71
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :   -0.11
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:23.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.16
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:23.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 6.42e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.95e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 5.80e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.31
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.63
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.66
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:06.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.24
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:07.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10243.53
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.5e-3

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10264.77
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:39.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4949.10
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.90
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:50.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4133.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.33
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11908.52
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11841.89
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:29.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.27
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000007864

Normal statistic for number of bits   :   0.062
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.47
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000094261

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 4.36e-3
p-value of test                       :    0.9955

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.65
p-value of test                       :    0.95

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   0.044
p-value of test                       :    0.48

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:12.97

 All tests were passed




Server wird beendet - Lösche Semaphor 12779534.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:40.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1259
p-value of test                       :    0.9979

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334379
  j =  1                              :        599997482
  j =  2                              :             1259
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5435
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:59.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4217
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:43.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:58.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:00.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:09.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:09.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:58.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:02.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.68
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:49.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:16.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:51.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.68
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.18
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.65
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.76
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:10.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.33
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.24
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.70
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  189.06
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.88
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:46.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.99
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:02.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7147.79
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.61
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.62
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.12
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:03.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.91
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   91.16
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:32.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5110.36
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:01.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45993
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869993
  j =  1                              :        399908016
  j =  2                              :            45989
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46044
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870044
  j =  1                              :        399907917
  j =  2                              :            46034
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:27.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:18.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.9999    *****

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:00.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:55.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:35.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.075
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:38.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.034
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:39.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.20
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.03
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.23
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.21
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.42
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.83
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.46
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:37.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.89
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.16
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.01
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:38.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17627.24
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.68
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.47
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.76
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.38
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.41
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.98
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.75
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.09
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.11
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.37
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.63
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.88
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.95
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.71
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.87
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.72
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.91
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.95
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.59
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.00
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.42
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.69
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.46
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.65
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.11
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.39
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.72
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.68
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.42
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.49
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :    0.72
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:22.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.45
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:22.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.61
p-value of test                       :  1.9e-4    *****

Anderson-Darling statistic = A2       :    5.02
p-value of test                       :  3.0e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.16
p-value of test                       :    0.02

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 2.06e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 9.10e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.56
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.22
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  239.67
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:07.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.92
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:05.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9962.36
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10100.61
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:40.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5004.10
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:47.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5120.48
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:49.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4213.16
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12078.33
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11826.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:29.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.69
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999951908

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.61
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000139138

Normal statistic for number of bits   :    1.10
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:19.90

 All tests were passed




Server wird beendet - Lösche Semaphor 13795342.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5438
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:04:02.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:43.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:45.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4218
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:02.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:13.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7171
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:14.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:04:10.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:04:12.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.30
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    2.62
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     853
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:52.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.18
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    2.25
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:18.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:50.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.63
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.20
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.86
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.81
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:10.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.61
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.01
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:32.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.00
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:31.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.27
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:31.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.65
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.07
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:54.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.48
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:05.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6897.45
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:56.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.44
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:37.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.32
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.97
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:40.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5128.60
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:09.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45752
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869752
  j =  1                              :        399908497
  j =  2                              :            45750
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45917
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869917
  j =  1                              :        399908168
  j =  2                              :            45913
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.91e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :  4.4e-3

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:31.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:19.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:49.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:06.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:38.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:24.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:24.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:24.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:47.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:48.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.29
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.05
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.52
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.94
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:51.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.60
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.85
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17570.04
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.02
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.68
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.04
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.59
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.39
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.87
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.27
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.98
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.74
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.00
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  108.54
p-value of test                       :    0.9912


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.73
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.33
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.93
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.72
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.61
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.21
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.83
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.62
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.09
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.79
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.02
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.69
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.13
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.48
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.48
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.22
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.06
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.23
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.21
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.67
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :   -1.09
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:22.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.44
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :   -0.98
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:22.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 4.29e-4
p-value of test                       :    0.9996    *****

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -2.06
p-value of test                       :    0.98

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 5.02e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.76
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.28
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.16
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:05.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.20
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:06.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10067.63
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10079.73
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:04:29.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.70
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:56.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.46
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:59.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3991.94
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4202.49
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11746.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:35.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11641.71
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:37.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.50
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000126925

Normal statistic for number of bits   :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.32
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000055660

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:11:04.13

 All tests were passed




Server wird beendet - Lösche Semaphor 14843918.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1243
p-value of test                       :    0.9995    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334363
  j =  1                              :        599997514
  j =  2                              :             1243
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5326
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:59.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7143
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:42.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4233
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:57.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:58.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:07.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:06.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:59.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:01.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.12
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    2.90
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:52.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:15.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:18.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:49.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.54
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.90
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.80
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.32
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.11
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  281.08
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.43
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:43.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.82
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:03.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7141.50
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.04
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:02.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.61
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:34.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5138.62
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:57.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45924
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869924
  j =  1                              :        399908156
  j =  2                              :            45916
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45737
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869737
  j =  1                              :        399908529
  j =  2                              :            45731
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:26.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:20.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:46.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:59.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:55.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:34.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.11e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.89e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:21.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:37.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:37.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.15
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.48
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.81
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.22
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.70
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.94
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.56
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.59
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.93
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.63
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.76
p-value of test                       :  7.6e-3

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.51
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17669.64
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:52.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.08
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.15
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.23
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.94
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.46
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.05
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.00
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.00
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.09
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.32
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.18
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.42
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.41
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.04
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.29
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.34
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.79
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.72
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.96
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.78
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.82
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.23
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5073.62
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  331.35
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.47
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.07
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.91
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5130.70
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.22
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.96
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.31
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:23.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.80
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.10

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 5.63e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.19e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.13
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.24
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.68
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:04.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9981

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.89
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:06.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10117.71
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10118.09
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:46.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4973.94
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.59
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:50.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4034.87
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.41
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11761.65
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11784.31
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:29.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.39
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000018706

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.01
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000002743

Normal statistic for number of bits   :   0.022
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:12.01
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14           0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15958030.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5369
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:02.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4223
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:44.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:45.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:00.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:02.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:12.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:13.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:08.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:04:13.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:52.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    8.60
p-value of test                       :  6.5e-5    *****

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     566
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    2.61
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:18.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.96
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    2.44
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:44.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.79
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.99
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.66
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.88
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.89
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.12
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.53
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:30.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.85
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:57.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1516.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:07.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7162.42
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:58.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.28
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.24
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:14.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.57
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:46.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.26
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:43.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5144.91
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:55.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46135
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870135
  j =  1                              :        399907742
  j =  2                              :            46111
  j =  3                              :               12
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45994
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869994
  j =  1                              :        399908018
  j =  2                              :            45982
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:31.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:20.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:54.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:10.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:56.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:38.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 5.68e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.85e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:24.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:24.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:44.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:44.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.22
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.72
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.81
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.57
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.90
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:53.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.71
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.59
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.53
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.09
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.07
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17415.95
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:54.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.04
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.66
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.87
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.73
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.96
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.04
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.41
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.26
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.89
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.92
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.73
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.76
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.75
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.60
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.32
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  209.61
p-value of test                       :  4.4e-4    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.67
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.56
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.95
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.37
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.20
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.97
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4992.41
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.73
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  162.81
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.15
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.19
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.72
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.11
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.50
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:34.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.73
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :   0.052
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:23.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.62
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :    1.06
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:25.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 7.37e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.56e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 4.96e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.03
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.42
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.26
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:06.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.89
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:06.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9808.07
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10315.38
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:04:36.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5013.34
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:52.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4867.19
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:55.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.79
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4030.30
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11741.91
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:34.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11569.17
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.26
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999998660

Normal statistic for number of bits   :  -0.011
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:09.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.86
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999970532

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:01.63
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs mNP, t = 5           6.5e-5
 77  RandomWalk1 H (L=1000, r=20)    4.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17006606.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:40.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1264
p-value of test                       :    0.9968

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334384
  j =  1                              :        599997472
  j =  2                              :             1264
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1504
p-value of test                       :  1.0e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334624
  j =  1                              :        599996992
  j =  2                              :             1504
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1274
p-value of test                       :    0.9929

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334394
  j =  1                              :        599997452
  j =  2                              :             1274
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5489
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:59.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:43.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7467
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:43.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:57.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:57.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:05.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7481
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:05.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:56.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7162
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:04:01.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.99
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:48.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.84
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     568
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    2.25
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     334
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:11.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.95
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.78
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    2.52
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:41.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.75
p-value of test                       :    0.9979

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.98
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.97
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.23
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:10.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.56
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.98
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.57
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.42
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.08
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:43.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1509.86
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:02.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7084.65
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.41
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.68
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:02.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.91
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.50
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:31.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5273.37
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:56.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46005
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870005
  j =  1                              :        399907993
  j =  2                              :            45999
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45684
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869684
  j =  1                              :        399908637
  j =  2                              :            45674
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:28.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:19.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 4.35e-3
p-value of test                       :    0.9953

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  8.9e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:02.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:34.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.95e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:34.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.14
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.38
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.72
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.84
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.87
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.88
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.71
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.50
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.07
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.48
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.92
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17702.29
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.48
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.02
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.12
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.12
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.05
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.51
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.84
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.68
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.65
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.19
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.83
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.18
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.68
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.14
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.64
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.96
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.47
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.56
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.13
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.05
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.18
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.67
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.06
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.02
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.69
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.36
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.06
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.57
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.28
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  251.35
p-value of test                       :  8.0e-3


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.44
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :  -0.055
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:24.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.64
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :   0.016
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:23.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.49e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.28e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.63
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.72
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.26
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:06.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.00
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:05.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10129.74
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10181.14
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.014
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:48.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4820.33
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:49.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.29
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:50.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.21
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3936.92
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12031.09
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11837.22
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:29.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.84
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999906119

Normal statistic for number of bits   :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.82
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000012613

Normal statistic for number of bits   :   0.100
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   0.078
p-value of test                       :    0.47

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:46.51
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           1.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18219022.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1257
p-value of test                       :    0.9983

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334377
  j =  1                              :        599997486
  j =  2                              :             1257
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5513
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:04:01.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:43.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:45.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:58.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:08.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:08.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:05.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:04:07.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:49.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:14.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:41.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.09
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.37
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.97
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.50
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.44
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:12.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.33
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.77
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.89
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  187.01
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.46
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.96
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:04.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6869.75
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:50.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.14
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:10.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.10
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.53
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4977.75
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:58.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45975
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869975
  j =  1                              :        399908059
  j =  2                              :            45957
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45764
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869764
  j =  1                              :        399908474
  j =  2                              :            45760
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:30.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:18.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:05.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:56.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:36.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.12e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 7.85e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.12
p-value of test                       :    0.9997    *****

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.66e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:39.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:40.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.03
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.85
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:51.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.05
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.04
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.40
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:46.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.65
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.03
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.99
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:40.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17351.28
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.84
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.10
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.41
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.38
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.49
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.59
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.90
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.08
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.68
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.83
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.92
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.50
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.71
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.92
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.79
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.56
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.85
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.87
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.80
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.73
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.44
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.09
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5019.88
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.57
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.27
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.85
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.07
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.50
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.71
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.61
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.91
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:23.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.12
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :   0.057
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:23.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    2.57
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.54e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 6.15e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.30
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.63
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.30
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:05.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.15
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:07.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9908.99
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10217.09
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:04:20.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.49
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4635.36
p-value of test                       :    0.9955

-----------------------------------------------
CPU time used                    :  00:01:53.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4813.18
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:55.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.20
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.07
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11753.53
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:33.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11769.90
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:32.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.00
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999900095

Normal statistic for number of bits   :   -0.79
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.74
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999953789

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.11
p-value of test                       :    0.9999    *****

Tests on the sum of all N observations
Standardized normal statistic         :  -0.066
p-value of test                       :    0.53

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.58
p-value of test                       :    0.94

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:11.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         : -2.76e-3
p-value of test                       :    0.50

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:12.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:53.90
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 53  SampleMean, r = 0               0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19267598.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5486
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:56.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:41.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:58.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:06.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:05.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:54.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:59.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     946
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:46.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.54
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:13.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.69
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:39.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.21
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.61
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.87
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.55
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.99
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.74
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.79
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  279.87
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.71
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1378.19
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:00.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6936.75
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:42.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.76
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:04.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.55
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.45
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:34.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5107.36
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:55.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45852
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869852
  j =  1                              :        399908303
  j =  2                              :            45838
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45704
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869704
  j =  1                              :        399908595
  j =  2                              :            45698
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:28.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:19.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:45.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:00.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:56.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:34.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 9.62e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.71e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.56e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.030
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:34.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:37.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.37
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.18
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.87
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:48.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.26
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.40
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.60
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:43.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.90
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17059.38
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.11
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.39
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.93
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.74
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.74
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.28
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.53
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.14
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.39
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.84
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.72
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.35
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.27
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.71
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.62
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.68
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  449.52
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.15
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   50.33
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.47
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.82
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5097.47
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.26
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.76
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.39
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.08
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4896.35
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.66
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.09
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:24.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.87
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   -1.47
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:25.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9971

Tests on the sum of all N observations
Standardized normal statistic         :   0.065
p-value of test                       :    0.47

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    2.45
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.25e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 8.44e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.37e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.98
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.88
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.17
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:06.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.99
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:07.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9965.79
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10033.99
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.079
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:43.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4999.31
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4825.77
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:49.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.62
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.59
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11938.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11963.12
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.26
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000039193

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.00
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000060040

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:18.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.22
p-value of test                       :    0.9916

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:36.72

 All tests were passed




Server wird beendet - Lösche Semaphor 20316174.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:19.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:22.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1556
p-value of test                       :  2.0e-7    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334676
  j =  1                              :        599996888
  j =  2                              :             1556
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:17.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5355
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:42.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4205
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:36.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:35.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:55.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7457
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:02.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:02.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:53.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:58.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.89
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:53.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    2.84
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     331
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:10.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.85
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:32.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.83
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.74
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.83
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.04
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.65
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:12.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.55
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.77
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.62
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.87
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.81
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:49.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1476.98
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:02.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7235.12
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.16
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:02.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.99
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  143.43
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5048.56
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:20.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46025
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870025
  j =  1                              :        399907951
  j =  2                              :            46023
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46198
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870198
  j =  1                              :        399907606
  j =  2                              :            46194
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:13.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:28.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:19.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:46.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:00.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:53.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 2.13e-3
p-value of test                       :    0.9978

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:34.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.07e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 7.43e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:38.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:38.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.04
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:49.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.13
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.82
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.09
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.96
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.53
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.79
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:43.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.14
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.65
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:31.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:29.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.37
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   92.74
p-value of test                       :    0.9944

-----------------------------------------------
CPU time used                    :  00:00:40.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17071.05
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.90
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.08
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.26
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.42
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.33
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.07
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.96
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.48
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.78
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.83
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.83
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.88
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.36
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.11
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.03
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:46.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.17
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.50
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.90
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.43
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.36
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.76
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.47
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4879.19
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.60
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.21
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.52
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.53
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5091.13
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.03
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.04
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.29
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:18.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.46
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:15.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.61
p-value of test                       :    0.05

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:12.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 7.16e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 5.70e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.79
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.18
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  249.67
p-value of test                       :  9.7e-3

-----------------------------------------------
CPU time used                    :  00:02:09.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.72
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:08.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10167.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10042.68
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:04:00.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4993.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4976.11
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4150.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3936.10
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11905.03
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11681.18
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:30.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.91
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000118897

Normal statistic for number of bits   :    0.94
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.58
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999994352

Normal statistic for number of bits   :  -0.045
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.58
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.28
p-value of test                       :    0.01

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.10

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    2.65
p-value of test                       :  4.5e-3

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:18:54.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           2.0e-7
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 622607.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:45.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:37.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:36.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:55.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4481
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:55.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:01.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:01.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:54.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:59.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.75
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     857
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.61
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.17
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:12.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.29
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:42.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.76
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.04
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    5.84
p-value of test                       :    0.9968

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.79
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.79
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.26
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.86
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.43
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.57
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:44.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1383.06
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:01.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6974.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:43.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.75
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:00.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.67
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.77
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:35.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5037.17
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:15.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:22.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45722
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869722
  j =  1                              :        399908559
  j =  2                              :            45716
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45715
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869715
  j =  1                              :        399908573
  j =  2                              :            45709
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:29.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:18.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:45.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:00.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:53.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:32.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 6.03e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.40e-5
p-value of test                       :    0.9922

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:21.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:33.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.51
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:48.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.96
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.00
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.02
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:43.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.40
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.69
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.56
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:30.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:31.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:10.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.19
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17506.19
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.45
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.08
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.28
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.12
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.90
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.21
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.66
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.32
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.83
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.21
p-value of test                       :    0.9971


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.89
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.53
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.39
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.07
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.76
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.34
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.23
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.07
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.37
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.69
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.86
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.62
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4952.04
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.85
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.10
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.91
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.12
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.48
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.46
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.25
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.29
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    0.45
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:21.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.29
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:22.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 5.31e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.30e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 5.48e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.30
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.93
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   40.00
p-value of test                       :  4.5e-3



-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.56
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:10.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.99
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:08.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9722.34
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10159.29
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:04:05.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4799.54
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:49.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.5e-3

Anderson-Darling statistic = A2       :    4.37
p-value of test                       :  6.0e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5166.01
p-value of test                       :  3.0e-3

-----------------------------------------------
CPU time used                    :  00:01:48.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4215.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4206.51
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12064.20
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11555.18
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:30.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.73
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000006778

Normal statistic for number of bits   :   0.054
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.99
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999997139

Normal statistic for number of bits   :  -0.023
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:52.88

 All tests were passed




Server wird beendet - Lösche Semaphor 1736719.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5388
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:47.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4242
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:38.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:37.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:03.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:03.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:54.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:58.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9932


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     548
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    4.40
p-value of test                       :  5.6e-3

Stat. AD after spacings (mNP2-S)      :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:14.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.84
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    2.11
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    3.96
p-value of test                       :  9.2e-3

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:44.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.09
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.13
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.84
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.38
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.14
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.57
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.03
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.44
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.44
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:43.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1495.53
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:01.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7171.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:41.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.89
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.11
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:00.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.72
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.90
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:34.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4788.35
p-value of test                       :    0.9943


-----------------------------------------------
CPU time used                    :  00:01:15.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:22.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45407
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869407
  j =  1                              :        399909187
  j =  2                              :            45405
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45818
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869818
  j =  1                              :        399908367
  j =  2                              :            45812
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:28.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9919

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:18.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  5.0e-3

Anderson-Darling statistic = A2       :    3.55
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  7.5e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:45.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:00.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:54.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:33.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.91e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 8.25e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:35.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -7.05e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:35.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.54
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.29
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.81
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.47
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.50
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:40.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.35
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 8.20e-3
p-value of test                       :    0.9912

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.15
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.10
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:29.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.22
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:29.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9965

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17428.09
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:52.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.82
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.87
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.52
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.96
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.00
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.26
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.97
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.42
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.33
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.97
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.57
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.96
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.97
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.16
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.99
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.84
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.69
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.36
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.69
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.70
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.40
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.49
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4933.87
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.88
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.68
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:36.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.50
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.17
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4897.50
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.05
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  160.91
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:36.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   28.53
p-value of test                       :  4.6e-3


-----------------------------------------------
Normal statistic for number of jumps  :    1.70
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:25.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.59
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :  -0.051
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:24.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :  -0.082
p-value of test                       :    0.53

Sample variance                       :    2.67
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.08e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 8.70e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 2.74e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.59
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.06
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:10.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:09.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9884.53
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.2e-3

Kolmogorov-Smirnov- statistic = D-    : 5.88e-3
p-value of test                       :    0.9938

Anderson-Darling statistic = A2       :    4.72
p-value of test                       :  4.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9572.51
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:47.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.94
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:49.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5018.75
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:49.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.89
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4261.68
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11864.41
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11505.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.04
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000125131

Normal statistic for number of bits   :    0.99
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.67
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999925073

Normal statistic for number of bits   :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.14
p-value of test                       :    0.9984

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:12.85

 All tests were passed




Server wird beendet - Lösche Semaphor 2719759.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5444
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:48.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:38.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:37.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:54.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:55.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:01.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:02.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:53.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:57.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:47.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.15
p-value of test                       :    0.9982

-----------------------------------------------
CPU time used                    :  00:02:12.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:41.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.27
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.14
p-value of test                       :    0.9923

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.98
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.60
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   27.84
p-value of test                       :    0.9988

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.71
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.05
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  265.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:44.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1472.65
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:00.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6919.89
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.59
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.83
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:02.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.22
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.51
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:35.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5138.51
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:17.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46236
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870236
  j =  1                              :        399907532
  j =  2                              :            46228
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45813
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869813
  j =  1                              :        399908377
  j =  2                              :            45807
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:28.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:19.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:46.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  6.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    4.17
p-value of test                       :  7.4e-3


-----------------------------------------------
CPU time used                    :  00:02:01.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:55.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:33.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.58e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.43e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 3.58e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.72
p-value of test                       :  3.3e-3

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:37.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:38.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  100.83
p-value of test                       :  4.7e-3

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.14
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.46
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.43
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.97
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.22
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.16
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:38.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.09
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:29.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.21
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:29.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  157.40
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17346.52
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.55
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.37
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.31
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.82
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.46
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.58
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.19
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.27
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.33
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.98
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.12
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.54
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.10
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.06
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.09
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.10
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.62
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.21
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.63
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.50
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  444.62
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.82
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.95
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.66
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.12
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  452.25
p-value of test                       :  9.3e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.30
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.05
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.89
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.67
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.75
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:25.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.66
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :    1.43
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:23.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.68
p-value of test                       :    0.95

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 3.23e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.16e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.75
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.15
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.37
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:09.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.44
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:11.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9866.60
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9859.58
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:55.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4989.28
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4965.29
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:49.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.11
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.26
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11661.32
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:29.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12215.43
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:01:30.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.71
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999998588

Normal statistic for number of bits   :  -0.011
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.78
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000081049

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :  -0.034
p-value of test                       :    0.51

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:31.31

 All tests were passed




Server wird beendet - Lösche Semaphor 3604495.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5346
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:51.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:39.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:37.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:05.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:06.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:59.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:04:00.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    3.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.81
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:12.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.95
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    3.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:39.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.22
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.49
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.12
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.61
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.27
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  192.38
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  487.41
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:52.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1380.75
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:07.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7128.31
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:56.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.84
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.41
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:17.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.41
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  153.83
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:37.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5150.01
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:04.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45718
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869718
  j =  1                              :        399908569
  j =  2                              :            45708
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45703
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869703
  j =  1                              :        399908597
  j =  2                              :            45697
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:31.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:19.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:49.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 9.17e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:06.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:58.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:37.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.42e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 4.46e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.033
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:49.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:50.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.86
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.11
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.73
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.33
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.16
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:50.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.70
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.19
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.67
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.61e-3
p-value of test                       :    0.9930

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.8e-3

Anderson-Darling statistic = A2       :    3.93
p-value of test                       :  9.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  175.57
p-value of test                       :  4.8e-3

-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17746.83
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.85
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.52
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.66
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.60
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.02
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:37.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.04
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.52
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.69
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.10
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.58
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.21
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.67
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.64
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.16
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.83
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.26
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.86
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.27
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  181.47
p-value of test                       :  5.6e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.75
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.38
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.60
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4873.21
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.71
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.34
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.50
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.48
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5007.41
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.90
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.93
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:34.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.33
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :   -1.61
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:24.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.52
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:26.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.16
p-value of test                       :    0.02

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 6.00e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:46.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.60
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.29
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.56
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:08.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.05
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:08.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9949.23
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10032.56
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:04:27.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.91
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:56.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4929.72
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:59.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4202.21
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:29.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11750.44
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:35.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11930.78
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:36.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.38
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000054394

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.69
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999928064

Normal statistic for number of bits   :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :  -0.018
p-value of test                       :    0.51

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:13.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:11:27.00

 All tests were passed




Server wird beendet - Lösche Semaphor 4521999.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:43.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1253
p-value of test                       :    0.9988

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334373
  j =  1                              :        599997494
  j =  2                              :             1253
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5437
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:51.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:38.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:55.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:03.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:03.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:54.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:59.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.61
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:13.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.65
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:44.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.20
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.63
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.98
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.68
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.01
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.71
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.01
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.62
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.80
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.09
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:43.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1354.48
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:02.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6812.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:43.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.86
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.73
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:01.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.66
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  149.58
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:35.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4936.47
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:59.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45950
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869950
  j =  1                              :        399908105
  j =  2                              :            45940
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45708
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869708
  j =  1                              :        399908586
  j =  2                              :            45704
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:27.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:19.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:46.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:01.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:34.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 9.36e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:22.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:21.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:33.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:36.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.95
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.95
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.37
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.92
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.83
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.94
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:46.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.77
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.46
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.14
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.091
p-value of test                       :    0.9929

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.82
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:37.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17156.35
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.41
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.71
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.72
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.24
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.81
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.00
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.80
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.23
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.44
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.03
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.00
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.89
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.92
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  102.89
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.45
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.82
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.06
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.80
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.42
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.34
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.83
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.31
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.54
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.38
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.12
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.78
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  313.37
p-value of test                       :    0.9965


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5095.01
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.02
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.64
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:36.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.22
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :   -0.48
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:27.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.87
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:28.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 4.47e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.23
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.62
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.66
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:07.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.44
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:05.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10211.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10034.86
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:53.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.24
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:49.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.60
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:49.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4244.00
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4187.92
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11950.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11927.22
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.59
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000002359

Normal statistic for number of bits   :   0.019
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.94
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999947432

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.62
p-value of test                       :  1.5e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    5.72
p-value of test                       :  1.4e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.79
p-value of test                       :    0.9974

Sample variance                       :    0.21
p-value of test                       :    0.9931

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9952

Tests on the sum of all N observations
Standardized normal statistic         :   0.091
p-value of test                       :    0.46

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:23.42

 All tests were passed




Server wird beendet - Lösche Semaphor 6029327.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5251
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:54.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:40.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:40.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:03.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:04.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:55.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:04:00.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.06
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:44.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    2.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:07.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.84
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:36.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.08
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.29
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.88
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.45
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.27
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.66
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.86
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  266.62
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.87
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:43.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1422.06
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:01.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7032.76
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:40.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.46
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.68
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:01.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.20
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.96
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:34.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5204.09
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:00.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46077
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870077
  j =  1                              :        399907848
  j =  2                              :            46073
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45761
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869761
  j =  1                              :        399908481
  j =  2                              :            45755
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:27.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:17.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 2.71e-3
p-value of test                       :    0.9971

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:44.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:58.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:55.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:33.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.25e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.46e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:33.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:33.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.19
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.08
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.49
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.67
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.26
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.92
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.04
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:44.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.09
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.37
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.41
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17532.26
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.20
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.82
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.78
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.25
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.88
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.50
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.72
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.66
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.04
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.45
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.32
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.07
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.75
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.26
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.46
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.42
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.70
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.35
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.04
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.61
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5176.76
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.01
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.00
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.43
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.99
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.15
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.53
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.38
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.12
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:24.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.34
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:24.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.80
p-value of test                       :    0.04

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.60

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 8.93e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 6.30e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.84
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.62
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.19
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:06.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.57
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:07.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10045.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.5e-3

Anderson-Darling statistic = A2       :    4.16
p-value of test                       :  7.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10332.25
p-value of test                       :  9.9e-3

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:50.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.55
p-value of test                       :  1.1e-3

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5065.17
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9970

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4910.52
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:49.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.01
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4159.85
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11752.42
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11940.78
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.24
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999871793

Normal statistic for number of bits   :   -1.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.46
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000038521

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:19.26

 All tests were passed




Server wird beendet - Lösche Semaphor 6946831.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1467
p-value of test                       :  3.1e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334587
  j =  1                              :        599997066
  j =  2                              :             1467
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5364
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:53.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4444
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:39.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:55.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4461
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:56.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:04.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:04.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:53.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:59.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:46.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     565
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.82
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     269
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.95
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:14.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.99
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    2.87
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:40.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.04
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.97
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.01
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.31
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.75
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.39
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.71
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:18.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.02
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:43.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1420.27
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:02.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7197.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:43.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.35
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.65
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:02.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.80
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.59
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:34.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5038.89
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:01.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45813
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869813
  j =  1                              :        399908376
  j =  2                              :            45809
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45953
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869953
  j =  1                              :        399908097
  j =  2                              :            45947
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:28.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:18.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:45.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:59.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:34.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.44e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.70e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:21.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.031
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:37.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:37.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.03
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.22
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.66
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.56
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.85
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:45.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.98
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.64
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.68
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.61
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17439.28
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.60
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.16
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.97
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.14
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.25
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.65
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.40
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.11
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.64
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.83
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.48
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.48
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.20
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.76
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.79
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.34
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.19
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.87
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.62
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.32
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.83
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.34
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.99
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.72
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.30
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.22
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.89
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5076.82
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.22
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.89
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.32
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:23.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.27
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    1.13
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:24.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.92
p-value of test                       :    0.03

Sample variance                       :    2.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.90e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 5.16e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:46.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.76e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 6.82e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.97
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.14
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.24
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:07.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.07
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:06.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9844.59
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9985

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9997.23
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:53.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4843.75
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:48.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.10
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:49.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4237.74
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.03
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11673.43
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11857.55
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:29.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.16
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000034216

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.68
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000049312

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:42.96

 All tests were passed




Server wird beendet - Lösche Semaphor 7897103.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997293
  j =  2                              :             1352
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5364
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:04:01.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:43.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:44.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:00.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:01.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:12.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:11.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:08.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:04:12.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    2.21
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:15.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.9900

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:39.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.94
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.76
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.43
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.44
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.69
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.10
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.18
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:29.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.01
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:59.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1452.71
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:09.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6983.91
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:05.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.92
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9996    *****

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.12
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:11.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.30
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:46.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.14
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4943.34
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:54.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45687
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869687
  j =  1                              :        399908632
  j =  2                              :            45675
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45902
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869902
  j =  1                              :        399908199
  j =  2                              :            45896
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:31.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:21.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:52.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:09.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:39.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 8.47e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:24.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:24.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:52.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:54.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.60
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.90
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.99
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   65.76
p-value of test                       :  2.5e-3

-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.43
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.81
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.10
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:54.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.52
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.67
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.53
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.39
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   99.13
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17577.76
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.97
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.85
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.76
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.17
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.62
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.64
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.90
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.53
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.09
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.05
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:39.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.18
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.69
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.52
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.89
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.11
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.84
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.18
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  442.86
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.20
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.19
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.69
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.86
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.45
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.76
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.77
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.21
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.89
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.54
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.39
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.51
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.68
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:26.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.66
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:24.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    2.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    2.81
p-value of test                       :  2.6e-3

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.91e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 9.21e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 6.16e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.25
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:40.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.68
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:38.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.87
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:27.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.94
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:27.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9988.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10163.72
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:04:22.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.84
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:53.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.93
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.24
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.30
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11647.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:33.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11983.31
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:34.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.31
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000063790

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.19
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999988256

Normal statistic for number of bits   :  -0.093
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :  -0.013
p-value of test                       :    0.51

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:38.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.6e-3

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.03
p-value of test                       :    0.02

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:40.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    2.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:09.71

 All tests were passed




Server wird beendet - Lösche Semaphor 8847375.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5516
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:56.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4200
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:40.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:04.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:03.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:55.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:00.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.9908

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    1.96
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     565
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    3.13
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.44
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     266
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    4.72
p-value of test                       :  3.9e-3

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:17.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    3.61
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     124
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:47.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.53
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.02
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.45
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.56
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.81
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.60
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.63
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  503.16
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:43.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1394.14
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:02.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7176.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:44.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.34
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.16
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:01.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.49
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.31
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:34.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5062.07
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:56.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45827
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869827
  j =  1                              :        399908352
  j =  2                              :            45815
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46227
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870227
  j =  1                              :        399907548
  j =  2                              :            46223
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:28.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:19.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:45.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:59.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  2.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.94
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:01:55.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 6.52e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.064
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:38.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:37.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.42
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.70
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.39
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.71
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.79
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:43.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.08
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.07
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.73
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:28.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:09.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.00
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17380.08
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.75
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.39
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.64
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.99
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.40
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.16
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.70
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.55
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.37
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.03
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.72
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.77
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.50
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.41
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.50
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.11
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.00
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.40
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  181.35
p-value of test                       :  5.7e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.26
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.98
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.91
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5036.00
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.16
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  150.32
p-value of test                       :    0.9964


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.99
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.36
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5207.35
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.74
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.35
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.16
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:25.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.04
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:25.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.03
p-value of test                       :    0.02

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.96
p-value of test                       :    0.02

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 8.58e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.14
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.38
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.89
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:05.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.09
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:06.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9915.86
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10097.35
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:51.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5006.42
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:48.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4779.86
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4170.68
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4116.62
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11857.98
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12195.01
p-value of test                       :  8.5e-3

-----------------------------------------------
CPU time used                    :  00:01:29.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.69
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000119419

Normal statistic for number of bits   :    0.94
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.26
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999998354

Normal statistic for number of bits   :  -0.013
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:52.62

 All tests were passed




Server wird beendet - Lösche Semaphor 10321935.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:39.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5512
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:56.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:41.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4445
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:57.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:59.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:07.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:07.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:00.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7478
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:04.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    4.04
p-value of test                       :  8.4e-3

-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.94
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:18.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.9901


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:45.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.97
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.78
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.44
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.58
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.24
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.31
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1420.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:00.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7112.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:48.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.04
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:07.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.13
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.43
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:36.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5115.08
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:03.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45680
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869680
  j =  1                              :        399908644
  j =  2                              :            45672
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46282
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870282
  j =  1                              :        399907438
  j =  2                              :            46278
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:30.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:20.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:48.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.29
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.57
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:08.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:57.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:37.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.67e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.10
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:49.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.17
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.63
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.94
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.91
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.77
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   66.43
p-value of test                       :  2.1e-3

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.86
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.21
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:47.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.77
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.26
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.11
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17340.94
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.28
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.40
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.30
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.08
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.93
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.47
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.69
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.50
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.33
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.83
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.86
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.07
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.12
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.51
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.98
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.11
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.58
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.00
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.53
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.71
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.43
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.85
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.76
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.31
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.07
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.36
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.91
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.91
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.86
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.08
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.64
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:22.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.38
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :    0.93
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:25.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 2.74e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.41
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.82
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.07
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:05.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.86
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:07.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9823.12
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9865.60
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.032
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:04:14.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4846.25
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:52.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4803.05
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:54.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4133.95
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4212.83
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12004.48
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:31.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11704.23
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:30.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.85
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000054214

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.77
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999875189

Normal statistic for number of bits   :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:48.44

 All tests were passed




Server wird beendet - Lösche Semaphor 11239439.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5560
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:55.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:41.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:57.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7147
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:05.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:05.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:55.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:01.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.21
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     852
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:50.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    2.12
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     663
p-value of test                       :  5.9e-3

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.93
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:16.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.72
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:43.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.44
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.09
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.85
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.00
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.56
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.03
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.76
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.79
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:42.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1575.16
p-value of test                       :  6.0e-3

-----------------------------------------------
CPU time used                    :  00:02:00.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7243.15
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.49
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:03.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.73
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.49
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:31.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4897.36
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:00.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46216
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870216
  j =  1                              :        399907572
  j =  2                              :            46208
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45367
p-value of test                       :    0.9917


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869367
  j =  1                              :        399909268
  j =  2                              :            45363
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:28.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:19.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:59.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    3.73
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.15e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.53e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:28.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:37.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:37.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.47
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.03
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.39
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.50
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   61.25
p-value of test                       :  7.3e-3

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.06
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.24
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:43.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.65
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.47
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.28
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.85
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17684.93
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.40
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.77
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.24
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.97
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.26
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.35
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.36
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.74
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.03
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.44
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:42.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.03
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.28
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.43
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.72
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.02
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.84
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.03
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.04
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.30
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.17
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:48.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.57
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.26
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4846.02
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.42
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.77
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:37.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  452.70
p-value of test                       :  8.9e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.84
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.45
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.38
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  246.33
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.74
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:24.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.83
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :   -0.86
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:23.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    2.45
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 7.50e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 4.76e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.86
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.49
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.20
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:06.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.53
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:08.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10085.47
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9899.50
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:39.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.00
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:48.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.36
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:50.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4026.58
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11667.59
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11607.98
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:29.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.73
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999998273

Normal statistic for number of bits   :  -0.014
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.79
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000114571

Normal statistic for number of bits   :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.053
p-value of test                       :    0.52

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    2.52
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:36.89

 All tests were passed




Server wird beendet - Lösche Semaphor 12320783.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:40.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1249
p-value of test                       :    0.9992    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334369
  j =  1                              :        599997502
  j =  2                              :             1249
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5480
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:57.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:41.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:56.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:58.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:06.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:05.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:56.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:04:01.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.90
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:16.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    5.10
p-value of test                       :  2.9e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.50
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:44.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.21
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.45
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.88
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.45
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:10.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.30
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.17
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.45
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.02
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.30
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:43.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1402.84
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:01.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6981.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:41.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.57
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:03.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.77
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:46.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.57
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:32.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4917.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:00.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46151
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870151
  j =  1                              :        399907700
  j =  2                              :            46147
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45975
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869975
  j =  1                              :        399908057
  j =  2                              :            45961
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:28.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :  3.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    4.75
p-value of test                       :  3.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9948


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:19.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:44.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:59.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:56.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:35.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.91e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:36.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:36.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.39
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   95.81
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.96
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.83
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.43
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.00
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:45.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.54
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.82
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.07
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.53
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17717.71
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.60
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.34
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.73
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.23
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.02
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.91
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.35
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.42
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.00
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.01
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.66
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.97
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.60
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.07
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.83
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  105.61
p-value of test                       :    0.9951


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.65
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.74
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.44
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.87
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.06
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.03
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  330.54
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.77
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.08
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.95
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.10
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.83
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.72
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.09
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :    1.31
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:24.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.79
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    2.54
p-value of test                       :  6.4e-3

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.18e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.45
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.67
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.34
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:06.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.96
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:09.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9973.45
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10174.67
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:39.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.62
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:48.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.86
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:49.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4133.02
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4028.60
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11912.94
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11918.50
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.22
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999885173

Normal statistic for number of bits   :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.64
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000044716

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.99
p-value of test                       :    0.98

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:41.40
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           0.9992 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13303823.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:40.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1493
p-value of test                       :  3.1e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334613
  j =  1                              :        599997014
  j =  2                              :             1493
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5585
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:55.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4432
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:41.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:56.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:58.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:05.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:06.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:56.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:02.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.63
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.80
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     948
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    2.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:48.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    2.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:15.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:41.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.82
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.78
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.78
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.95
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.43
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.11
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.98
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.64
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.18
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.17
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:42.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1386.39
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:00.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7061.54
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.64
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:05.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.72
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.78
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:29.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5041.24
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:00.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45787
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869787
  j =  1                              :        399908430
  j =  2                              :            45779
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45981
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869981
  j =  1                              :        399908041
  j =  2                              :            45975
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:28.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:18.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:00.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:57.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.05e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 9.32e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:21.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:34.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:32.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.46
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.84
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.81
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:50.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.10
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.10
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.50
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9905

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.05
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.06
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.58
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.81
p-value of test                       :  3.7e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  179.44
p-value of test                       :  2.7e-3

-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17559.19
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.69
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.41
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.93
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.98
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.05
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.35
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.73
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.11
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.62
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.64
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.40
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.25
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.40
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.88
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.84
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.14
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.49
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.39
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.29
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.72
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.21
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.75
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.93
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.08
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.26
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.06
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.46
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.52
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.81
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.46
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.40
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :    1.46
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:24.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.06
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:24.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.68
p-value of test                       :    0.05

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 2.63e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.60
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.54
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:09.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.48
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:07.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10088.81
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  8.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.41
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9682.54
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:55.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:37.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4961.01
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.34
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4207.66
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4021.89
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11772.04
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11808.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.45
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000086500

Normal statistic for number of bits   :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.39
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999972065

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:43.65
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  6  CollisionOver, t = 3            3.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14352399.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5325
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:55.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:41.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:56.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:57.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:05.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:05.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:56.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:04:01.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9955

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:46.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:14.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.78
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     116
p-value of test                       :    0.9977

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:48.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.78
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.50
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.69
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   83.80
p-value of test                       :  5.8e-3

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.78
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.93
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.26
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.78
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.83
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:42.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1373.13
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:01.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7029.55
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:41.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.21
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.87
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:03.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   16.76
p-value of test                       :  5.0e-3


-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.74
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:33.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4942.16
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:55.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45820
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869820
  j =  1                              :        399908364
  j =  2                              :            45812
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46058
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870058
  j =  1                              :        399907886
  j =  2                              :            46054
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:27.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:17.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:45.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.68e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 2.44e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:21.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:37.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:37.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.69
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.96
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.90
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.25
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.55
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.12
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:43.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.19
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.81
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.02
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:17.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.78
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17318.69
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.62
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   16.73
p-value of test                       :    0.9962


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   47.88
p-value of test                       :  3.9e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.70
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.80
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:38.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.06
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.74
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.83
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.58
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.16
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.69
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.35
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.76
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.98
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.95
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.12
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.59
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.97
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.07
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.67
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.19
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.01
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.90
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.40
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.67
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.54
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.61
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.59
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.03
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.71
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.98
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:25.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.52
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :    0.95
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:24.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 7.69e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.30e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.04
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.56
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.01
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:06.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:06.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10028.52
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10169.83
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:41.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.90
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4817.38
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:49.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4232.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3978.03
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11593.25
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11809.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:28.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.03
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000064672

Normal statistic for number of bits   :    0.51
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.06
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  7999962255

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:21.23

 All tests were passed




Server wird beendet - Lösche Semaphor 15368207.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5410
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:56.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4466
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:42.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:57.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:58.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:05.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:05.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:55.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:01.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    3.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.31
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:15.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:42.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.03
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.10
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.70
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.42
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.95
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.00
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.38
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.31
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:43.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1443.62
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:02.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6939.56
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:42.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.45
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 6.43e-3
p-value of test                       :    0.9932

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   41.21
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:02.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.63
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.91
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5140.92
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:00.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45979
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869979
  j =  1                              :        399908045
  j =  2                              :            45973
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45775
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869775
  j =  1                              :        399908453
  j =  2                              :            45769
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:27.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:19.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  7.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.44
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:44.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:59.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:36.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 4.54e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 5.43e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:35.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:37.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.44
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.28
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.99
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.93
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.24
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.35
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:43.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.12
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.21
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.21
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.20
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.92
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.84
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17222.33
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.45
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.84
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.80
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.82
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.97
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.63
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.03
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.47
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.94
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.45
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.11
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.84
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.40
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.94
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.84
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.57
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.63
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  440.34
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.33
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.47
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.80
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.02
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4959.41
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.75
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.95
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:36.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.71
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  302.03
p-value of test                       :    0.9993    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5110.56
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.43
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.22
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:36.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.47
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:23.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.62
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :    1.46
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:23.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.68
p-value of test                       :    0.95

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.20

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 6.06e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:46.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.65e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.23
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.96
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.77
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:07.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.51
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:06.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10250.40
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.77
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:41.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.76
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:47.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5023.71
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:49.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4010.40
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4207.18
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11834.98
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11744.10
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.22
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999996026

Normal statistic for number of bits   :  -0.031
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.62
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000055054

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:23.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         : 6.20e-3
p-value of test                       :    0.50

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:35.22
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 M (L=10000, r=15)   0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16384015.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:40.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:49.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5361
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:56.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:42.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:57.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:59.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7503
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:07.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:06.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7453
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:55.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:02.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.50
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.46
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:14.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:42.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.39
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.71
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.01
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.30
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.18
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.17
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  191.06
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:44.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1394.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:03.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7056.39
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:42.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.43
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:05.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.17
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.99
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:30.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4911.53
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:58.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45627
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869627
  j =  1                              :        399908748
  j =  2                              :            45623
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46355
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870355
  j =  1                              :        399907293
  j =  2                              :            46349
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:27.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:17.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:45.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:58.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:55.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:34.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.48e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 3.47e-4
p-value of test                       :  8.0e-3

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:31.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:34.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.83
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.92
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.98
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:50.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.23
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:50.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.67
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.89
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:38.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.87
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.83
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.99
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.82
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.39
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:40.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17413.20
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.45
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.71
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.55
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.56
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.26
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.42
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.17
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.97
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.12
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.02
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:37.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.39
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.58
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  448.80
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.60
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.25
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.30
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.13
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.07
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.06
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.61
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.58
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.49
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.00
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  427.27
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.33
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.82
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5085.46
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.99
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.35
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.68
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:22.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.38
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:23.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9994    *****

Tests on the sum of all N observations
Standardized normal statistic         :  -0.087
p-value of test                       :    0.53

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.50e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 6.04e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:46.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.46e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 7.51e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.67
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.27
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.33
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:08.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.19
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:07.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9846.73
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9780.14
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:55.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:38.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4991.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:48.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.86
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.25
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11957.98
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11918.92
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.56
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999999161

Normal statistic for number of bits   : -6.63e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.32
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000114706

Normal statistic for number of bits   :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.57

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-3
p-value of test                       :    0.9987

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:50.45

 All tests were passed




Server wird beendet - Lösche Semaphor 17432591.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:40.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1491
p-value of test                       :  3.7e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334611
  j =  1                              :        599997018
  j =  2                              :             1491
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5356
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:56.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:41.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:59.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7461
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:06.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:06.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:53.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7120
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:59.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    1.76
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    3.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.29
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    2.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:13.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.72
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:44.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.04
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.65
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.23
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.84
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.52
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.02
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.44
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.66
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:43.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1474.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:02.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7002.59
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:43.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.10e-3
p-value of test                       :    0.9969

Kolmogorov-Smirnov- statistic = D-    :    0.59
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   52.23
p-value of test                       :  7.2e-3

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.53
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:02.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.85
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:47.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.62
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:35.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4791.64
p-value of test                       :    0.9938


-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:03.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45864
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869864
  j =  1                              :        399908275
  j =  2                              :            45858
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45404
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869404
  j =  1                              :        399909196
  j =  2                              :            45396
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:27.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:20.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:45.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:58.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:56.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:34.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 7.84e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.095
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:37.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.34
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:49.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.96
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.91
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.77
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.83
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.81
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.08
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.76
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  6.9e-3

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.91
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.68
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.85
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.06
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17252.31
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.55
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.06
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.77
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.08
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.55
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.85
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.80
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.80
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.92
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.53
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.15
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.32
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  450.11
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.08
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.99
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.13
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.32
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.84
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.48
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.66
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.55
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.99
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4923.39
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.25
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.22
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.49
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.22
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.82
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.09
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.15
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.66
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :   0.079
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:22.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.40
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:24.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 6.87e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:46.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.67e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 9.96e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.88
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.11
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.17
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:07.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.84
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:08.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9864.69
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9815.07
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:47.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:48.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5012.81
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:50.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4266.32
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4292.48
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11738.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11787.94
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.90
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000072964

Normal statistic for number of bits   :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.87
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999916922

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   0.051
p-value of test                       :    0.48

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:43.94
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  7  CollisionOver, t = 7            3.7e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18382863.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:50.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5393
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:54.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4450
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:43.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:59.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:01.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:10.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:09.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:01.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7503
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:04:04.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     960
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:13.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.76
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:44.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.80
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.79
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.01
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.67
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.85
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.11
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.83
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  486.65
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:50.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1401.13
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:04.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7119.64
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.82
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:08.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.94
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.49
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:36.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4946.11
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:04.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45881
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869881
  j =  1                              :        399908244
  j =  2                              :            45869
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46105
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870105
  j =  1                              :        399907798
  j =  2                              :            46089
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:34.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:22.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:49.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:07.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:36.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 6.76e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.62e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 4.77e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.062
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.055
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:46.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.65
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.79
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.28
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.74
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   54.35
p-value of test                       :  2.9e-3

-----------------------------------------------
CPU time used                    :  00:01:46.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.50
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.41
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.51
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.87
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.64
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17365.21
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.70
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.33
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.36
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.42
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.66
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.09
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.21
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.64
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.95
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.08
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.59
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.28
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.96
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.22
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.06
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.83
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.55
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.41
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.39
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.30
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.60
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.41
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5077.43
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.01
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.31
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.78
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.26
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4898.37
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.73
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.54
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.18
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  : 7.45e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:25.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.06
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:26.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.68
p-value of test                       :    0.05

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.99e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 9.15e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.12e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 9.00e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.55
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.27
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.88
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:08.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:07.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10043.17
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.20e-3
p-value of test                       :    0.9967

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9630.45
p-value of test                       :    0.9959

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.00
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:04:20.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4988.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:55.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4735.03
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:54.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.29
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.03
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11644.79
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:31.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11948.86
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:33.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.38
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000006445

Normal statistic for number of bits   :   0.051
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.69
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999874787

Normal statistic for number of bits   :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.076
p-value of test                       :    0.47

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:51.71

 All tests were passed




Server wird beendet - Lösche Semaphor 19398671.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:51.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5517
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:56.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:42.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4238
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:56.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4441
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:57.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:06.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:05.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:55.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:04:01.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.07
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    3.50
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     654
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:15.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    2.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:43.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.04
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.68
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.59
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.25
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.56
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.65
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  508.42
p-value of test                       :  7.8e-3

-----------------------------------------------
CPU time used                    :  00:01:43.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.84
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:02.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6886.13
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:41.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.25
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.28
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:00.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.22
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.26
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:34.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5018.08
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:00.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45919
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869919
  j =  1                              :        399908165
  j =  2                              :            45913
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46148
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870148
  j =  1                              :        399907706
  j =  2                              :            46144
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:28.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:19.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:46.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:01.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:57.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:35.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.67e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.53e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:34.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:35.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   38.16
p-value of test                       :    0.9982

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.98
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.90
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.42
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.08
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.77
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.46
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:43.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.12
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.13
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17195.46
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.42
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.05
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.38
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.23
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.54
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.17
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.50
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.13
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.31
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.00
p-value of test                       :    0.9932


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.00
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.69
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.26
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.17
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.76
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.26
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.51
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.91
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.44
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.58
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.59
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.70
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4993.88
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.21
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.68
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.95
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.05
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4927.76
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.32
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.78
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.52
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:24.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.61
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:23.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.98e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 5.01e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 8.43e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.49
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.64
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9960

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.14
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:05.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:05.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10161.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10091.40
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:30.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4787.45
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:43.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4998.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4234.51
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:16.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3963.20
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11587.74
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11423.98
p-value of test                       :    0.9958

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.92
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999993722

Normal statistic for number of bits   :  -0.050
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.86
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000211420

Normal statistic for number of bits   :    1.67
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.57

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   0.033
p-value of test                       :    0.49

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:18.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:16.29

 All tests were passed




Server wird beendet - Lösche Semaphor 20480015.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:48.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1463
p-value of test                       :  4.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334583
  j =  1                              :        599997074
  j =  2                              :             1463
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:17.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:23.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:16.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5417
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:42.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:36.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:35.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:55.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:02.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:01.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:54.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:00.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.22
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     949
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.16
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    2.46
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     272
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:14.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:36.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.92
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.96
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.78
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.34
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.37
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.12
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.66
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  387.30
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1459.68
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:02.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7163.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:46.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.67
p-value of test                       :  4.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    3.38
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.18
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.38
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:00.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.78
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  156.39
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:33.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5055.42
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:06.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46013
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870013
  j =  1                              :        399907981
  j =  2                              :            45999
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45462
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869462
  j =  1                              :        399909080
  j =  2                              :            45454
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:31.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:18.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:44.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:58.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:53.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:34.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 8.13e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 3.04e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:21.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:22.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:33.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:36.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.62
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.98
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.09
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.40
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.14
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.35
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.33
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:43.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.12
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:31.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.87
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17370.63
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.90
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.32
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.64
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.28
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.48
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.68
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.88
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.21
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.40
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.49
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.97
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.94
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.86
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.67
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:46.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.16
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.18
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.56
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.28
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.86
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.05
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.81
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5198.65
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.05
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.09
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.52
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.59
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4945.36
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.37
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.74
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.20
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :  -0.042
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:30.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.48
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:23.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   0.087
p-value of test                       :    0.47

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 6.09e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.32e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.92
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.83
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.44
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:11.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:12.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10023.15
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10017.09
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.44
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:45.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4936.19
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5085.60
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:49.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4232.42
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.76
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11657.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11952.73
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.69
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  7999851498

Normal statistic for number of bits   :   -1.17
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.70
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000007336

Normal statistic for number of bits   :   0.058
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:29.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 1.60e-3
p-value of test                       :    0.9984

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.35
p-value of test                       :    0.9907

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:17:39.43

 All tests were passed




Server wird beendet - Lösche Semaphor 655376.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5495
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:41.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:36.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:35.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:54.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:54.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:01.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:02.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:52.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:58.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:11.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.80
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:40.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.93
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.93
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.81
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.43
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.32
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.83
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.05
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.82
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  482.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:44.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1293.69
p-value of test                       :    0.9971

-----------------------------------------------
CPU time used                    :  00:02:02.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7077.44
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.54
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.64
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:02.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.87
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.71
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:35.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5139.27
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:03.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46224
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870224
  j =  1                              :        399907555
  j =  2                              :            46218
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45687
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869687
  j =  1                              :        399908630
  j =  2                              :            45679
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:33.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:20.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:46.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:00.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:55.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:34.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 4.51e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:22.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.042
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:29.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:31.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.43
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:48.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.73
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.76
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.92
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.84
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.09
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.18
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.67
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.08
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.13
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.6e-3

Anderson-Darling statistic = A2       :    3.58
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  163.71
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17050.11
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:55.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.33
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.47
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.19
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.18
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.85
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.27
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.39
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.41
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.82
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.03
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.36
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.19
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.69
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  174.91
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.78
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.31
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.00
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  449.55
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.97
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.25
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.83
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.66
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.44
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.33
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.00
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.58
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.05
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.06
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.70
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.37
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:36.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.86
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:28.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.04
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    1.40
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:27.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.09
p-value of test                       :    0.98

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.28e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.01
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.66
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.14
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:06.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.30
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:10.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10102.24
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10018.51
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:46.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4823.54
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4841.79
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:48.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4278.13
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.01
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11809.02
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11859.02
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:29.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.82
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000100720

Normal statistic for number of bits   :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.43
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000056029

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.66

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:29.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   0.087
p-value of test                       :    0.47

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:27.88

 All tests were passed




Server wird beendet - Lösche Semaphor 1277968.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:11.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5307
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:42.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:35.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:34.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:54.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:54.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7163
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:01.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:02.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7121
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:52.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:59.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.10
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    2.18
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     958
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:47.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:13.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.60
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    2.17
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:41.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.39
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.02
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:55.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.00
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.63
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.69
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.48
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.87
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.42
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:42.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1456.24
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:01.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6936.75
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:43.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.63
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:00.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.90
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.90
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:31.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5085.00
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:59.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46074
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870074
  j =  1                              :        399907857
  j =  2                              :            46064
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45860
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869860
  j =  1                              :        399908284
  j =  2                              :            45852
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:32.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:18.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:46.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:59.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:34.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.31e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.90e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.093
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:22.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:31.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.87
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:48.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.55
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.38
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.24
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.96
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.23
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.48
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.64
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17492.01
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.88
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.12
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.18
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.49
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.17
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.43
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.18
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.05
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.96
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.25
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.26
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.09
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.71
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.60
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.60
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.82
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.57
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.85
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.20
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.57
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.79
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.68
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5235.58
p-value of test                       :  1.0e-2


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.77
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.05
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.69
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.74
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4928.96
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.08
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.79
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:37.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.26
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :   -0.79
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:27.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.86
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   -0.40
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:24.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 8.26e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.43
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.11
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.81
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:04.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:07.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9798.19
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10007.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:46.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4895.63
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:48.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4843.20
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:50.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.80
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11746.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11809.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:29.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.37
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000102889

Normal statistic for number of bits   :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.47
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000091624

Normal statistic for number of bits   :    0.72
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   0.037
p-value of test                       :    0.49

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:22.20

 All tests were passed




Server wird beendet - Lösche Semaphor 2228240.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5343
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:47.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:38.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:36.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4428
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:54.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:55.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:02.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:01.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:53.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7172
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:59.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    2.50
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     958
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    2.55
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:46.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     557
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.68
p-value of test                       :  4.3e-3

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:11.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.95
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.72
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:39.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.71
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.00
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.41
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.38
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.65
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  480.12
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:43.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1503.44
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:02.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7179.05
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.80
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:16.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.42
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:03.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.20
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:47.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.81
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:36.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5145.17
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:01.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45699
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869699
  j =  1                              :        399908610
  j =  2                              :            45683
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45652
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869652
  j =  1                              :        399908697
  j =  2                              :            45650
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:31.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:19.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:44.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:59.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:33.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:34.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.84
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.72
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.46
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.41
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.88
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.12
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.29
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:36.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.58
p-value of test                       :  5.4e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    5.79
p-value of test                       :  1.3e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   18.16
p-value of test                       :    0.9988

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.31
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.74
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.64
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17541.24
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.10
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.11
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.68
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.49
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.75
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.39
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.59
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.13
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.38
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.73
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.70
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.59
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.22
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.51
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.33
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.62
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.99
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.95
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.83
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.55
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.88
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.41
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4912.12
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.83
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  246.20
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:36.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.73
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.51
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5093.39
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.93
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.26
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.46
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :    1.24
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:27.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.16
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:25.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :  -0.054
p-value of test                       :    0.52

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 4.56e-4
p-value of test                       :    0.9995    *****

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.75
p-value of test                       :    0.96

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.58e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 8.39e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.07
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.69
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.75
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:04.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.74
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:05.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9908.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.51
p-value of test                       :  5.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10414.38
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:51.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4777.88
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:51.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4996.94
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:50.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4196.07
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4129.76
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12084.23
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11907.03
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:29.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.44
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999957335

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.87
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000163432

Normal statistic for number of bits   :    1.29
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    2.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:23.84

 All tests were passed




Server wird beendet - Lösche Semaphor 3276816.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5407
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:51.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:39.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:39.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:55.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:02.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:03.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:55.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:59.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:46.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:12.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    2.04
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     172
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.90
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:38.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.54
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.57
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.16
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.73
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.68
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.89
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  269.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.04
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:49.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.77
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:06.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7133.01
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:48.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.61
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.57
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.14
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:08.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.55
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.48
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:36.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4960.04
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:56.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46074
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870074
  j =  1                              :        399907855
  j =  2                              :            46068
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45623
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869623
  j =  1                              :        399908755
  j =  2                              :            45621
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9909


-----------------------------------------------
CPU time used                    :  00:02:32.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:21.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:50.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:04.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9904

-----------------------------------------------
CPU time used                    :  00:01:17.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.16e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.88e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:38.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.13
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.80
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.91
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   61.62
p-value of test                       :  6.7e-3

-----------------------------------------------
CPU time used                    :  00:00:51.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.29
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.89
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.08
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:46.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.53
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.84
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.62
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.74
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17500.07
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.96
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.16
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.93
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.78
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.67
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.39
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.46
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.49
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.08
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.65
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.29
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.69
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.90
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.09
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.56
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.50
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.41
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.79
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.27
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.43
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.59
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.80
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4982.64
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.02
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.73
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.86
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.28
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.80
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.88
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.86
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.07
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:23.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.51
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:26.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.39
p-value of test                       :    0.9916

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 3.82e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.21e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 9.03e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.13
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.60
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.51
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:05.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:06.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10057.94
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10003.88
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.087
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:04:24.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5005.84
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:53.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4793.02
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:53.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.84
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12031.19
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:33.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11519.77
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:32.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.11
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999979142

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.44
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000128593

Normal statistic for number of bits   :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.86
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:06.87

 All tests were passed




Server wird beendet - Lösche Semaphor 4358160.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5469
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:52.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:38.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4214
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:55.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:56.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:03.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:04.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:53.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:58.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.64
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:13.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:42.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.13
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.71
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.33
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.64
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.24
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   25.93
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  183.94
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:01:17.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.88
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:44.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.54
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:02.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7087.71
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.03
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.94
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:03.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.52
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.09
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:33.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4866.91
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:00.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45862
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869862
  j =  1                              :        399908277
  j =  2                              :            45860
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45876
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869876
  j =  1                              :        399908248
  j =  2                              :            45876
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:30.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:18.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:44.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:59.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:34.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.62e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 6.31e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:22.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.05e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:32.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:32.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.04
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:48.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.87
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.99
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.85
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:49.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.08
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.31
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:41.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.61
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.49
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.72
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.85
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17412.15
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.00
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.70
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.30
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.94
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.43
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.33
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.23
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.00
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.37
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.74
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:36.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.05
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  109.51
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.10
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.90
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.14
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.56
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.65
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.08
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.10
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.51
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.49
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.44
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5048.06
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.55
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  161.76
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.70
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.83
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.19
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.38
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.47
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.22
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :    1.07
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:25.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.06
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:27.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.72
p-value of test                       :    0.04

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.31e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 9.39e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.99
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.35
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.79
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:07.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.88
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:06.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.16
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9983.25
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:44.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4833.81
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.70
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:49.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.00
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.34
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11660.48
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11941.19
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.64
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999959873

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.51
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000010177

Normal statistic for number of bits   :   0.080
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:37.23
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 33  CouponCollector, r = 27         0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5505040.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5544
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:56.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:40.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:57.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:04.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:04.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:53.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:59.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    2.12
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:46.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    2.06
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:12.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:43.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.81
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.80
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.69
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.96
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.21
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.45
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.01
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.65
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.36
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:43.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1453.89
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:01.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7053.39
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:41.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.06
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.91
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:03.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.56
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.02
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:32.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5010.21
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:05.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46096
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870096
  j =  1                              :        399907810
  j =  2                              :            46092
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46209
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870209
  j =  1                              :        399907586
  j =  2                              :            46201
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:29.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:18.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:44.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:58.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:54.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:34.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:21.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:34.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:34.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.74
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:48.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.72
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.13
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:48.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.76
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.88
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:12.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.69
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.70
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.89
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9993    *****

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17460.26
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.53
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.79
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.06
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.05
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.32
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.73
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.44
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.63
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.91
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.76
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.26
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.99
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.90
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.81
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.79
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.80
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.25
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.54
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.56
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.47
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.66
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.93
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5014.54
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.98
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.86
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.67
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.30
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.87
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  323.87
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.24
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.73
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:25.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.84
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:26.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.49e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.31
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.67
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:04.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.75
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:05.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-3
p-value of test                       :    0.9984

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10271.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9916.99
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      : -7.23e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:56.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    3.11
p-value of test                       :  9.3e-4    *****

-----------------------------------------------
CPU time used                    :  00:03:44.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4770.42
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4942.83
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:49.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.69
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.00
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11837.75
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:29.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11781.03
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:29.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   28.66
p-value of test                       :    0.9982


-----------------------------------------------
Total number of bits:  7999948260

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.44
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  7999865049

Normal statistic for number of bits   :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :  -0.099
p-value of test                       :    0.54

Sample variance                       :    2.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    2.02
p-value of test                       :    0.02

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    2.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:56.07
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 94  HammingCorr, L = 1200           9.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6553616.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:50.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5325
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:59.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:42.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:57.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:59.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:07.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7166
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:06.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:59.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:04:01.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    2.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.12
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:17.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.19
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:47.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.40
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.52
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.52
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.19
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.71
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.79
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.03
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.11
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.86
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.62
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:49.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1393.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:05.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7072.39
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:50.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.84
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.07
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:11.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.02
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.81
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:37.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5130.64
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:12.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45896
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869896
  j =  1                              :        399908211
  j =  2                              :            45890
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45613
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869613
  j =  1                              :        399908778
  j =  2                              :            45605
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:30.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:19.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:04.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:36.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.39e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.98e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.067
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:44.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:44.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.01
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.11
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.74
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.37
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.99
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.84
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.96
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.90
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.60
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.10
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:39.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17279.85
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.41
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.07
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.36
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.23
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.38
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.94
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.85
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.82
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.42
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.55
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.48
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.68
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.23
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.70
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   50.01
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.26
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.14
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.00
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.13
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.14
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:43.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.35
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.29
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.34
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  439.82
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.97
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.08
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.04
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.27
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.17
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.36
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.15
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:23.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.09
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :   -1.85
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:25.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.80e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 9.73e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 8.84e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.12
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.94
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.33
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:06.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:05.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9982.74
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9849.45
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:04:23.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4817.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:55.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.59
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:55.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.97
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.49
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11995.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:32.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11938.92
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:32.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.48
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999883493

Normal statistic for number of bits   :   -0.92
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.98
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000005218

Normal statistic for number of bits   :   0.041
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.80

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:16.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:11:48.15

 All tests were passed




Server wird beendet - Lösche Semaphor 7569424.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:51.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5313
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:56.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7095
p-value of test                       :    0.9956


-----------------------------------------------
CPU time used                    :  00:02:41.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:57.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:04.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:04.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:54.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:00.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:54.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.02
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:21.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:51.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.67
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.80
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   34.36
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.44
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.42
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.50
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.99
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.08
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  499.83
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:43.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1387.08
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:03.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6969.57
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.30
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.91
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:03.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.58
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:46.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.27
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:31.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4953.98
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:55.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46110
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870110
  j =  1                              :        399907784
  j =  2                              :            46102
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46139
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870139
  j =  1                              :        399907723
  j =  2                              :            46137
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:28.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:17.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:43.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:58.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :  4.2e-4    *****

Anderson-Darling statistic = A2       :    6.71
p-value of test                       :  4.7e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:55.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:34.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 6.69e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:35.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:36.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.51
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.64
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.72
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:48.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.04
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.29
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:40.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.82e-3
p-value of test                       :    0.9971

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.05
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.72
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.87
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.00
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17473.58
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.10
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.26
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.07
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.12
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.01
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.48
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.02
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.63
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.16
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.63
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.54
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.98
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.35
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.14
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.89
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.08
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.25
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  576.10
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.12
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.17
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.92
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.17
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4910.61
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.28
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.90
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.72
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.93
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5118.02
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.56
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.38
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.23
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:22.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.35
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :   -2.27
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:02:22.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 4.73e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.49
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.08
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.68
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:06.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9988.72
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.03
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:50.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.16
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:51.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4787.88
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:50.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3982.53
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3919.93
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12239.38
p-value of test                       :  3.8e-3

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11977.94
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.09
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  7999963104

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.29
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000072970

Normal statistic for number of bits   :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9950

Tests on the sum of all N observations
Standardized normal statistic         :   0.025
p-value of test                       :    0.49

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:22.01
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 50  SampleProd, t = 8               4.7e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8749072.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:50.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5505
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:57.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7464
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:43.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:58.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:58.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:05.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:04.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:54.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:00.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.72
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:50.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:16.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:47.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.53
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.47
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.51
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.62
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.53
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.90
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.56
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.55
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  475.49
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1498.68
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:04.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7015.56
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.87
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.32
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:01.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.69
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.94
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4980.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:01.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45768
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869768
  j =  1                              :        399908467
  j =  2                              :            45762
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46141
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870141
  j =  1                              :        399907721
  j =  2                              :            46135
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:26.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-3
p-value of test                       :    0.9989

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:26.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:18.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:45.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:00.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:55.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:35.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.079
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:36.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:37.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.24
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.28
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.51
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:49.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.61
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.74
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:39.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.08
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.79
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.80
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.83
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17436.15
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.02
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.16
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.02
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.49
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.24
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.38
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.95
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.05
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.08
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.68
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.55
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.17
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.96
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.39
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.42
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.15
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.85
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.89
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.39
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.55
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.86
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.65
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5073.22
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.94
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.71
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.12
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.03
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.81
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.78
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:34.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.07
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:22.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.85
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :   -1.34
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:22.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 6.90e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.44
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.42
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.27
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:07.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:06.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9940.35
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10043.25
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:40.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5018.83
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:48.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4814.13
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4196.78
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4179.04
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11653.00
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11759.74
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.83
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999857126

Normal statistic for number of bits   :   -1.13
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.43
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999916271

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.60
p-value of test                       :  3.0e-4    *****

Anderson-Darling statistic = A2       :    5.24
p-value of test                       :  2.4e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.76
p-value of test                       :  2.9e-3

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:29.11

 All tests were passed




Server wird beendet - Lösche Semaphor 9797648.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:50.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5355
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:00.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:43.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7192
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:45.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:00.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4462
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:00.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7162
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:08.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7162
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:06.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:55.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:00.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.71
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:53.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.57
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.64
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:18.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:47.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.49
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.58
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.60
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.73
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.14
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.20
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.98
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:43.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1548.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6895.51
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:42.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.27
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.27
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:01.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.95
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:34.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5060.99
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:03.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46045
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870045
  j =  1                              :        399907912
  j =  2                              :            46041
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46022
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870022
  j =  1                              :        399907959
  j =  2                              :            46016
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:28.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:19.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:45.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.12
p-value of test                       :    0.9998    *****

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:59.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:55.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.50e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.59e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:36.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:37.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.04
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:48.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.21
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.61
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.95
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.70
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:41.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.01
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.97
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.24
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.56
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17274.74
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.54
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.88
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.73
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.20
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.26
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.70
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.66
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.42
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.45
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.12
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.06
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.71
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  439.28
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.30
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.38
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.62
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.94
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.59
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.53
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.01
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.47
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.58
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4799.43
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.33
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.82
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.65
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.79
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5036.09
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.77
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.11
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.39
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :    1.41
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:22.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.99
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :    1.47
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:22.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.60
p-value of test                       :    0.94

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 5.36e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.98e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 9.69e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.02
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.56
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.12
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:08.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.41
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:08.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9885.33
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10259.50
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:37.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.23
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.02
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:49.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.16
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4319.28
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12018.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11813.12
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:29.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.81
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  7999994871

Normal statistic for number of bits   :  -0.041
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.48
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999953576

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.87

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:36.68

 All tests were passed




Server wird beendet - Lösche Semaphor 10846224.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997213
  j =  2                              :             1392
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:58.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:43.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:44.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:59.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:07.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:08.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:56.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:04:00.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.48
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:14.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:45.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.62
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.79
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.87
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.36
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.08
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.68
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  272.80
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.64
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:44.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1395.20
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:02.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6996.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:43.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.78
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.74
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:03.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.31
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.42
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:31.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4933.94
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:57.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46088
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870088
  j =  1                              :        399907828
  j =  2                              :            46080
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45924
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869924
  j =  1                              :        399908154
  j =  2                              :            45920
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:28.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:19.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:45.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:00.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:55.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:34.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 2.54e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.82e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : -8.07e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.36
p-value of test                       :    0.9908

-----------------------------------------------
CPU time used                    :  00:01:33.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:33.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.37
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:48.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.60
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.93
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.95
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.93
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.84
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:45.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.46
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.38
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.54
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.83
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17365.43
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.82
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.16
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.02
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.67
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.22
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.02
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.05
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.65
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.06
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.11
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.69
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.70
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.21
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.15
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.01
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.30
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.68
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.46
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.65
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.38
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.89
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.36
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4906.07
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.93
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.84
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.81
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.59
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5096.81
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.16
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.56
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.17
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:23.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.17
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -1.04
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:23.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:10.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :  -0.092
p-value of test                       :    0.54

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.73e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 7.23e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 5.11e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.41
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.09
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.36
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:06.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.52
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:07.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9907.86
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10021.06
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:38.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5066.20
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:48.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4976.16
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:49.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.50
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.75
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12162.40
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12109.35
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:29.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.64
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  8000019576

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.92
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000002089

Normal statistic for number of bits   :   0.017
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.012
p-value of test                       :    0.50

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:10.15

 All tests were passed




Server wird beendet - Lösche Semaphor 11894800.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1494
p-value of test                       :  2.8e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334614
  j =  1                              :        599997012
  j =  2                              :             1494
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5397
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:04:01.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:43.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:44.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:00.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:59.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:07.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:08.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7501
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:58.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:01.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    3.50
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9930

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    2.66
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:15.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:45.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.22
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.63
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.46
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.48
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.65
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.91
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.40
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:44.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:02.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7158.32
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:42.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.06
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.54
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:03.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.62
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.22
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:33.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4976.86
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:11.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:01.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45880
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869880
  j =  1                              :        399908244
  j =  2                              :            45872
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45687
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869687
  j =  1                              :        399908627
  j =  2                              :            45685
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:28.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:20.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:45.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:00.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:35.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:42.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:45.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.14
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:48.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.04
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.84
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.23
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.46
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.86
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:44.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.22
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.18
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.97
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.06
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.97
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17250.42
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.10
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.03
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.73
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.21
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.25
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.00
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.33
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.53
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.31
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.56
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.45
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.08
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.62
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.88
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.17
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.45
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.59
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.98
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.55
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.93
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.07
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.26
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4905.08
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.16
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.00
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.78
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.01
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.93
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.72
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.41
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.65
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:24.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.87
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:24.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:10.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.92e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 8.28e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.13
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.57
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.41
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:05.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.71
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:06.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9795.58
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10025.20
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:41.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4768.34
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:48.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.38
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:49.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.33
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4195.24
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11762.32
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12016.13
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:29.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.02
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000039613

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.22
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999998843

Normal statistic for number of bits   : -9.15e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:03.05
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           2.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12845072.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:49.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5477
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:00.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:43.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:59.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:07.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:07.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:56.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:01.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    2.27
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     854
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.99
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     543
p-value of test                       :    0.9903

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    2.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:15.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:46.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.99
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.93
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.26
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.67
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.86
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.61
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:38.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.72
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:39.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.78
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:39.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.12
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:44.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1470.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:03.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6767.37
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.95
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.31
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:58.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.16
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:30.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5035.35
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:01.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45766
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869766
  j =  1                              :        399908469
  j =  2                              :            45764
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46014
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870014
  j =  1                              :        399907975
  j =  2                              :            46008
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:27.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:19.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:45.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:59.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:35.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 7.67e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.099
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:32.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.76
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:48.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.11
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:48.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.14
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.98
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:40.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.08
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.85
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.73
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.89
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.26
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.38
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17357.77
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.20
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.70
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.64
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.60
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.31
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.07
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.32
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.69
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.61
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.71
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.40
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.51
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.08
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.48
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.22
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.57
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  193.33
p-value of test                       :  5.3e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.28
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.13
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.78
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.11
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.17
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.29
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.91
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  246.72
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:36.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.04
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.65
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5181.23
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.01
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.87
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.81
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:24.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.75
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :   -1.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:23.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.91
p-value of test                       :    0.97

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.26e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.13e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 6.82e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.57
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.18
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.04
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:06.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:06.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10030.99
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.70
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:40.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4802.41
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:47.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.23
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:49.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.19
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11723.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11659.55
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:30.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.23
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000037438

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.35
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000121792

Normal statistic for number of bits   :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.71
p-value of test                       :    0.96

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:07.13

 All tests were passed




Server wird beendet - Lösche Semaphor 13860880.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5359
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:58.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:42.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:42.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:58.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4499
p-value of test                       :  7.3e-3


-----------------------------------------------
CPU time used                    :  00:01:58.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:08.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:07.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:55.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:01.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.61
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:14.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.73
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:43.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.87
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.16
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.58
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.29
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.84
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.50
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  199.74
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.35
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:48.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1499.47
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:05.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7080.71
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:46.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.40
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.20
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:03.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.86
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.53
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:32.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5127.99
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:01.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45738
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869738
  j =  1                              :        399908526
  j =  2                              :            45734
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45779
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869779
  j =  1                              :        399908447
  j =  2                              :            45769
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:27.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:21.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:02.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:56.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:34.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.97e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.80e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:21.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:35.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:36.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.66
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.14
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.10
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.87
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:48.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.92
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.65
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.37
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:38.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.21
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.07
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17451.31
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   17.27
p-value of test                       :    0.9965


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.71
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.45
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.27
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.96
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.90
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.87
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.61
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.55
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.13
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.73
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.70
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.40
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.04
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.55
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.97
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.49
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.70
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.87
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.93
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.69
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.06
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5095.68
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.14
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.15
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.48
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.51
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5169.76
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.21
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.39
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.79
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :   0.088
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:23.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.92
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:22.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    2.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:10.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.36e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.17e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 7.93e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.07
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.04
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.74
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:05.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.62
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:06.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10120.50
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9859.12
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:39.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.03
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:48.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4852.93
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:49.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.15
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4191.54
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11827.28
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11762.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:29.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.60
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999992876

Normal statistic for number of bits   :  -0.056
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.65
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  7999916778

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    2.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:16.52

 All tests were passed




Server wird beendet - Lösche Semaphor 14909456.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5410
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:59.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:43.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:44.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:57.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:58.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7448
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:06.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:08.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:56.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:02.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.60
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     837
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.06
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:13.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    5.10
p-value of test                       :  2.6e-3

-----------------------------------------------
CPU time used                    :  00:02:42.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.95
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.14
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.48
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.31
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.60
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.91
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.34
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.05
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:44.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1549.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:03.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6840.57
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:43.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.08
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:03.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.32
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.81
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:31.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4986.94
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:01.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45831
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869831
  j =  1                              :        399908341
  j =  2                              :            45825
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46001
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870001
  j =  1                              :        399908003
  j =  2                              :            45991
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 5.90e-3
p-value of test                       :    0.9926

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :  2.6e-3

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:26.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:21.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:00.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 4.42e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:35.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:34.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.81
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.48
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.84
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   73.48
p-value of test                       :  3.3e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.25
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.62
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.95
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:39.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.41
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.75
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.31
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.33
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.02
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:38.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 4.88e-3
p-value of test                       :    0.9949

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  2.8e-3

Anderson-Darling statistic = A2       :    3.35
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17873.22
p-value of test                       :  9.2e-3



-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.53
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.24
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.56
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.14
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.02
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.66
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.90
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.34
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.99
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.18
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.59
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.08
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.58
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.68
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.75
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.06
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.84
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.88
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.98
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.78
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.17
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.04
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5121.23
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  319.36
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.95
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.36
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.75
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4866.69
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.65
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.99
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.07
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :    0.19
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:24.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.15
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :   -0.11
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:23.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.18e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 6.83e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9907

-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.54e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.14
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.12
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:03.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.74e-3
p-value of test                       :    0.9972

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.58
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  261.20
p-value of test                       :  2.4e-3

-----------------------------------------------
CPU time used                    :  00:02:04.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.54
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9922.61
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:46.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.90
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5080.33
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:49.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.83
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3991.09
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12047.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11760.48
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.04
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000090019

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.93
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999998660

Normal statistic for number of bits   :  -0.011
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:00.92
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 62  WeightDistrib, r = 0            3.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15925264.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  1.1e-3


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5392
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:59.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:43.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:44.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:58.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:59.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:06.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:08.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:58.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:02.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:49.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    3.36
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.72
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    2.20
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:16.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    8.30
p-value of test                       :  9.8e-5    *****


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:45.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.28
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.41
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.05
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.44
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.41
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.08
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  170.94
p-value of test                       :    0.9990    *****

-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  491.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:44.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.53
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:02.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6923.89
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:44.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.11
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.97
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:03.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.85
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.15
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5094.44
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:11.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:01.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45714
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869714
  j =  1                              :        399908575
  j =  2                              :            45708
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46086
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870086
  j =  1                              :        399907833
  j =  2                              :            46076
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:27.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:20.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:47.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:01.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:33.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.86e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.83e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.17e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.089
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:31.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:32.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.88
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.04
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.16
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.40
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.78
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.82
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:38.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.33
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.70
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.28
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.66
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.08
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17110.55
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.35
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.21
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.62
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.44
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.16
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.92
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.71
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.44
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.54
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.49
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.70
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.83
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.59
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.29
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.39
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.45
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.36
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.00
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.33
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.12
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.12
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.74
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4987.57
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.29
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.29
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.34
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.90
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5235.16
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.28
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.23
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.40
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :    1.42
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:22.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.79
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:24.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 7.40e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.40e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 7.29e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.25
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.37
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:05.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.24
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:05.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9975.35
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9837.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : -6.81e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:40.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5050.82
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:47.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4984.78
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:49.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.46
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.13
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11860.65
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11771.03
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:28.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.96
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999921047

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.22
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000179641

Normal statistic for number of bits   :    1.42
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.90

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:51.40
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs NP, t = 16           9.8e-5
 34  Gap, r = 0                      0.9990 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16973840.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5511
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:04:00.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4534
p-value of test                       :  1.5e-3


-----------------------------------------------
CPU time used                    :  00:01:44.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:44.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:59.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:02.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:08.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:11.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:04:04.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:04:10.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:50.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    3.00
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.97
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:15.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:45.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.80
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.49
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.65
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.94
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.54
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.02
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.44
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.36
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:49.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1456.27
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:05.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6919.24
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:47.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.16
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:05.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.38
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.81
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5068.07
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:12.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:03.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45908
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869908
  j =  1                              :        399908188
  j =  2                              :            45900
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46015
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870015
  j =  1                              :        399907975
  j =  2                              :            46005
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:29.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:17.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 5.42e-3
p-value of test                       :    0.9940

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:02.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:56.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.76e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.95e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 5.51e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.086
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:42.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:43.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.60
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:55.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.48
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:55.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.35
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.66
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.23
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.36
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   71.32
p-value of test                       :  1.7e-3

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.38
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.23
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.23
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17291.22
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.09
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.34
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.26
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.13
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.71
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.95
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.21
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.56
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.58
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.87
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.59
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.49
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.83
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.86
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.08
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.30
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.67
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.83
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.05
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.86
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.87
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.50
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.48
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.44
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.92
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.63
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.34
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4863.82
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.22
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.44
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.04
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :    1.37
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:21.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.76
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:23.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 5.94e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.01e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 5.02e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.24
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.42
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.52
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:06.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:05.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    5.85
p-value of test                       :  1.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9554.13
p-value of test                       :    0.9993    *****

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10012.36
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:04:13.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4836.60
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:51.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:53.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.12
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4240.73
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11836.01
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:30.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11858.73
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:30.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.76
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000236488

Normal statistic for number of bits   :    1.87
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.47
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999848564

Normal statistic for number of bits   :   -1.20
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.47
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.53
p-value of test                       :    0.9943

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.23
p-value of test                       :    0.99

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:14.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 90  HammingWeight2, r = 0           0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17989648.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5366
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:04:00.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4227
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:43.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7146
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:43.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:59.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:06.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:06.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:59.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:04:03.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:48.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.66
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:17.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:48.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.43
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.72
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.32
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.83
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.21
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.37
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.12
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.81
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.62
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:43.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.01
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:02.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6952.06
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:43.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.97
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.67
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:02.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.07
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.48
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5064.97
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:12.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:01.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46088
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870088
  j =  1                              :        399907826
  j =  2                              :            46084
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46071
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870071
  j =  1                              :        399907861
  j =  2                              :            46065
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:28.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:18.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :  7.7e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    5.76
p-value of test                       :  1.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9979


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:45.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:59.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:55.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.10e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.40
p-value of test                       :    0.9919

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:31.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.053
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:31.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.60
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:48.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.47
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.83
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:49.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.56
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.23
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:38.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.23
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.81
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.81
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17250.78
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.45
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.48
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.24
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.69
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.46
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.91
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.17
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   43.99
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.04
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.57
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.35
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.87
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  437.21
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.16
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.89
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.44
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.88
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.54
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.66
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.96
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.15
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.23
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.74
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.19
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.77
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.31
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.77
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.23
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.44
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.40
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.58
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:21.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.04
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:21.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.80
p-value of test                       :    0.04

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    1.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.48e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 2.69e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.51
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.20
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.74
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:04.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.03
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:05.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9968.51
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9904

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.55
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:39.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4946.55
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4943.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:50.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4237.73
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.05
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12031.47
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12061.16
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.50
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000073315

Normal statistic for number of bits   :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.54
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999999137

Normal statistic for number of bits   : -6.82e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    2.32
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:24.76

 All tests were passed




Server wird beendet - Lösche Semaphor 19005456.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5410
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:59.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:43.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:43.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:59.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:07.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:07.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:58.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:04:02.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:53.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    2.69
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     331
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:16.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.89
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:47.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.78
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.37
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.16
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.45
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.61
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  469.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:43.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1379.57
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:02.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7012.51
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:42.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.58
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:03.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.91
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.83
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5100.17
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:12.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:58.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46091
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870091
  j =  1                              :        399907822
  j =  2                              :            46083
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45832
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869832
  j =  1                              :        399908339
  j =  2                              :            45826
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:28.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:19.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:01.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:54.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:33.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 8.21e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:35.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.29
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.94
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.05
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.72
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:49.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.46
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.38
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.16
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:44.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.17
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.07
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 1.18e-3
p-value of test                       :    0.9988

Anderson-Darling statistic = A2       :    3.49
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   91.94
p-value of test                       :    0.9953

-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17520.31
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.68
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.40
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.87
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.68
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.52
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.71
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.28
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.86
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.11
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.60
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.60
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.05
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  446.74
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.63
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.26
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.81
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.63
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.93
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.77
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   50.93
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.68
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.85
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.42
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.17
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.19
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.62
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.64
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.33
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.50
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.51
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.41
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   -1.15
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:21.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.33
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:23.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.73e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 9.76e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.04e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.99
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.42
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:05.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.35
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:04.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10069.05
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10077.09
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:43.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4780.39
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:47.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4924.12
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:48.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.21
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.22
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12002.45
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11705.91
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.37
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999984701

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.74
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999864581

Normal statistic for number of bits   :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         : -3.80e-3
p-value of test                       :    0.50

Sample variance                       :    0.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    2.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:57.04

 All tests were passed




Server wird beendet - Lösche Semaphor 20054032.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:16.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:20.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:18.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5444
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:42.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:36.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:35.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:53.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:03.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:03.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7172
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:57.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:00.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:52.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9913

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:09.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:37.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.64
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.18
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.93
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.48
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.07
p-value of test                       :    0.9923

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.22
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.75
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.94
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.14
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:47.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1394.14
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:07.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7004.84
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:49.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.87
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.79
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:12.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.91
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:47.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.51
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:39.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5096.37
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:27.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45796
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869796
  j =  1                              :        399908410
  j =  2                              :            45792
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45862
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869862
  j =  1                              :        399908280
  j =  2                              :            45854
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:29.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:17.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:43.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:57.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:54.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:36.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.25e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.54e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 3.56e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : -5.10e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:49.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:48.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.70
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.85
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:55.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.29
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:55.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   62.10
p-value of test                       :  6.0e-3

-----------------------------------------------
CPU time used                    :  00:00:51.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.64
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:52.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.31
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9954

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.97
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:32.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.33
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:32.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9958

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.51
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17387.90
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:50.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.78
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.49
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.37
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.07
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.28
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.02
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.33
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.56
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.92
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.15
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.42
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.12
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.27
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.71
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.61
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.73
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.69
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.40
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.48
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  105.65
p-value of test                       :  9.2e-3


-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.47
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.63
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4790.48
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.25
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  153.16
p-value of test                       :    0.9941


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.95
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.85
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5101.63
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.18
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.26
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.21
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:26.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.62
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:30.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    3.35
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.16
p-value of test                       :    0.98

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 4.88e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:47.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.91e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.00
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:29.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.30
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.30
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:09.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.20
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:08.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9929.68
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10083.44
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : 7.28e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:04:19.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.09
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:52.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4973.52
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:53.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4130.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4023.17
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11768.87
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:36.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11876.72
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.40
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000010570

Normal statistic for number of bits   :   0.084
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.52
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000083536

Normal statistic for number of bits   :    0.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.65
p-value of test                       :  6.7e-5    *****

Anderson-Darling statistic = A2       :    7.73
p-value of test                       :  1.7e-4    *****

Tests on the sum of all N observations
Standardized normal statistic         :    3.47
p-value of test                       :  2.6e-4    *****

Sample variance                       :    0.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    5.15
p-value of test                       :  2.6e-3

Tests on the sum of all N observations
Standardized normal statistic         :    3.06
p-value of test                       :  1.1e-3

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   0.012
p-value of test                       :    0.50

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:21:03.68
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 103  AutoCor, d=1, r=0               2.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 688145.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:46.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5398
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:48.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:38.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7131
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:37.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:55.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:55.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7470
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:03.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:03.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7170
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:55.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:59.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    2.68
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     970
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:48.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.13
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.17
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:17.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    3.56
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     122
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:48.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.49
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.99
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.25
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.59
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.96
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.42
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.06
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.27
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.75
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1494.61
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:00.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7029.06
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.38
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   85.45
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:03.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.98
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.43
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:37.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5047.38
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9927


-----------------------------------------------
CPU time used                    :  00:03:06.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46083
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870083
  j =  1                              :        399907835
  j =  2                              :            46081
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46055
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870055
  j =  1                              :        399907896
  j =  2                              :            46043
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:27.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:17.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 3.64e-3
p-value of test                       :    0.9961

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.49
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  3.4e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:59.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:54.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:34.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.97e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.40e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.058
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:21.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.072
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:32.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:31.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.62
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:48.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.61
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.20
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.25
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.56
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.93
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.96
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.97
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  8.0e-3

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.70
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.28
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:28.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  156.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:39.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17258.42
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.63
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.15
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.13
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.94
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.83
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.07
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.63
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.66
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.46
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.37
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.26
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.21
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.10
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.67
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.16
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.24
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.46
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.74
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.54
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.06
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.77
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.05
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5072.78
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  330.59
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.65
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.04
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.39
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.12
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.59
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.58
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.08
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :    1.31
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:29.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.18
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :    0.82
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:29.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :  -0.033
p-value of test                       :    0.51

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 4.44e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:47.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.83e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 4.98e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9908

-----------------------------------------------
CPU time used                    :  00:00:46.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.46
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.52
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.87
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:07.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:09.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9795.71
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10168.35
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.51
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:47.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4928.35
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.75
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:49.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4161.70
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4173.85
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11764.74
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:29.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11589.85
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:31.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.97
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000107890

Normal statistic for number of bits   :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.64
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999791063

Normal statistic for number of bits   :   -1.65
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.2e-3

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.11

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:11.28

 All tests were passed




Server wird beendet - Lösche Semaphor 2064401.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5481
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:49.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:39.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:38.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:55.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7540
p-value of test                       :  5.0e-3


-----------------------------------------------
CPU time used                    :  00:03:03.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:03.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:53.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:59.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:48.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:16.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.20
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:45.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.81
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.37
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.78
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.45
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.17
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.00
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  270.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.86
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:44.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1420.14
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:01.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7031.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.26
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:02.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.10
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.20
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:35.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5078.29
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:03.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46225
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870225
  j =  1                              :        399907552
  j =  2                              :            46221
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46515
p-value of test                       :  1.5e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870515
  j =  1                              :        399906972
  j =  2                              :            46511
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:27.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:18.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 6.80e-3
p-value of test                       :    0.9923

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:45.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9983


-----------------------------------------------
CPU time used                    :  00:02:00.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:55.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.65e-4
p-value of test                       :  4.9e-3

Kolmogorov-Smirnov- statistic = D-    : 2.19e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:33.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:34.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.98
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.10
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.71
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.52
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.17
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.42
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.40
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.40
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17342.16
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.87
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.21
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.57
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.63
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.17
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.18
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.01
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.45
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.38
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.05
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.58
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.37
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.15
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.98
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.86
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.54
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.97
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.24
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.25
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.71
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  317.34
p-value of test                       :    0.9944


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.02
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4933.57
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.33
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.79
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.18
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.27
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.18
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  326.86
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  246.51
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.63
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :   -1.36
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:25.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.71
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :   -1.58
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:26.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.71

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :  5.1e-3

Kolmogorov-Smirnov- statistic = D-    : 4.85e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:47.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.68e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.84
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.61
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.26
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:07.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.33
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:10.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9827.57
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9884.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:50.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4988.19
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5058.70
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:49.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.90
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.71
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11841.63
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12144.64
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:29.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.13
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000072694

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.58
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999835526

Normal statistic for number of bits   :   -1.30
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :  -0.099
p-value of test                       :    0.54

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:20.71

 All tests were passed




Server wird beendet - Lösche Semaphor 2981905.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:43.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:55.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5435
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:49.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:39.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:37.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:54.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:03.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:04.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:55.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:01.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     929
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:48.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.88
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.75
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:15.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.29
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:44.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.01
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.71
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.09
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.44
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.52
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:11.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.36
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.39
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.46
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.32
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  486.33
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1467.40
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:04.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6874.07
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:50.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.34
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.58
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:14.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.94
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.94
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:37.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5021.85
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:59.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45847
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869847
  j =  1                              :        399908307
  j =  2                              :            45845
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46001
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870001
  j =  1                              :        399908005
  j =  2                              :            45987
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:29.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:18.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9996    *****


-----------------------------------------------
CPU time used                    :  00:02:02.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.39e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:56.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:36.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 9.51e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:43.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:43.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.14
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.95
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.55
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.60
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:50.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.29
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.39
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.29
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.40
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.43
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.74
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17364.14
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.35
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.26
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.37
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.47
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.95
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.31
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.73
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.51
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.37
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.33
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.16
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  567.62
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.36
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.30
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.87
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.17
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.15
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.02
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.64
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.84
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.71
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5179.22
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.10
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.48
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.55
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.58
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4862.21
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.60
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.21
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.31
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :   -0.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:28.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.81
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:25.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.73
p-value of test                       :    0.04

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.11e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 4.79e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:00:46.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.60
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.21
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.09
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:08.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.83
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:09.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9936.20
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9841.93
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:04:23.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.06
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4772.98
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:55.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.06
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4210.89
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11872.75
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:31.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11927.54
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:30.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.29
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999990056

Normal statistic for number of bits   :  -0.079
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.46
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000228409

Normal statistic for number of bits   :    1.81
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:10.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:15.86
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 49  MaxOft AD, t = 32               0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3899409.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5433
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:53.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4450
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7448
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:41.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:59.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:59.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:08.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:10.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:04:07.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:04:15.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.18
p-value of test                       :    0.9940

Test on the Nm values of W_{n,i}(mNP1):    2.00
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     853
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:49.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    2.08
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:15.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:45.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.99
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.77
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.83
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.05
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.08
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.27
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.20
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.01
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:29.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.36
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1429.64
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:01.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6956.30
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:55.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.42
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9916

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.96
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:15.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.68
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:47.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.46
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:44.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5194.77
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:01.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45910
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869910
  j =  1                              :        399908181
  j =  2                              :            45908
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45884
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869884
  j =  1                              :        399908235
  j =  2                              :            45878
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:33.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:21.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:52.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:11.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:57.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:39.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 8.62e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.31
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:24.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:24.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:47.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -1.83e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.51
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.86
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.74
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.88
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.82
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.75
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:50.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.48
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.34
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:28.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.11
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17638.96
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.37
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.99
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.28
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.60
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.05
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.17
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.33
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.58
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.88
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.83
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.15
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.74
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.88
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.59
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.97
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.70
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  190.12
p-value of test                       :  8.2e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.12
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.36
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.68
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.41
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.89
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4851.65
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  447.23
p-value of test                       :  8.1e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.66
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.89
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.00
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4885.27
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.31
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.38
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.97
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:24.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.21
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :   -1.53
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:24.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 3.33e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 8.93e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.75
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.28
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.36
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:07.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.27
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:08.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10106.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10046.51
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:04:30.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4974.68
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:55.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.21
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:58.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4161.19
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4252.31
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:29.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11796.37
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:35.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11753.44
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:37.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.39
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000016645

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.56
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999859922

Normal statistic for number of bits   :   -1.11
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:11:02.22

 All tests were passed




Server wird beendet - Lösche Semaphor 5079057.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5306
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:55.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:43.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:00.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:01.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:12.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:13.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:09.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:15.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.53
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    2.13
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.95
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     563
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    2.29
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.47
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:14.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:42.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.74
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.03
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.82
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.23
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.49
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.09
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:31.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  382.37
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:51.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1501.62
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:04.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6971.09
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.56
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:12.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.31
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:47.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.26
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:40.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5005.67
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:29.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:55.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46114
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870114
  j =  1                              :        399907780
  j =  2                              :            46098
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46115
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870115
  j =  1                              :        399907776
  j =  2                              :            46103
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:31.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:24.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:52.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.08
p-value of test                       :  8.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  5.6e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:08.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:58.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:38.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.20e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:24.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:44.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.084
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:48.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.88
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.49
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.28
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.93
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.80
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:50.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.92
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.86
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:29.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.90
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.03
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17396.92
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.60
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.64
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.89
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.88
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.29
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.50
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.38
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.84
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.26
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.77
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.96
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.61
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.62
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.85
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.57
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.77
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.68
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.75
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.79
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.60
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.52
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.96
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.47
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.43
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.79
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.28
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.41
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.26
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.61
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.75
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.46
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :   -1.60
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:25.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.91
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:25.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 2.96e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.23e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 9.77e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.65
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:32.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.08
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:34.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:22.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:22.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.8e-3

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9764.09
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10095.38
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:04:29.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.46
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:51.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.92
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4152.15
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.40
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11914.96
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:32.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11656.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:35.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.90
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  7999954158

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.85
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999931382

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.32

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:22.57

 All tests were passed




Server wird beendet - Lösche Semaphor 6258705.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5420
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:55.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:41.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:56.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:58.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:05.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:06.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:56.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:02.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:51.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:19.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.68
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:46.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.23
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   36.00
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.17
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.29
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.52
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.47
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.55
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.08
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1512.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:01.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7046.74
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.16
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.81
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:02.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.54
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  144.32
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:34.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4965.74
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:02.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46199
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870199
  j =  1                              :        399907605
  j =  2                              :            46193
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45612
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869612
  j =  1                              :        399908779
  j =  2                              :            45606
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:28.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 4.39e-4
p-value of test                       :    0.9996    *****

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  6.4e-3

Anderson-Darling statistic = A2       :    6.58
p-value of test                       :  5.5e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  7.6e-5    *****


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:20.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:44.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-3
p-value of test                       :    0.9985

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:59.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:37.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 8.64e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.35e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 4.45e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:39.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:39.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.58
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.93
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.44
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.92
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.53
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:45.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.29
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.03
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17469.33
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.35
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.03
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.79
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.41
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.39
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.85
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.79
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.58
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.59
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.95
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.01
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.72
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.44
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.64
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.83
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.30
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.36
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.18
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.18
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.79
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.89
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.85
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4856.46
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.67
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.15
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.03
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.29
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4957.06
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.60
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.40
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.70
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :    2.18
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:02:24.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.59
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :    1.01
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:24.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.93
p-value of test                       :    0.97

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   0.043
p-value of test                       :    0.48

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.92e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 7.84e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 6.12e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.31
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.27
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:04.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.67
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:06.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9953.39
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10000.24
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.057
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:35.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4984.76
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:46.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.70
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.61
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.46
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12144.53
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11598.91
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.18
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999896903

Normal statistic for number of bits   :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.06
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000145216

Normal statistic for number of bits   :    1.15
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.55
p-value of test                       :    0.94

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:13.61
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 47  MaxOft, t = 16                  7.6e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7405585.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5357
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:55.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:41.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4224
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:58.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:05.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:06.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:56.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:04:01.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.9905


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.72
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    2.03
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:16.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.31
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:46.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.79
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.27
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.64
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.56
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.78
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.79
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.58
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.96
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.08
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.85
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1441.27
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:02.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7070.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.01
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.23
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:01.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.29
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.16
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:32.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5104.69
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  8.9e-3


-----------------------------------------------
CPU time used                    :  00:02:55.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45677
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869677
  j =  1                              :        399908649
  j =  2                              :            45671
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46007
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870007
  j =  1                              :        399907987
  j =  2                              :            46005
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:29.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:17.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:44.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:00.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9937

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:36.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:21.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:38.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:36.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.25
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.97
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.95
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.47
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.99
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.29
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:42.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.54
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.13
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.82
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.71
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.67
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17654.79
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.00
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.03
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.59
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.42
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.49
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.31
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.74
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.31
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.56
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.37
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.83
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.61
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.29
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.51
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.32
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.12
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.64
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.11
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.86
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  112.76
p-value of test                       :  2.5e-3


-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.45
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.07
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.16
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.93
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.08
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.08
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.94
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.89
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.78
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.37
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.06
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:22.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.44
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :   -1.12
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:21.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.06e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.50e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.25
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.46
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.30
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:07.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    3.88
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  154.76
p-value of test                       :    0.9924

-----------------------------------------------
CPU time used                    :  00:02:08.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10210.93
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9838.52
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:55.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:37.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.16
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4985.72
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:49.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.03
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.72
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12043.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11905.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.11
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999984467

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.67
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000062131

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.051
p-value of test                       :    0.52

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:42.37

 All tests were passed




Server wird beendet - Lösche Semaphor 8421393.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5515
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:55.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:56.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:57.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:06.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:05.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:55.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:04:00.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:52.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.83
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    3.35
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     561
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    7.82
p-value of test                       :  1.4e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:19.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:50.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.23
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.68
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.25
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.18
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.46
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.85
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.38
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.76
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  480.47
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1391.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:01.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7132.98
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:42.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.67
p-value of test                       :  4.8e-3

Anderson-Darling statistic = A2       :    3.94
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   52.12
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.36
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:02.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.29
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.03
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:33.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5134.34
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:54.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45912
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869912
  j =  1                              :        399908178
  j =  2                              :            45908
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45929
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869929
  j =  1                              :        399908146
  j =  2                              :            45921
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:27.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:18.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:44.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:00.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:37.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.95e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 8.32e-6
p-value of test                       :    0.9972

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.43e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.041
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:37.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:35.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.53
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.81
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.96
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.52
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.11
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.96
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   12.68
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:01:41.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.81
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.95
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.83
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.13
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.39
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17186.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.06
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.22
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.09
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.39
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.15
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.46
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.37
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   49.35
p-value of test                       :  2.6e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.26
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.48
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.33
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.98
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.08
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.72
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.76
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  196.16
p-value of test                       :  3.6e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.45
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.71
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.46
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.57
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.05
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.59
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.59
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.03
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.23
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.06
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.01
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4936.45
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.66
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  160.74
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.24
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :   -0.51
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:21.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.73
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :    1.47
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :  -0.033
p-value of test                       :    0.51

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  2.8e-3

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.72
p-value of test                       :    0.96

Sample variance                       :    0.21
p-value of test                       :    0.9933

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.03e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.71e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 9.94e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.70
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.10
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 8.19e-3
p-value of test                       :    0.9912

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.83
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:06.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.08
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:06.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10300.53
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9795.29
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.22
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.100
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:42.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4820.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4801.82
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:49.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.05
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4180.51
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11717.59
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12038.99
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:29.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.83
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000078061

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.89
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000067777

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:53.92
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs mNP2S, t = 5         1.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9437201.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:39.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5279
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:53.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:40.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4244
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:59.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:09.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:08.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:04:02.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:04:05.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:49.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.96
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:15.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.10
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:45.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.68
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.04
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.09
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.71
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.56
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.54
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.75
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1434.03
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:00.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7120.59
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:47.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.34
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.65
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:07.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.32
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.82
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:35.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4920.11
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:52.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45955
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869955
  j =  1                              :        399908092
  j =  2                              :            45951
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46520
p-value of test                       :  1.4e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870520
  j =  1                              :        399906962
  j =  2                              :            46516
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:29.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:19.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:05.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 2.16e-3
p-value of test                       :    0.9978

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.21e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:41.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:44.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.03
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.37
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.78
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.68
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   47.02
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:44.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.39
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.07
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17858.18
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.83
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   57.54
p-value of test                       :  9.5e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.79
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.81
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.56
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.44
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   56.08
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.74
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.71
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.34
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.64
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.91
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.18
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.44
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.27
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.47
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.02
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.99
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.37
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.06
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.03
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.15
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5007.15
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.35
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.12
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.07
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.75
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4960.49
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.27
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.14
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.41
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:23.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.54
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:24.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 7.79e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 4.67e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.64
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.69
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.40
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:07.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.69
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:07.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10149.54
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.50e-3
p-value of test                       :    0.9985

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9727.43
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.10
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:04:09.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.93
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:52.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4945.25
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:52.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.78
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4017.81
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11665.52
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:29.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12033.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.17
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999998195

Normal statistic for number of bits   :  -0.014
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.91
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999956573

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 5.10e-3
p-value of test                       :    0.9947

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.98
p-value of test                       :    0.98

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:28.79

 All tests were passed




Server wird beendet - Lösche Semaphor 10453009.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:51.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5401
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:54.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:42.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4090
p-value of test                       : 1 -  8.0e-5    *****


-----------------------------------------------
CPU time used                    :  00:01:58.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4251
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:59.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:07.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:09.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:04:03.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:04:07.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    3.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:50.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:16.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:48.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.64
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.91
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.55
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.89
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.42
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.04
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.28
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.89
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.43
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.28
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:49.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1404.72
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:00.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7032.35
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:48.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.66
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:08.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.45
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.81
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:36.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5192.85
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:03.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45843
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869843
  j =  1                              :        399908316
  j =  2                              :            45839
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46249
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870249
  j =  1                              :        399907503
  j =  2                              :            46247
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:30.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:20.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:48.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:08.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:56.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9931

-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.61e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:22.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:44.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:45.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.19
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:49.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   96.84
p-value of test                       :  1.0e-2

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.75
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.11
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.85
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.85
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.53
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:46.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.39
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.1e-3

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.78
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.01
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:16.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.41
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17319.93
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:52.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.92
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.37
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.55
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.02
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.49
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.87
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.21
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.85
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.07
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.32
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.05
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.43
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.91
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.24
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.55
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.97
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.73
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.75
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  101.80
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.37
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.78
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.39
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.08
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.67
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.69
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.99
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.71
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4804.03
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.55
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.21
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.58
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:25.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.19
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:24.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 9.51e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.20
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.84
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.36
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:05.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.60
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:05.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10148.16
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10022.67
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:04:12.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.88
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:52.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4821.40
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:53.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4032.81
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4129.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12209.88
p-value of test                       :  6.6e-3

-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11979.04
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.69
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000020659

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.83
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999934349

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.67
p-value of test                       :    0.05

Sample variance                       :    1.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.16
p-value of test                       :    0.9975

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 6.17e-3
p-value of test                       :    0.9935

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.77
p-value of test                       :    0.04

Sample variance                       :    2.35
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:11.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:51.76
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 16  BirthdaySpacings, t = 7        1 -  8.0e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11436049.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5437
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:54.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:40.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:41.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4235
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:57.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:06.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:07.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7494
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:55.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:01.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:06.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.84
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     650
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.23
p-value of test                       :  7.1e-3

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:16.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     130
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9944

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:46.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.84
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.01
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.15
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.28
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.53
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.17
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.90
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.95
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:42.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.38
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:01.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6853.74
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:44.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.75
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.55
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:01.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.92
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  152.19
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:34.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5131.30
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:01.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45716
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869716
  j =  1                              :        399908574
  j =  2                              :            45704
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45888
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869888
  j =  1                              :        399908226
  j =  2                              :            45884
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 6.57e-3
p-value of test                       :    0.9915

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:28.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:18.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:44.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:59.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:58.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:34.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.50e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.35e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:22.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.41
p-value of test                       :    0.9919

-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:45.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.22
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.25
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.34
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.77
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.36
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.98
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:43.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.00
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.73
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.94
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.83
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.38
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17347.22
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.33
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.78
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.37
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.28
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.84
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:38.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.51
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.77
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   42.30
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.25
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.51
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.20
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.64
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.50
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.32
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.36
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.28
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.30
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.66
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.74
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.98
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.89
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.40
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4924.68
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  431.88
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.04
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.84
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.40
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5084.97
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.47
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.53
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.56
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :   0.070
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:22.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.54
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:23.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:47.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.22e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.16
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.54
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.77
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:06.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.06
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:06.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10140.74
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10120.55
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:10.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:04:19.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4993.96
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.58
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:50.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4216.54
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4210.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11711.35
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11753.16
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.95
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999780956

Normal statistic for number of bits   :   -1.73
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.87
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999990530

Normal statistic for number of bits   :  -0.075
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    1.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:28.75

 All tests were passed




Server wird beendet - Lösche Semaphor 12484625.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5491
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:54.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:41.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:58.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:05.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:05.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:55.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:00.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    2.43
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     838
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:49.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.84
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:15.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    2.17
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:45.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.30
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.99
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.85
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.28
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.63
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.03
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.81
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.06
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  202.68
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:44.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:02.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7126.92
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.75
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.73
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:01.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.25
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.30
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:32.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4980.94
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:01.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45693
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869693
  j =  1                              :        399908617
  j =  2                              :            45687
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45670
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869670
  j =  1                              :        399908665
  j =  2                              :            45660
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:28.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:18.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:44.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:59.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:58.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:34.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.30e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.64e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:21.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:37.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:39.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.28
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  100.01
p-value of test                       :  5.5e-3

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.48
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.16
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:49.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.75
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.91
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.60
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.32
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.64
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  156.25
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17462.87
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.28
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.39
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.19
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.44
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.90
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.59
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.00
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.99
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.81
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.79
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:39.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.67
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.74
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.92
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.76
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.08
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.14
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.14
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.66
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.47
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.52
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.82
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.62
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.65
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.32
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.09
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.67
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.92
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.90
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.07
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.60
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.96
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  :    2.39
p-value of test                       :  8.4e-3



-----------------------------------------------
CPU time used                    :  00:02:24.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.14
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :   -0.37
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:24.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.22e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 6.24e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.15
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.55
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.50
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:05.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.48
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:07.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9921.15
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10080.65
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.08
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:40.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4790.39
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:47.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5031.87
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:49.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.84
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.25
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11699.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11787.99
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.31
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999938717

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.06
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000028228

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:41.97

 All tests were passed




Server wird beendet - Lösche Semaphor 13500433.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5489
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:56.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:58.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:06.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7181
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:06.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:57.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:04:01.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:47.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     637
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     272
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:15.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.01
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:42.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.58
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.43
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.26
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.44
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.55
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.85
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.12
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  517.25
p-value of test                       :  3.6e-3

-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1347.76
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:02.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7099.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:40.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.91
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:01.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   15.23
p-value of test                       :  9.4e-3


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.43
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:33.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4995.10
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:59.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46096
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870096
  j =  1                              :        399907814
  j =  2                              :            46084
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45809
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869809
  j =  1                              :        399908382
  j =  2                              :            45809
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:29.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:19.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:46.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:00.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 2.26e-3
p-value of test                       :    0.9976

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:35.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.43e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:39.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.80
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  104.78
p-value of test                       :  2.2e-3

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.42
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.55
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.05
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.99
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.93
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.45
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:28.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.09
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  157.21
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17334.98
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.71
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.62
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.22
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.51
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.44
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.57
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.32
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.68
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.21
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.86
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.05
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.01
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.46
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.81
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.56
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.55
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.91
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.06
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.63
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.95
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.44
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.51
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.02
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.78
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.26
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.17
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.01
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.95
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.90
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.34
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.13
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :   -1.57
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:26.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.26
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :   -1.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:24.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.31e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 4.26e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.02
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.41
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.93
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:04.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.60
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:05.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10119.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10076.32
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:41.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5044.63
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4905.26
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:48.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4196.09
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4007.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11719.38
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12029.87
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.04
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000034552

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.69
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000024742

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.71
p-value of test                       :    0.96

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :  -0.044
p-value of test                       :    0.52

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:59.54

 All tests were passed




Server wird beendet - Lösche Semaphor 14516241.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5388
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:55.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:58.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:05.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:05.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:55.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:00.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.70
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:47.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.00
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:15.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9934

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:43.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.52
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   45.42
p-value of test                       :  3.6e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.93
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.18
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:10.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.08
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.96
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.00
p-value of test                       :    0.9950

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.57
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.81
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:43.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1500.54
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:01.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7096.07
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:42.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.96
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.09
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:03.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.17
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.88
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:35.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5097.01
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:58.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45829
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869829
  j =  1                              :        399908346
  j =  2                              :            45821
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45919
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869919
  j =  1                              :        399908166
  j =  2                              :            45911
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:28.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:18.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:44.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:58.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:35.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.89e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 3.02e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.060
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:37.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:40.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.83
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:48.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.27
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   63.21
p-value of test                       :  4.6e-3

-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.65
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.24
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.92
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:44.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.57
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.02
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.35
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.46
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.34
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17375.20
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.24
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.08
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.40
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.31
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.91
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.45
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.54
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.73
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.26
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.14
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.14
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.24
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.19
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  178.76
p-value of test                       :  8.2e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.62
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.67
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.32
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.57
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.54
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.91
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.62
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.55
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4872.30
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.36
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.39
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.21
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.01
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4821.52
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  328.13
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.04
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.71
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:26.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.56
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :   -2.64
p-value of test                       :    0.9958



-----------------------------------------------
CPU time used                    :  00:02:23.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    2.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.12e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 9.92e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :  7.8e-3

Kolmogorov-Smirnov- statistic = D-    : 7.19e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.24
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.68
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.44
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:05.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.33
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:06.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9973.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9979.63
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:40.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5025.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:47.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.52
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:51.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3952.54
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.23
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11733.10
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11769.49
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:28.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.30
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  8000015601

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.80
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999956348

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.28

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:03.90
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 28  SimpPoker, r = 0                3.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15532049.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5393
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:54.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:40.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:56.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:58.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:06.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:06.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7097
p-value of test                       :    0.9952


-----------------------------------------------
CPU time used                    :  00:03:56.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:04:01.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.72
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    2.92
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.02
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:15.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.20
p-value of test                       :  7.7e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:43.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.28
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.50
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.46
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.86
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.54
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.57
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.10
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.66
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.70
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:43.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1421.99
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:01.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7072.42
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:40.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.98
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.75
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:02.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.91
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.62
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:33.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5088.72
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:01.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46055
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870055
  j =  1                              :        399907894
  j =  2                              :            46047
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45712
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869712
  j =  1                              :        399908580
  j =  2                              :            45704
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:27.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.08e-3
p-value of test                       :    0.9913

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:18.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:46.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:58.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:56.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 6.20e-3
p-value of test                       :    0.9930

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:37.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:36.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.31
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:40.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.27
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.82
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.92
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:49.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.21
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.68
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.27
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:44.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.85
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:29.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.79
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:38.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17377.20
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.18
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.59
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.07
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.23
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.70
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.50
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.70
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.27
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.04
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.46
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.05
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.77
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  569.11
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.75
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.62
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.01
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.42
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.60
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.22
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.13
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.66
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.22
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.62
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.16
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  249.41
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.58
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.63
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4729.71
p-value of test                       :    0.9970


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.81
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  143.15
p-value of test                       :    0.9991    *****


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.37
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :   -1.24
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:22.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.39
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:22.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 6.48e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.51e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.61
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.30
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 9.33e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.66
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:06.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.72
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:08.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9878.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10146.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:37.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4959.52
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:47.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4989.28
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4002.94
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4359.49
p-value of test                       :  4.3e-3

-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11796.52
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11860.70
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.94
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000135370

Normal statistic for number of bits   :    1.07
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.88
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999945872

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.57

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:10.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 C (L=10000, r=15)   0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16580625.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1246
p-value of test                       :    0.9994    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334366
  j =  1                              :        599997508
  j =  2                              :             1246
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.99

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5442
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:54.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:40.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:39.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:56.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:58.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:06.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:05.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:56.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:00.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.00
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     948
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:48.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.34
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:13.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.9903

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:44.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.36
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.65
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.26
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.35
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.93
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.82
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.48
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.05
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.61
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:44.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1501.37
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:00.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7136.71
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:41.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.99
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:02.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.95
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.22
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:32.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4893.78
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:00.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45952
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869952
  j =  1                              :        399908097
  j =  2                              :            45950
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46032
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870032
  j =  1                              :        399907941
  j =  2                              :            46022
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  8.6e-3

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:28.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:19.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:58.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.07e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 3.35e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:37.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:38.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.94
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.69
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.57
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.80
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:48.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.43
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.90
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:44.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.43
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.46
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.15
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9921

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17461.76
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.09
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.71
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.54
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.91
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.65
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.97
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.71
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.34
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.60
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.43
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.08
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.36
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.73
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.65
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.51
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.19
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.84
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  559.14
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.26
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   46.55
p-value of test                       :    0.9948


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.99
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.56
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4906.93
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.81
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.13
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.89
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.03
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4940.72
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.40
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.52
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.10
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :  -0.060
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:23.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.46
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:22.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.72
p-value of test                       :    0.04

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.70
p-value of test                       :    0.04

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.78e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.26
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.64
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.82
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:04.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.84
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:07.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9951.65
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10098.62
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:38.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.76
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:48.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4962.47
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:49.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4335.26
p-value of test                       :  8.9e-3

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.15
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11864.83
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11846.45
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:29.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.14
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999878435

Normal statistic for number of bits   :   -0.96
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.10
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999879515

Normal statistic for number of bits   :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 8.73e-3
p-value of test                       :    0.9906

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.93
p-value of test                       :    0.97

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :  -0.014
p-value of test                       :    0.51

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.038
p-value of test                       :    0.52

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:31.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14           0.9994 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17596433.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1487
p-value of test                       :  5.4e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334607
  j =  1                              :        599997026
  j =  2                              :             1487
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5443
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:52.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:40.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:56.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4437
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:57.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:05.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:06.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:57.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:01.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:49.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:15.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:41.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.44
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.63
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   37.59
p-value of test                       :  4.4e-3

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.00
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.83
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:11.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.85
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.19
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.15
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.07
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:44.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1568.17
p-value of test                       :  8.5e-3

-----------------------------------------------
CPU time used                    :  00:02:01.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6996.21
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.74
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.03
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:02.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.21
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.11
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:33.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5137.84
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:58.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45856
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869856
  j =  1                              :        399908291
  j =  2                              :            45850
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45751
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869751
  j =  1                              :        399908503
  j =  2                              :            45741
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:27.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:18.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:45.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9907


-----------------------------------------------
CPU time used                    :  00:01:59.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:35.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 8.51e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.31e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.095
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:38.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:36.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.66
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.48
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.01
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.19
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.42
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.14
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.36
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:43.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.63
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.37
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:28.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.72
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-3
p-value of test                       :    0.9981

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  174.72
p-value of test                       :  5.4e-3

-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17193.22
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.32
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.83
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.79
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.08
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.98
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.67
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.29
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.04
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.65
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.30
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.88
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.98
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.04
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.14
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.32
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.51
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.85
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  550.20
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.87
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.24
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.14
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.33
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4888.43
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.72
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.49
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.10
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.25
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4874.66
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.56
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.99
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.86
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:24.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   26.56
p-value of test                       :  8.9e-3


-----------------------------------------------
Normal statistic for number of jumps  :   -1.13
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:23.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.74
p-value of test                       :    0.96

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.56e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 6.74e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.15e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.78
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.11
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  8.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  162.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:05.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.57
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:07.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10129.01
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10119.12
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:40.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4851.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4907.92
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:51.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.76
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4226.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11615.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11919.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:29.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.18
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999984704

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.03
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000020824

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:11.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           5.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18579473.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  3.4e-3


-----------------------------------------------
CPU time used                    :  00:00:50.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5282
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:55.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4220
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7525
p-value of test                       :  8.2e-3


-----------------------------------------------
CPU time used                    :  00:02:41.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:57.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:58.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:05.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:05.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:56.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:01.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     958
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:49.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    2.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:18.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    2.40
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    2.51
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:44.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.77
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.51
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.49
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.85
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.39
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.90
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.23
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:44.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1537.39
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:01.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7019.78
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:40.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.65
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.22
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:01.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.25
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.31
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:33.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5126.81
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:00.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46235
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870235
  j =  1                              :        399907533
  j =  2                              :            46229
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45848
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869848
  j =  1                              :        399908307
  j =  2                              :            45842
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:28.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:20.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:46.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:02.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:57.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:35.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:36.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:36.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.00
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.85
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.92
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.11
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.41
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.98
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:43.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.22
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.40
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17515.09
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.42
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.14
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.04
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.84
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.96
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.56
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.46
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.02
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.87
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.60
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.09
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.48
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.33
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.99
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.81
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.50
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.24
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.71
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.60
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.77
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.94
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.64
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.57
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.99
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.21
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.61
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.44
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5112.52
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.66
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.78
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    1.46
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:25.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.16
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:24.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.43e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 7.79e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.52e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 7.91e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.56
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.54
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:08.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.24
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:08.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 2.79e-3
p-value of test                       :    0.9971

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9746.15
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10052.98
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.040
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:39.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4786.64
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4772.52
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:51.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4068.90
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4071.44
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11780.94
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11855.73
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:29.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.61
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999830231

Normal statistic for number of bits   :   -1.34
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.24
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999974738

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.19
p-value of test                       :    0.12

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:20.25

 All tests were passed




Server wird beendet - Lösche Semaphor 19660817.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5462
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:55.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7198
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:41.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4443
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:57.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:05.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:05.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:56.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:04:02.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.50
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     946
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.87
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:15.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.22
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.99
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:45.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.29
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.11
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.50
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.43
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.45
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.25
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.17
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.22
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:44.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1443.04
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:02.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6906.74
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.60
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:01.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.61
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.73
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:33.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5142.75
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:00.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46142
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870142
  j =  1                              :        399907719
  j =  2                              :            46136
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45636
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869636
  j =  1                              :        399908731
  j =  2                              :            45630
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:28.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:18.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:45.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:59.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :  2.9e-3

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:55.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:35.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:36.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:35.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.32
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.70
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.06
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.06
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.31
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.79
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:44.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.21
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:28.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.96
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.00
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17455.45
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.29
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.38
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.65
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.26
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.02
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.04
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.73
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.13
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.29
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:38.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.11
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.85
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.26
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.42
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.24
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.08
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.42
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.21
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.72
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.17
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.73
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.97
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5071.00
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.90
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.21
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.19
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.91
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.56
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.05
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.87
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.12
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:24.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.64
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:23.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 6.18e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 8.99e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.71
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.72
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.22
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:02.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.23
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:03.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10096.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10062.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:26.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.05
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:39.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.92
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:40.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.28
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4223.90
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11864.99
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11959.85
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.04
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999868436

Normal statistic for number of bits   :   -1.04
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.30
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000070087

Normal statistic for number of bits   :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :  -0.095
p-value of test                       :    0.54

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:00:24.12

 All tests were passed




Server wird beendet - Lösche Semaphor 20676625.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:19.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:20.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1254
p-value of test                       :    0.9987

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334374
  j =  1                              :        599997492
  j =  2                              :             1254
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:19.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5535
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:43.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:37.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:35.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:54.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:55.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:02.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:01.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:53.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:58.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.84
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     951
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:51.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    3.43
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.59
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:09.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:34.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.84
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.86
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.86
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.25
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.28
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.35
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.46
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:43.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1529.46
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:02.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7103.75
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:44.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.76
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.29
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:04.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.52
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.83
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:38.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5078.76
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:15.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:19.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45958
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869958
  j =  1                              :        399908087
  j =  2                              :            45952
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45864
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869864
  j =  1                              :        399908274
  j =  2                              :            45860
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  2.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:28.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:18.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:44.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:00.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:53.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:31.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.58e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 9.28e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:26.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:39.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:38.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.94
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.69
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.58
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.80
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:47.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.10
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.34
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.02
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.01
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.96
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:30.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.57
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:29.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:10.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.07
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17132.99
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:56.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.39
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.86
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.85
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.65
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.31
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.45
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.17
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.58
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.92
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.77
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.38
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.70
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  172.45
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.95
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  200.34
p-value of test                       :  1.9e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.30
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.64
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  105.30
p-value of test                       :  9.8e-3


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.95
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.14
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4911.69
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.52
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.20
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.65
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.53
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4961.04
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.93
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.31
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:34.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.81
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:15.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.14
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :   -1.58
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:19.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
p-value of test                       :    0.9925

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.80
p-value of test                       :    0.96

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.71e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 9.93e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.50e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.83
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:29.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.18
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.11
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:10.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.13
p-value of test                       :  7.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  256.94
p-value of test                       :  4.1e-3

-----------------------------------------------
CPU time used                    :  00:02:08.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9854.19
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9891.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:04:13.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4776.06
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:49.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4887.01
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4282.48
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4036.12
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11990.76
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11831.04
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:32.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.28
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000139990

Normal statistic for number of bits   :    1.11
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.14
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  8000092581

Normal statistic for number of bits   :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   0.011
p-value of test                       :    0.50

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.91

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.80
p-value of test                       :    0.96

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:18:57.45

 All tests were passed




Server wird beendet - Lösche Semaphor 720914.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5324
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:47.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:38.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:37.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4413
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4445
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:56.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:05.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:07.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7186
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:03.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:04.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:47.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     566
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.65
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:15.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:45.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.15
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.50
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.46
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.41
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:11.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.46
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.57
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.29
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.76
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:29.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.53
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1503.44
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:08.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7277.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:55.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.20
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:16.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.36
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.94
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4961.25
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:04.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45561
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869561
  j =  1                              :        399908882
  j =  2                              :            45553
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45675
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869675
  j =  1                              :        399908652
  j =  2                              :            45671
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:31.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:16.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:45.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:03.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:57.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:38.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.65e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 2.91e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:26.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.32
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:24.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:45.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.080
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:46.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.93
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.00
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.62
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.54
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.32
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.86
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:50.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.70
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.84
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.03
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.09
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  160.33
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17608.15
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.04
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.91
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.61
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.90
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.92
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.74
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.75
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.01
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.14
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.28
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.59
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.26
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.52
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.54
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:46.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.32
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.89
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.83
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  171.97
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.03
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.96
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.88
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5090.09
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.98
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.25
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.23
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.71
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5050.91
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.96
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.92
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:36.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.16
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:26.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.95
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :  -0.069
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:27.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 8.19e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.24e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 4.10e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.30
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.64
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:08.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:08.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10072.00
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10144.99
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:10.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:04:28.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.20
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:54.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5048.62
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:58.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4031.55
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.66
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12016.06
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:35.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11825.86
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:33.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.23
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000041152

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.59
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999975218

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.30
p-value of test                       :    0.01

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   0.053
p-value of test                       :    0.48

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:11.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:15:02.17

 All tests were passed




Server wird beendet - Lösche Semaphor 1933330.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:47.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5499
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:50.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4471
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:39.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:38.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4464
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:56.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:04.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:04.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:55.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:04:02.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     866
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.94
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:16.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:46.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.85
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.61
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.80
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.64
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.71
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.21
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.92
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.36
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.90
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.55
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1399.02
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:58.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6962.50
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:49.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.71
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   40.48
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:03.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.41
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.32
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:35.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5118.15
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:57.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45640
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869640
  j =  1                              :        399908724
  j =  2                              :            45632
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45489
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869489
  j =  1                              :        399909027
  j =  2                              :            45479
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:26.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:17.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:45.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:01.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:55.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:33.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.035
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.020
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:34.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:34.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.10
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.38
p-value of test                       :    0.9919

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.18
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.74
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.08
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:41.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.05
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.47
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:38.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17436.37
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:55.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.56
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.53
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.22
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.07
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.36
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.29
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.66
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.40
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.37
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.50
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.83
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.52
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.08
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.54
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.31
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.73
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.42
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.15
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.18
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.48
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  440.72
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.43
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4900.64
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.87
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  246.15
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.77
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.69
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4848.09
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.47
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.26
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.27
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :   -1.48
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:24.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.78
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:26.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.74
p-value of test                       :    0.04

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.83
p-value of test                       :    0.03

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:47.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 6.11e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.51
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.96
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:08.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:08.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9859.62
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9885.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:43.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.43
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:50.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4742.25
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:50.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.13
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3969.58
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11676.35
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11778.40
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.90
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999967955

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.74
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000056467

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:14.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:32.04

 All tests were passed




Server wird beendet - Lösche Semaphor 3178514.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5427
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:49.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:39.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:38.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:55.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4250
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:03.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:02.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7506
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:55.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7471
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:01.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:48.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    2.28
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:15.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:42.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.56
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.10
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.13
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.01
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.22
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.97
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.77
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:16.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.18
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:42.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1405.22
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:00.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7111.16
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.94
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.85
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:02.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.86
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.21
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5133.98
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:57.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45860
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869860
  j =  1                              :        399908285
  j =  2                              :            45850
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45959
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869959
  j =  1                              :        399908086
  j =  2                              :            45951
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:26.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:17.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:59.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:59.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:39.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.31e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:22.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:33.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.55
p-value of test                       :  5.4e-3

-----------------------------------------------
CPU time used                    :  00:01:34.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.62
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.37
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.85
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.88
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:50.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.92
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.16
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.71
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:43.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.55
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.17
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.86
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.78
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17189.40
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.80
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.53
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.19
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.37
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.31
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.27
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.38
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.95
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.13
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.00
p-value of test                       :    0.9978


-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.88
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.15
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.83
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.77
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.54
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.99
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.84
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.47
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.93
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.65
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.33
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.39
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.55
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.15
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.81
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:36.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.33
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.24
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4861.01
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.65
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.00
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.35
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:26.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.75
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:24.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.00e-3
p-value of test                       :    0.9925

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.10
p-value of test                       :    0.02

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.72e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 9.37e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 5.58e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.45
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.01
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.34
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:06.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.15
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:08.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10028.10
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.8e-3

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10255.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:52.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4973.04
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:50.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.56
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:50.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4228.68
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4286.19
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12140.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12064.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:29.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.49
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999988313

Normal statistic for number of bits   :  -0.092
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.39
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000100201

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.90

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.09
p-value of test                       :    0.98

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:23.27

 All tests were passed




Server wird beendet - Lösche Semaphor 4096018.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:55.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5398
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:50.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:39.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:56.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:03.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:03.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:54.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:01.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    3.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:48.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.02
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:15.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.19
p-value of test                       :    0.9926

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:42.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.97
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.11
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.16
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.32
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.14
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.33
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.90
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.11
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.37
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:45.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.06
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:00.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6788.82
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:43.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.81
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.89
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:02.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.42
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.64
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:34.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4995.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:01.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46023
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870023
  j =  1                              :        399907958
  j =  2                              :            46015
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45915
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869915
  j =  1                              :        399908174
  j =  2                              :            45907
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:26.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:19.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:46.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:01.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:55.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:33.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 8.54e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 6.27e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -2.59e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:33.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   94.94
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.00
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.02
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.68
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.28
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   62.19
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.38
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:43.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.55
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.25
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.87
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17430.31
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.53
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.59
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.77
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.38
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.28
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.64
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.59
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.44
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.80
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.82
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.88
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  189.64
p-value of test                       :  8.8e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.14
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.38
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.14
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.04
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.74
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  441.81
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.27
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.18
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.09
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.33
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.46
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  317.94
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.51
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.85
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  439.02
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4829.06
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.48
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.64
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.65
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:26.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.01
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:26.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  2.8e-3

Kolmogorov-Smirnov- statistic = D-    : 2.55e-3
p-value of test                       :    0.9974

Anderson-Darling statistic = A2       :    7.10
p-value of test                       :  3.3e-4    *****

Tests on the sum of all N observations
Standardized normal statistic         :   -3.64
p-value of test                       :    0.9999    *****

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 5.42e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.65e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.77
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.54
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.76
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:08.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.51
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:08.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9775.72
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10072.44
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:45.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4852.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:48.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4789.64
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:49.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4227.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4199.11
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11871.42
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11531.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:30.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.59
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999960305

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.07
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000011893

Normal statistic for number of bits   :   0.094
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.59
p-value of test                       :    0.06

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9903

Tests on the sum of all N observations
Standardized normal statistic         :  -0.077
p-value of test                       :    0.53

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:06.02
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 83  LempelZiv, r = 15               0.9999 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5013522.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5554
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:52.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4437
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:40.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:39.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4193
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:57.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:03.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:05.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7604
p-value of test                       :  4.6e-4    *****


-----------------------------------------------
CPU time used                    :  00:03:59.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:03.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    4.29
p-value of test                       :  6.3e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     958
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.56
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    2.33
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:15.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:45.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.50
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.43
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.03
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.32
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.08
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.36
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.04
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.40
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1550.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:02.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7112.04
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:50.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.07
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   41.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:12.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.52
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.05
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:36.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5217.03
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:58.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45915
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869915
  j =  1                              :        399908173
  j =  2                              :            45909
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45615
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869615
  j =  1                              :        399908771
  j =  2                              :            45613
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:29.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:17.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:45.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:02.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:35.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.95e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:42.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.018
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:43.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.33
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.08
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.48
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.78
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.8e-3

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.43
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.53
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.04
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.59
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:43.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17475.94
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.64
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.74
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.12
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.41
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.64
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.96
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.44
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.35
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.83
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.03
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.94
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.73
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  563.08
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.60
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.24
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.98
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.46
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.01
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.79
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.53
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.35
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.77
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.27
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.52
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.28
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.48
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.85
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4836.22
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.07
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.48
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.13
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :   -0.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:23.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.26
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:26.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.80

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.87e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.21
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.62
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:07.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.94
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:09.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9890.35
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10080.91
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:09.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:04:22.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  6.9e-3

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4818.63
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:52.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4927.69
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:55.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4221.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.14
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11777.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:31.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11599.82
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:29.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.40
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000016537

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.65
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999955865

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    4.17
p-value of test                       :  7.6e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.50
p-value of test                       :  6.2e-3

Sample variance                       :    2.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         : 2.00e-4
p-value of test                       :    0.50

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:11.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:11.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:57.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 20  BirthdaySpacings, t = 16        4.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5963794.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1467
p-value of test                       :  3.1e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334587
  j =  1                              :        599997066
  j =  2                              :             1467
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5329
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:52.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:39.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:39.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:08.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:07.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7160
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:04:00.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:04:05.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.66
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:48.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.58
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     563
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    2.16
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.83
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:14.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.10
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:47.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.69
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.37
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.63
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.60
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.63
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.20
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.94
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.27
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1506.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:59.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7136.97
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:50.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.70
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.96
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:07.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.98
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  165.51
p-value of test                       :  3.1e-3


-----------------------------------------------
CPU time used                    :  00:01:35.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5153.21
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:03.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46217
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870217
  j =  1                              :        399907568
  j =  2                              :            46213
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45668
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869668
  j =  1                              :        399908666
  j =  2                              :            45664
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:29.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:19.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:02.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:36.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 5.24e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.83e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 2.54e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.85
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:23.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.011
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:46.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.56
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.46
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.25
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.10
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.73
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.19
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:28.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.052
p-value of test                       :    0.9969

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:18.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.12
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17298.51
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.75
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.58
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.30
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.14
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.45
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.65
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.42
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.28
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.97
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.87
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.19
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.80
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  438.90
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.54
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.22
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.80
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.84
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.93
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.99
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.90
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.46
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.32
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5107.45
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.80
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.10
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.19
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.10
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.47
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.66
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  160.68
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.17
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:23.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.72
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:23.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.33e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.89e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 6.97e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.50
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.13
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:05.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.72
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:07.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10184.21
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9850.50
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:04:12.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4695.12
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:53.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4992.71
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:55.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.35
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11746.64
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:30.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11789.97
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:29.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.61
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999969605

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.39
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000014884

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:10.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:38.21

 All tests were passed




Server wird beendet - Lösche Semaphor 7045138.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1480
p-value of test                       :  1.0e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334600
  j =  1                              :        599997040
  j =  2                              :             1480
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5334
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:54.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:40.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:40.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:05.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:04.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:56.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:00.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     856
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.72
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     638
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     272
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:13.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.40
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:40.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.59
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.43
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.58
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.45
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.03
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.64
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.35
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  262.81
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.59
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1433.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:05.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7013.34
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:43.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.13
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.09
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:01.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.83
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  145.48
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:31.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5166.04
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:01.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45806
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869806
  j =  1                              :        399908389
  j =  2                              :            45804
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45790
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869790
  j =  1                              :        399908424
  j =  2                              :            45782
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9961


-----------------------------------------------
CPU time used                    :  00:02:27.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 5.45e-3
p-value of test                       :    0.9936

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:18.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:45.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:58.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:33.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.22e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 6.14e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.84e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.069
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:38.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.039
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:40.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.03
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.80
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.92
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.01
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.07
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.85
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:43.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.92
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.10
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.99
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17250.49
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.54
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.40
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.35
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.71
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.67
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.82
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.45
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.73
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.28
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.63
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.89
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.87
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.54
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.31
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.45
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.92
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.70
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.73
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.85
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.50
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.48
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.77
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5089.81
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.14
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.96
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.88
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.31
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.11
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.76
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.66
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.86
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:25.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.82
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :   -1.56
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:24.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.91
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.35
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   40.00
p-value of test                       :  4.5e-3



-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:05.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.23
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:07.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9880.66
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10048.00
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:45.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.82
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:48.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:49.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.70
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.82
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11941.00
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11814.52
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:29.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.34
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000181261

Normal statistic for number of bits   :    1.43
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.94
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000004174

Normal statistic for number of bits   :   0.033
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.71
p-value of test                       :    0.04

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    1.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.45
p-value of test                       :    0.93

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:30.13

 All tests were passed




Server wird beendet - Lösche Semaphor 8126482.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5430
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:56.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:42.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:43.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:00.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:01.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:12.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:12.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:09.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:04:14.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.88
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:15.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:47.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.84
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   18.30
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.03
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.59
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:12.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.54
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.81
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.09
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.88
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.12
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:32.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.46
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:58.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1456.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:04.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7101.96
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:55.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.62
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 1.55e-3
p-value of test                       :    0.9984

Anderson-Darling statistic = A2       :    4.21
p-value of test                       :  7.6e-3

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   13.20
p-value of test                       :    0.9966

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.53
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:15.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.59
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.34
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:42.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5061.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:57.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46218
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870218
  j =  1                              :        399907569
  j =  2                              :            46208
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45484
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869484
  j =  1                              :        399909034
  j =  2                              :            45480
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:31.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:20.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:54.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.35
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:11.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:37.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.13e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:24.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:24.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:24.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:50.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.77
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.45
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.63
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.37
p-value of test                       :    0.9925

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.56
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:51.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.48
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.93
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.54
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:29.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.43
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:29.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.21
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9982

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17441.53
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.45
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.66
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.59
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.50
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.84
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.11
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.01
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.77
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.44
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.67
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.60
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.19
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.63
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.16
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.48
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.72
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.03
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.36
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.31
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.28
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.10
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.36
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.48
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.61
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.59
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.66
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.47
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5175.87
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.00
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.97
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.60
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:24.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.86
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:25.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.3e-3

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.17
p-value of test                       :    0.01

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.58e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:46.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 4.76e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.50
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.84
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.76
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:07.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.71
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:06.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9994.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9932.14
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:11.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:04:30.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4995.21
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:53.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4802.01
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:58.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.78
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4012.53
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11814.42
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:34.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11787.79
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:36.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.29
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000137122

Normal statistic for number of bits   :    1.08
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.58
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000095425

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:10.29

 All tests were passed




Server wird beendet - Lösche Semaphor 9109522.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:51.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1263
p-value of test                       :    0.9971

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334383
  j =  1                              :        599997474
  j =  2                              :             1263
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5358
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:59.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:42.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:43.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:00.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:12.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7476
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:10.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:15.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.78
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    2.25
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.06
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:14.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.85
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:44.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.13
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.41
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.37
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.59
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:13.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.77
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.65
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.94
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.35
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.51
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.60
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:58.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1381.66
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:03.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6823.56
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:53.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.72
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:09.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.22
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:47.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.92
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:40.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4900.99
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:28.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  3.8e-3


-----------------------------------------------
CPU time used                    :  00:02:55.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45769
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869769
  j =  1                              :        399908464
  j =  2                              :            45765
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46292
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870292
  j =  1                              :        399907421
  j =  2                              :            46282
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:30.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 2.96e-3
p-value of test                       :    0.9968

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9917


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:23.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:53.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:06.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:57.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:38.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 6.34e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:24.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:51.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:52.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.01
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.17
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.13
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.42
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:50.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.73
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.38
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.75
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:50.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.13
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.28
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.34
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.13
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.50
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17102.33
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.68
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.78
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.50
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.44
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.53
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.68
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.32
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.92
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.56
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.18
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.68
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.33
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.89
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  175.79
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  106.95
p-value of test                       :  7.4e-3


-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.54
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.41
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.18
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.99
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.33
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.35
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.45
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.28
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.71
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.95
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.34
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.47
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5144.69
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.44
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.44
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.29
p-value of test                       :    0.9931


-----------------------------------------------
Normal statistic for number of jumps  :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:24.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.38
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :    2.94
p-value of test                       :  1.7e-3



-----------------------------------------------
CPU time used                    :  00:02:26.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.37e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:46.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.69e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.05
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.95
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.24
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:11.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:06.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9647.84
p-value of test                       :    0.9941

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10149.67
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:04:38.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.29
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:51.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5022.74
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:56.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4201.64
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4057.80
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11648.01
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:32.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11650.24
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:35.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.38
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999979931

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.87
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999930428

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.16
p-value of test                       :    0.98

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   0.060
p-value of test                       :    0.48

Sample variance                       :    0.22
p-value of test                       :    0.9923

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:44.45

 All tests were passed




Server wird beendet - Lösche Semaphor 10354706.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:59.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:44.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:01.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:02.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7186
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:13.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7186
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:12.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:10.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:15.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.15
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    3.91
p-value of test                       :  9.6e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     956
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    3.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:15.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    3.29
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:45.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.59
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.18
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.82
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.18
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.43
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.11
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.39
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.07
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:29.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:53.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1397.72
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:57.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7194.42
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.07
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.21
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:14.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.51
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.62
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:43.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5080.56
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:01.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45784
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869784
  j =  1                              :        399908433
  j =  2                              :            45782
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45805
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869805
  j =  1                              :        399908397
  j =  2                              :            45791
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:31.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:21.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9973


-----------------------------------------------
CPU time used                    :  00:01:54.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 7.82e-3
p-value of test                       :    0.9909

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:10.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:39.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.06e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 3.33e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:24.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:44.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:49.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.63
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.72
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.64
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.85
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.83
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:51.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.68
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.4e-3

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.01
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.96
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.46
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17354.77
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.62
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.65
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.82
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.00
p-value of test                       :    0.9945


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.52
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.59
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.27
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.24
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.73
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.99
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.63
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.24
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.97
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.74
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.63
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.69
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.58
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.85
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.34
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.73
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.78
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.42
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5096.66
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.36
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.03
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:36.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.40
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.67
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5256.56
p-value of test                       :  5.7e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.05
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.04
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.03
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :    2.16
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:25.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.62
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :    0.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:23.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.45
p-value of test                       :    0.93

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.32e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 9.74e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.50e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.75
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.85
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.60
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:05.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.87
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:06.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10104.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9833.51
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:10.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.090
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:04:29.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.26
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.05
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:59.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.34
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4013.56
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11955.31
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:36.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11823.72
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:38.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.89
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999999821

Normal statistic for number of bits   : -1.42e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.05
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000003130

Normal statistic for number of bits   :   0.025
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.70
p-value of test                       :    0.04

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    2.66
p-value of test                       :  4.3e-3

-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:53.51

 All tests were passed




Server wird beendet - Lösche Semaphor 11534354.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1267
p-value of test                       :    0.9959

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334387
  j =  1                              :        599997466
  j =  2                              :             1267
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5301
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:56.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:42.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:58.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:06.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:06.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:55.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:01.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    3.62
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    2.42
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:14.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    2.59
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:40.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.38
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.87
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.59
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.70
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.22
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.36
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.52
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.42
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:42.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1343.98
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:00.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6999.15
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:41.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.05
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:02.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   15.02
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.77
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:35.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5257.61
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:02.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46059
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870059
  j =  1                              :        399907884
  j =  2                              :            46055
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45883
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869883
  j =  1                              :        399908240
  j =  2                              :            45871
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:29.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:19.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:00.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:57.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:35.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 4.95e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:34.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:36.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.64
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.87
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.58
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.51
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.64
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.74
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:42.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.36
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.22
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.50
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.39
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17379.79
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.24
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.99
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.25
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.00
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.05
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.54
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.73
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.12
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.78
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.49
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.99
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.71
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  567.44
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.33
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.41
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.90
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.52
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.48
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.24
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.13
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.21
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.59
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.40
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.47
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  153.83
p-value of test                       :    0.9934


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.92
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.00
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4866.30
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.45
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.57
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.95
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:22.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.70
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :   -1.70
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:23.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.092
p-value of test                       :    0.46

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 4.25e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 4.46e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.05
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.61
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.83
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:05.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:05.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10015.42
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9857.03
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:38.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9906

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.57
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4889.57
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:50.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4272.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11771.43
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11742.79
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.02
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999925208

Normal statistic for number of bits   :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   31.37
p-value of test                       :    0.9942


-----------------------------------------------
Total number of bits:  7999862973

Normal statistic for number of bits   :   -1.08
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.07
p-value of test                       :    0.98

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   0.057
p-value of test                       :    0.48

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :  -0.056
p-value of test                       :    0.52

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:49.15

 All tests were passed




Server wird beendet - Lösche Semaphor 12615698.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:49.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5431
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:57.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:43.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:59.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:01.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:09.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:09.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:04:05.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:04:07.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    3.90
p-value of test                       :  9.7e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     835
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    3.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:03.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    2.43
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     654
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.94
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:15.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:45.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.71
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.14
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.62
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.88
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.02
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.75
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.53
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  274.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.34
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:51.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1412.62
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6896.32
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:50.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.81
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.46
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:09.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.49
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.57
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:37.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5102.05
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:04.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45959
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869959
  j =  1                              :        399908085
  j =  2                              :            45953
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45914
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869914
  j =  1                              :        399908175
  j =  2                              :            45908
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:33.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:20.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:05.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:01:56.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:36.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.90e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 9.64e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.021
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:46.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.15
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:50.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.69
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.42
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.72
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.34
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.98
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.57
p-value of test                       :  5.9e-4    *****

Anderson-Darling statistic = A2       :    5.04
p-value of test                       :  2.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   66.15
p-value of test                       :  5.8e-3

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.73
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.23
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.88
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17423.31
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.86
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.63
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.45
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.08
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.82
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.17
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.38
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.93
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.04
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.84
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.23
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.17
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.49
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.17
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.38
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.07
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.24
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.18
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.06
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.74
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.99
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  442.33
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5071.19
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.94
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.07
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.31
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.76
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4861.05
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.46
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.29
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.89
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :   -1.42
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:23.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.96
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:23.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 6.36e-3
p-value of test                       :    0.9933

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.78
p-value of test                       :    0.96

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.70e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:46.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.80e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.60
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.74
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.45
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:04.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.70
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:05.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9871.30
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9883.59
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:04:19.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4813.24
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:51.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4761.82
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:53.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.78
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.22
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11780.34
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11771.69
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:31.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.37
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000168274

Normal statistic for number of bits   :    1.33
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.16
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000000289

Normal statistic for number of bits   : 2.28e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    0.22
p-value of test                       :    0.9917

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:17.20

 All tests were passed




Server wird beendet - Lösche Semaphor 13664274.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:49.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5342
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:57.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:41.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4434
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:57.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:58.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7174
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:06.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:06.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:55.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7161
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:04:01.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.38
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9951


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     633
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.03
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.14
p-value of test                       :    0.9990

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:13.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:44.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.52
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.12
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.04
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.63
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.20
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.48
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.08
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.68
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:06.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7287.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.03
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:02.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.48
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.94
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:33.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4994.86
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:00.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45668
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869668
  j =  1                              :        399908667
  j =  2                              :            45662
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45665
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869665
  j =  1                              :        399908673
  j =  2                              :            45659
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:28.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:17.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:44.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:58.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:35.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 5.76e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.98e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 3.04e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:22.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:40.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.75
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.09
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.29
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.70
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.90
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.26
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.54
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.35
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.27
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.12
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17350.85
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.35
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.10
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.25
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.54
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.64
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.96
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.12
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.33
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.58
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.49
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.81
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.58
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  448.58
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.48
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.04
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.76
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.31
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  452.11
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.03
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.46
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.34
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.88
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4814.05
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.33
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.39
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.32
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.97
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4850.39
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.26
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.34
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.88
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:22.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.51
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:22.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.55e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 6.61e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.95
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.39
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.64
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:04.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.56
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:06.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9949.05
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9896.71
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.096
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:37.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.23
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:47.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.41
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4231.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:18.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4395.89
p-value of test                       :  1.3e-3

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11864.67
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:28.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11994.29
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.69
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999926237

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.17
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999981935

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:39.55

 All tests were passed




Server wird beendet - Lösche Semaphor 14712850.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1469
p-value of test                       :  2.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334589
  j =  1                              :        599997062
  j =  2                              :             1469
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5358
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:56.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:41.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4427
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:58.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:06.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:06.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:56.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:01.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.32
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.00
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    2.70
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     656
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.78
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:14.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:42.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.75
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.27
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.31
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.19
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:11.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.43
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.63
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.42
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:44.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1467.88
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7041.72
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:42.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.23
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:02.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.95
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.26
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:33.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5034.04
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:58.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46305
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870305
  j =  1                              :        399907394
  j =  2                              :            46297
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45898
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869898
  j =  1                              :        399908204
  j =  2                              :            45898
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:28.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :  7.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    6.41
p-value of test                       :  6.6e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9995    *****


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:18.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:43.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:58.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:56.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:35.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.56e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.95e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:35.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:35.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.05
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.27
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.15
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.55
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.96
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:42.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.44
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.50
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.19
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.6e-3

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  103.87
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17322.26
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.47
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.38
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.17
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.47
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.26
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.42
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.09
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.33
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.08
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.89
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.63
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.35
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.01
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.35
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.54
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.75
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.71
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.54
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.67
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.80
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.54
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.86
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4916.67
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.95
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.80
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.97
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.95
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5075.82
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.01
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.12
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.24
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :    0.99
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:22.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.86
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:22.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 7.87e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.04e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.39
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.67
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.34
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:06.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  239.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:07.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10077.98
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10092.11
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:54.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:35.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.41
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:46.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  6.9e-3

Anderson-Darling statistic = A2       :    3.54
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5099.78
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.81
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11736.08
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12028.71
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.34
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999926891

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.28
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000012022

Normal statistic for number of bits   :   0.095
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 5.06e-3
p-value of test                       :    0.9947

Anderson-Darling statistic = A2       :    3.72
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.81
p-value of test                       :    0.9975

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:12.15
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 47  MaxOft, t = 16                  0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15728658.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5485
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:56.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4489
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:42.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:58.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:06.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:06.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:56.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:04:01.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.64
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    2.26
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    3.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     561
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.72
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.19
p-value of test                       :    0.9920

-----------------------------------------------
CPU time used                    :  00:02:15.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    2.79
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:46.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.02
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.98
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.80
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.60
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.78
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.75
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  196.50
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:43.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1407.72
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:00.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7347.15
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.01
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:01.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.74
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.34
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:33.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4909.53
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:02.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45554
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869554
  j =  1                              :        399908895
  j =  2                              :            45548
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46075
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870075
  j =  1                              :        399907853
  j =  2                              :            46069
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:28.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:19.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:44.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:58.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:37.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.12e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.48e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 9.39e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:37.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:35.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.56
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.11
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.82
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.25
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.79
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.82
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.46
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:41.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.53
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.17
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.53
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17337.97
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   56.81
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.46
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.57
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.50
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.88
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.51
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.43
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.77
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.76
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.94
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.23
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.49
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.43
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.76
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.69
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.33
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.46
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.73
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.26
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  100.24
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  457.28
p-value of test                       :  5.9e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.95
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4991.46
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.41
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.82
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.34
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.92
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4859.25
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.27
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.69
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.10
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:23.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.01
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:24.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.80

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.15e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.41e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 9.60e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.88
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.53
p-value of test                       :    0.9922

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 2.64e-3
p-value of test                       :    0.9973

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  157.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:05.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.69
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:07.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 6.73e-5
p-value of test                       : 1 -  6.7e-5    *****

Anderson-Darling statistic = A2       :    4.57
p-value of test                       :  4.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9545.10
p-value of test                       :    0.9994    *****

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10117.27
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:40.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.86
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:47.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4982.35
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:49.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.58
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.58
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11874.40
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11680.22
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.08
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000169999

Normal statistic for number of bits   :    1.34
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.17
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999860366

Normal statistic for number of bits   :   -1.10
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.01
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    3.48
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -1.97
p-value of test                       :    0.98

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:57.90
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 90  HammingWeight2, r = 0           0.9994 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16777234.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5348
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:55.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:58.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:06.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:05.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:56.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:04:00.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:49.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.19
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:16.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:46.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.63
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.23
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.27
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.06
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.75
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.21
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.20
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  366.16
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:01:42.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.48
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:01.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7022.38
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:41.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.11
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:02.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.96
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.86
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:34.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5137.39
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9918


-----------------------------------------------
CPU time used                    :  00:03:00.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45713
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869713
  j =  1                              :        399908577
  j =  2                              :            45707
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46015
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870015
  j =  1                              :        399907975
  j =  2                              :            46005
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:28.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:18.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:46.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.95e-3
p-value of test                       :    0.9933

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:37.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.55e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 3.04e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.02e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:22.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:22.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:37.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:39.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:49.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.50
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.91
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.85
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.74
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.68
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.86
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:40.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.26
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.70
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.30
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17390.97
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.26
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.24
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   44.40
p-value of test                       :  9.8e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.39
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.86
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.52
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.76
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.21
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.92
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.25
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.52
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.56
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.30
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.07
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.54
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.48
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.58
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.26
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.02
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.03
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.27
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.86
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5201.39
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.42
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.97
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.86
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.56
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.65
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  432.49
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  252.65
p-value of test                       :  6.9e-3


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.06
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:21.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.16
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -1.35
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:23.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.80
p-value of test                       :    0.96

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.24e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 3.02e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.04
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.51
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.04
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:05.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.86
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:06.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10033.20
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9933.36
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:37.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5031.22
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:46.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.52
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:49.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.02
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.23
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11748.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11658.03
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.08
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000064120

Normal statistic for number of bits   :    0.51
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.38
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000096766

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.35

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :  -0.050
p-value of test                       :    0.52

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:24.28

 All tests were passed




Server wird beendet - Lösche Semaphor 17825810.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5404
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:56.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:42.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4563
p-value of test                       :  3.4e-4    *****


-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:58.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:07.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7464
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:06.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:55.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7479
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:01.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    3.32
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     825
p-value of test                       :    0.9940

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    4.93
p-value of test                       :  3.1e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     531
p-value of test                       :    0.9978

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:15.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:46.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.65
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.51
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.48
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.79
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.45
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.84
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.28
p-value of test                       :    0.9917

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.45
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.36
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:42.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1479.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:01.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7150.24
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.81
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.60
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:01.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.98
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  147.59
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:34.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5050.59
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:57.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45583
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869583
  j =  1                              :        399908836
  j =  2                              :            45579
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45592
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869592
  j =  1                              :        399908822
  j =  2                              :            45580
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:28.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:18.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:00.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:36.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 9.34e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.98e-4
p-value of test                       :  1.8e-3

Kolmogorov-Smirnov- statistic = D-    : 3.49e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.56
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:37.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:37.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.94
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.92
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.89
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.72
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.10
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.85
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:42.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.09
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.09
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.37
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.69
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 7.78e-3
p-value of test                       :    0.9917

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   98.94
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17554.20
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.62
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.81
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.47
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.44
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.04
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.19
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.47
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.05
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.74
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.32
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.57
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.48
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  550.33
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.97
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.41
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.45
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.57
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.39
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.62
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.67
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.62
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.17
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.68
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.12
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.50
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.85
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.48
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5064.50
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.48
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.42
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   34.13
p-value of test                       :  6.4e-4    *****


-----------------------------------------------
Normal statistic for number of jumps  :    1.88
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:24.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.04
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:22.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.57
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.78
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.65
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:05.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.31
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:06.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9847.49
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9987.45
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:55.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:35.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4741.97
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:45.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.92
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:49.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.68
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4148.67
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11685.75
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11851.82
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:29.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.55
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000102673

Normal statistic for number of bits   :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.36
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000023644

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:19.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 16  BirthdaySpacings, t = 7         3.4e-4
 80  LinearComp, r = 0               6.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18841618.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:39.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:49.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5445
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:57.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:42.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:57.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:58.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:06.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:06.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:57.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:01.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.43
p-value of test                       :  5.6e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    2.31
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:14.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:44.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.99
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.42
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.79
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.40
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.73
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.37
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.26
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.57
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.45
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:42.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1509.61
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:00.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7189.56
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.49
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.86
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:03.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.79
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.00
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:32.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5012.46
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:00.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45715
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869715
  j =  1                              :        399908571
  j =  2                              :            45713
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45989
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869989
  j =  1                              :        399908023
  j =  2                              :            45987
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:29.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:17.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  6.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.45
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:44.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:58.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9994    *****

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:36.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 7.61e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.27e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:35.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:38.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.66
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.52
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.61
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.51
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.58
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.10
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:41.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.07
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.81
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.15
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.97
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 2.68e-3
p-value of test                       :    0.9973

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17071.70
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.02
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.77
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.93
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.04
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.01
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.37
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.99
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.48
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.25
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.36
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.94
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.11
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.34
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.00
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.41
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.07
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.43
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.34
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.90
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.69
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.06
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.05
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4942.31
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  318.65
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.78
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.50
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.51
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4909.34
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.34
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.34
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:23.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.83
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :   -1.19
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:22.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.17e-3
p-value of test                       :    0.9978

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.52
p-value of test                       :  5.8e-3

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 7.26e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.29e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 8.38e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.88
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.30
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.52
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:05.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.25
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:04.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9881.28
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10056.24
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:40.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4723.49
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:47.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4779.24
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:48.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.54
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11741.99
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11874.22
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.15
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999969695

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.49
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000050242

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:10.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 50  SampleProd, t = 8               0.9994 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19824658.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:48.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1234
p-value of test                       :    0.9998    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334354
  j =  1                              :        599997532
  j =  2                              :             1234
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1261
p-value of test                       :    0.9975

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334381
  j =  1                              :        599997478
  j =  2                              :             1261
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5386
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:59.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:43.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7198
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:45.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:01.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4221
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:02.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:13.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:12.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:04:09.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:04:10.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    3.80
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:49.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:15.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:44.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.18
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.40
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.58
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.30
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.07
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.19
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.23
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.02
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  280.48
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.44
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:55.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.16
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:05.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7086.04
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:55.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.76
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9961

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.68
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:15.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.20
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:37.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4912.05
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:59.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46033
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870033
  j =  1                              :        399907936
  j =  2                              :            46029
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45754
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869754
  j =  1                              :        399908497
  j =  2                              :            45744
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:33.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 7.84e-3
p-value of test                       :    0.9902

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:21.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:53.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:08.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:58.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:37.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 7.32e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 3.12e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:24.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:46.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.56
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.65
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.21
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.20
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:43.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.47
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.93
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.12
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.27
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17493.73
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:48.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.13
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.91
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.37
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.11
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.94
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.80
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.23
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.65
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.57
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.46
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.48
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.68
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.69
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.04
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.08
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:40.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.12
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.45
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.26
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.59
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.93
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:40.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.12
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.95
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.51
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.31
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.77
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:32.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.62
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.53
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5187.61
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.16
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.14
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:32.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.39
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :   -0.10
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:11.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.48
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:11.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.20

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.55e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:40.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.67
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.68
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.99
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:54.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:54.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9949.41
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10136.32
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:17.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4946.36
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:43.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4995.43
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3953.34
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:15.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.98
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11861.75
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11852.92
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.49
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999886613

Normal statistic for number of bits   :   -0.90
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.89
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000009325

Normal statistic for number of bits   :   0.074
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:18.77
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  7  CollisionOver, t = 7            0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 20873234.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:19.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:21.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:17.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5424
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:43.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:36.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:35.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:55.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:01.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:01.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:55.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7485
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:00.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.73
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:52.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.63
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.28
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.46
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    3.52
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     271
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:13.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     173
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9926

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:33.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.56
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.53
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.23
p-value of test                       :    0.9952

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.74
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.60
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.69
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.78
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.87
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  499.65
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:47.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1476.16
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:03.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6815.46
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:45.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.17
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.64
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   87.94
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:03:01.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.03
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.08
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:35.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4967.93
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:15.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:11.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46118
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870118
  j =  1                              :        399907768
  j =  2                              :            46110
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46029
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870029
  j =  1                              :        399907944
  j =  2                              :            46025
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:30.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:18.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:45.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:59.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:53.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:34.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.71e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:22.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 2.43e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:38.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.09
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:49.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.63
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.88
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.45
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:49.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.08
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.75
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:41.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.93
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.14
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:31.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:32.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.89
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17557.70
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.47
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.11
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.13
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.10
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.10
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.35
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   65.93
p-value of test                       :  1.2e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.40
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.99
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.19
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.24
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.02
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.97
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.75
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.72
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:46.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.24
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.58
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.25
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.79
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.78
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.50
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.14
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4889.94
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.41
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.53
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.37
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.55
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.70
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.94
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.80
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.83
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:27.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.25
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:19.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:43.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.55e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.53
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.51
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.38
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:10.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.32
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:10.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10051.27
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10138.85
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:47.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4918.46
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4757.07
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:50.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.71
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.97
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11701.58
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11673.09
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:30.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.53
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999946424

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.85
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000000031

Normal statistic for number of bits   : 2.45e-4
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :  -0.055
p-value of test                       :    0.52

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:29.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:18:01.72

 All tests were passed




Server wird beendet - Lösche Semaphor 753683.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5474
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:42.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:36.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:34.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:55.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:55.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:01.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7456
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:00.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:52.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:58.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.14
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:46.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.86
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    3.58
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.80
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    2.60
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:11.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.26
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:41.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.82
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.34
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.67
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.14
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.34
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.17
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  194.88
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.86
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1494.56
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:02.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6927.60
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:44.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.34
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.06
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:00.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.63
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.11
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:33.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5162.90
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:04.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46003
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870003
  j =  1                              :        399907998
  j =  2                              :            45995
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45720
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869720
  j =  1                              :        399908565
  j =  2                              :            45710
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:11.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 2.82e-3
p-value of test                       :    0.9968

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:32.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:19.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:46.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:00.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:54.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:34.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.08e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.05e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 7.24e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:22.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.084
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:31.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:34.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.87
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.51
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.68
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:48.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.30
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.52
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:38.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.93
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:10.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.05
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17473.41
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.77
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.36
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.85
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.65
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.15
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:39.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.22
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.08
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.93
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.55
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.86
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.84
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  188.54
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.22
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.30
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.76
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:46.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.97
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.72
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.07
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.46
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.55
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.48
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.12
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.98
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  326.48
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  255.50
p-value of test                       :  4.9e-3


-----------------------------------------------
CPU time used                    :  00:00:36.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.88
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.27
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.85
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.69
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.61
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.97
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:26.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.35
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   -0.63
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:25.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.36e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 7.65e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.57
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.25
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.69
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:08.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.96
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:11.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10015.21
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.78
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:57.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4913.00
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:48.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5025.97
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4205.88
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4037.27
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11754.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11763.57
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:28.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.07
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000067423

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.62
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000011428

Normal statistic for number of bits   :   0.090
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    2.46
p-value of test                       :  8.4e-3

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:29.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.87
p-value of test                       :    0.03

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:21.59

 All tests were passed




Server wird beendet - Lösche Semaphor 1310739.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1461
p-value of test                       :  4.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334581
  j =  1                              :        599997078
  j =  2                              :             1461
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5450
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:42.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:36.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:36.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:55.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4491
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:02.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:03.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:53.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:04:00.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     566
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    3.27
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:13.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    2.68
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:43.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.02
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.96
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.36
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.71
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:10.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.70
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.40
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.87
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.00
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.31
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1502.11
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:01.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7006.01
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:42.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.01
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.74
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:00.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.25
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.17
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:33.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5190.58
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:04.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45841
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869841
  j =  1                              :        399908320
  j =  2                              :            45837
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45670
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869670
  j =  1                              :        399908664
  j =  2                              :            45662
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:32.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:19.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:43.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:58.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:56.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 8.76e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 5.38e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:22.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:31.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.44
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.22
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.39
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.54
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.68
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.87
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:39.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.05
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.97
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.16
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17629.37
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.34
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.25
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.21
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.66
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:39.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.96
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.44
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.28
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.02
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.40
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.10
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.70
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.15
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.28
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.12
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.08
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.94
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.28
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.58
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.71
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.06
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.87
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.91
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.81
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.25
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.72
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.11
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4823.49
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.31
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.12
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.07
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:24.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.63
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:23.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.40

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.66
p-value of test                       :    0.05

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.32e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:47.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.84
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.55
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.85
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:07.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:08.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10022.91
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10139.19
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:48.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4801.26
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:48.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4821.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:50.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4027.72
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4209.35
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11880.27
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11997.36
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:30.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.24
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999955391

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.28
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000063628

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   0.070
p-value of test                       :    0.47

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:22.29

 All tests were passed




Server wird beendet - Lösche Semaphor 2359315.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:39.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5384
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:48.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:37.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:36.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:54.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:56.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:02.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:02.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7487
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:54.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:57.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:45.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:12.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.72
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    5.11
p-value of test                       :  2.6e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     187
p-value of test                       :  2.0e-3

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:39.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.05
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.29
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.78
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.69
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.56
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.76
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.21
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.52
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.33
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:06.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7093.68
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.23
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:08.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.87
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.73
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:37.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4938.27
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:59.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45883
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869883
  j =  1                              :        399908237
  j =  2                              :            45877
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45806
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869806
  j =  1                              :        399908391
  j =  2                              :            45800
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:32.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9920

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:19.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:46.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:04.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:36.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 6.69e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.32e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 2.72e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.085
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:39.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 3.98e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:40.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.58
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.00
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.84
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.79
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.53
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.51
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.13
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:45.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.73
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.01
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.74
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:29.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.51
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  163.70
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17211.02
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.41
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   58.19
p-value of test                       :  8.2e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.11
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.74
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.05
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.26
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.40
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.85
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.32
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.60
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.48
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.87
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.72
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.49
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.25
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.46
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.95
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.78
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.67
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.29
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5077.84
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.39
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  155.09
p-value of test                       :    0.9919


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.16
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.09
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4845.78
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.19
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.46
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.67
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :  -0.100
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:26.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.03
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:23.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.59e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 9.50e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.05e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 9.04e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.77
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.14
p-value of test                       :    0.9972

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.32
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:07.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.12
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:09.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9802.58
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9792.79
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:04:23.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4759.14
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:52.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.78
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:54.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4196.06
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4036.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11723.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:34.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11979.94
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:32.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.06
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999982412

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.88
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000026218

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   0.063
p-value of test                       :    0.47

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:06.30

 All tests were passed




Server wird beendet - Lösche Semaphor 3407891.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1231
p-value of test                       :    0.9999    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334351
  j =  1                              :        599997538
  j =  2                              :             1231
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5422
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:50.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4203
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7524
p-value of test                       :  8.5e-3


-----------------------------------------------
CPU time used                    :  00:02:38.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:55.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4483
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:03.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:03.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:54.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:59.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:47.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.68
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9902

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:12.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.07
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.76
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.18
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.33
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:10.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.81
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.31
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.98
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.62
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.27
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:45.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1355.42
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:00.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7154.55
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:43.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.63
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.44
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:00.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.36
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.09
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:33.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4949.53
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:02.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45859
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869859
  j =  1                              :        399908284
  j =  2                              :            45855
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45688
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869688
  j =  1                              :        399908625
  j =  2                              :            45686
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:29.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:19.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:47.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:02.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:54.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:33.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.072
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:31.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:34.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.92
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:49.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.78
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.04
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.42
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:48.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.45
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.51
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:37.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.27
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.60
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.46
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:28.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.22
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:28.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.98
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17333.16
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.29
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.81
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.76
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.48
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.04
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   63.23
p-value of test                       :  3.3e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.94
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.25
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.59
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.32
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.23
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.28
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.28
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.61
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.00
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.67
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.36
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.15
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.14
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.73
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.70
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.57
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5187.49
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  328.09
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.83
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.47
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.88
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5118.85
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.14
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.55
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.76
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :    1.23
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:25.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.55
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :   -2.15
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:24.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.69
p-value of test                       :    0.95

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.63e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.20e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.08
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.77
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.06
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:07.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.46
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:08.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9925.21
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10213.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:44.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4929.63
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4978.19
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:49.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3988.14
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4258.92
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11961.71
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11875.21
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:29.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.51
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999919940

Normal statistic for number of bits   :   -0.63
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.74
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999892784

Normal statistic for number of bits   :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.88

Sample variance                       :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.65
p-value of test                       :    0.05

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:04.32
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           0.9999 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4718611.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1270
p-value of test                       :    0.9948

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334390
  j =  1                              :        599997460
  j =  2                              :             1270
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:52.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:39.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:38.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:57.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:03.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:03.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:53.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7079
p-value of test                       :    0.9975


-----------------------------------------------
CPU time used                    :  00:03:59.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.82
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     946
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.57
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:13.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.53
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.86
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:35.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.65
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.66
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   42.56
p-value of test                       :  9.2e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.79
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.53
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.54
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.25
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.06
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.40
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:43.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1445.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:01.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6764.13
p-value of test                       :    0.9918

-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.87
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.37
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:02.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.12
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.24
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:34.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4986.34
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:56.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45960
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869960
  j =  1                              :        399908082
  j =  2                              :            45956
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46153
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870153
  j =  1                              :        399907700
  j =  2                              :            46141
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:29.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:17.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:44.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:59.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:32.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:33.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:34.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.65
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.82
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.62
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:48.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.93
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.00
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:39.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.88
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.39
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.81
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.81
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17287.11
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.99
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.67
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.02
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.99
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.81
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.62
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.99
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.63
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.06
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.70
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.72
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.16
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.45
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.37
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.76
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.85
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.00
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.12
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.68
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.02
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.81
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.42
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4879.06
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.97
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.56
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:36.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.39
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.56
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4978.29
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.90
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.17
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.26
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  :    2.45
p-value of test                       :  7.1e-3



-----------------------------------------------
CPU time used                    :  00:02:26.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.99
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :   -1.38
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:24.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 2.47e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.51e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 9.08e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.84
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.69
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.54
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:05.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.74
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:09.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10196.50
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9812.24
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:46.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.85
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:48.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.31
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:50.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4048.85
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.66
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11912.38
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11592.32
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.53
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999959072

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.03
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999781283

Normal statistic for number of bits   :   -1.73
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.73
p-value of test                       :    0.96

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:10.97
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 29  SimpPoker, r = 25               9.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5603347.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5422
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:54.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:40.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:40.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:57.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7168
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:05.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:04.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:53.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:59.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    2.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.95
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.18
p-value of test                       :    0.9949

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:15.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.75
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:44.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.40
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.77
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.19
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.67
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.44
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.46
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.35
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:44.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1533.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6986.95
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.85
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:00.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.02
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.12
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:31.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4886.01
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:01.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45570
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869570
  j =  1                              :        399908863
  j =  2                              :            45564
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45672
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869672
  j =  1                              :        399908662
  j =  2                              :            45660
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:28.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:18.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:44.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:58.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:35.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.73e-7
p-value of test                       : 1 -  3.1e-5    *****

Kolmogorov-Smirnov- statistic = D-    : 3.01e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.79
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:21.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.063
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:21.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:32.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:33.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.51
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:48.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.32
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.13
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.14
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.80
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.27
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.89
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:38.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.91
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.34
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.08
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.46
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:38.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17460.69
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.78
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   56.78
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.23
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.06
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.55
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:37.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.90
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.55
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.11
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.99
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.93
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.19
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.37
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.77
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.93
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.13
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.83
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.41
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  563.18
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.51
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.17
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.23
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.73
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.72
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.23
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.06
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.25
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.95
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4893.10
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.89
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.76
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.82
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:24.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.74
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:24.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
p-value of test                       :    0.9929

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 6.28e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 6.94e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.56
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.65
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.88
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:04.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.19
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:05.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10299.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9875.29
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.54
p-value of test                       :  5.5e-3

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:42.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5035.06
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.40
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:48.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3953.40
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.38
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11963.29
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11973.60
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.26
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999798392

Normal statistic for number of bits   :   -1.59
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.59
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999915422

Normal statistic for number of bits   :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.72
p-value of test                       :    0.04

Sample variance                       :    2.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:21.87

 All tests were passed




Server wird beendet - Lösche Semaphor 6619155.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5446
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:58.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4442
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:42.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4193
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:57.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:58.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:07.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:06.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7191
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:58.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:01.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.98
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     952
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    2.17
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    3.87
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     263
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:15.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.71
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.25
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   34.38
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.80
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.71
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.87
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.31
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  263.67
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.34
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1409.74
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:04.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7058.88
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:48.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.11
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.68
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:08.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.07
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.64
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4996.07
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:57.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45679
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869679
  j =  1                              :        399908647
  j =  2                              :            45669
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45623
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869623
  j =  1                              :        399908757
  j =  2                              :            45617
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:29.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:18.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:47.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:02.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 8.06e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 3.54e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:37.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:39.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.29
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.23
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:55.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.77
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.90
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.92
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:46.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.5e-3

Anderson-Darling statistic = A2       :    3.43
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   62.13
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.84
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.03
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  158.19
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17565.17
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.96
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.33
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.61
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.71
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.49
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.62
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.85
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.40
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.81
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.09
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.58
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.40
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.23
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.85
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.66
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.55
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.07
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.45
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.99
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.48
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.89
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.84
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.64
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.71
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.37
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.89
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.93
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5101.86
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.35
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.47
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.24
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :   -1.27
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:24.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.54
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :   -0.96
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:23.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 9.06e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.62
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.56
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.95
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:05.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.23
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:06.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9911.92
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10114.11
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:04:12.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4799.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:52.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.10
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:53.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.24
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.96
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11784.92
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:30.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11729.26
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:31.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.72
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000067570

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.32
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000010399

Normal statistic for number of bits   :   0.082
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.61
p-value of test                       :  4.6e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.71
p-value of test                       :    0.9966

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:11.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:12.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:19.43

 All tests were passed




Server wird beendet - Lösche Semaphor 7602195.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5461
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:59.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:45.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:00.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:01.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:12.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:12.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:08.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:13.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:47.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:11.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    4.24
p-value of test                       :  6.7e-3

Stat. AD after spacings (mNP2-S)      :    3.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:42.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.99
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.64
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.15
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.11
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.03
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.38
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:29.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.18
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:57.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1441.43
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:08.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7059.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:58.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.66
p-value of test                       :  6.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.48
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   14.27
p-value of test                       :    0.9932

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.29
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:13.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.54
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.50
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4932.19
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:55.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45866
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869866
  j =  1                              :        399908274
  j =  2                              :            45854
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46219
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870219
  j =  1                              :        399907563
  j =  2                              :            46217
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.20e-3
p-value of test                       :    0.9905

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:30.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:23.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:52.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:09.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:38.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.00e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:24.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:24.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:42.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:41.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.14
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.64
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.04
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.73
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.31
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.37
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:52.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.96
p-value of test                       :  9.5e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   61.50
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.11
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.30
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:28.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.85
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  156.95
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17408.87
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.89
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.12
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.58
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.62
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.47
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.60
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.01
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.47
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.94
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.67
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.97
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.48
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.06
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.96
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.90
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.54
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.46
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.11
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.69
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.68
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.97
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.82
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4960.38
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.63
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.92
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.94
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.59
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.12
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  304.26
p-value of test                       :    0.9978


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.74
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.12
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:23.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.73
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :    1.73
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:22.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.66
p-value of test                       :    0.95

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 7.02e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 9.66e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.44
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.70
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.20
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:20.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.69
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:10.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9810.96
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10090.41
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:12.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.054
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:04:35.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5047.64
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:52.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4754.30
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.40
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3984.17
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11867.16
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:32.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12098.19
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:35.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   29.36
p-value of test                       :    0.9975


-----------------------------------------------
Total number of bits:  7999845564

Normal statistic for number of bits   :   -1.22
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.26
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000063475

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:10.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:35.93

 All tests were passed




Server wird beendet - Lösche Semaphor 8683539.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:40.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5379
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:54.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:05.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:05.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:55.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:59.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    2.42
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:47.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    2.49
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     656
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    4.98
p-value of test                       :  2.9e-3

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.57
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.74
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:13.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:41.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.30
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.80
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.09
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.52
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.47
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.68
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.44
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  389.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:43.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1443.26
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:02.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7178.97
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.54
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:03.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.73
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.29
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:32.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5068.41
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:12.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:54.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45823
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869823
  j =  1                              :        399908357
  j =  2                              :            45817
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46142
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870142
  j =  1                              :        399907719
  j =  2                              :            46136
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:28.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:17.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:44.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:58.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:35.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:21.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:33.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:35.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.86
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.00
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.41
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.86
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.80
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:44.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.07
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.05
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.41
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.21
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 2.64e-3
p-value of test                       :    0.9973

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  102.96
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17489.37
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.73
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.05
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.45
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.10
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.52
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.55
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   55.94
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.22
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.78
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.43
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.38
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.29
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.64
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.83
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.85
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.11
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.13
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.53
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.31
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.43
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.50
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.25
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.73
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.39
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.44
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.98
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.74
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.70
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.99
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.15
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.89
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:23.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.33
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :    1.52
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:23.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.56e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:46.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 4.00e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.86
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.09
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.19
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:07.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:08.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10103.76
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9845.65
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.065
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:47.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4758.24
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:48.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4791.07
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:49.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4147.45
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11707.65
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12113.15
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:29.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.06
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000103585

Normal statistic for number of bits   :    0.82
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.11
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000044377

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.75
p-value of test                       :    0.96

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:36.59

 All tests were passed




Server wird beendet - Lösche Semaphor 10092563.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5552
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:56.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:43.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4236
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:57.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:58.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:05.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:06.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:56.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:01.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    3.33
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     956
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    4.37
p-value of test                       :  5.8e-3

Stat. AD after spacings (mNP2-S)      :    1.97
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:50.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.94
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     627
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:17.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:47.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.75
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.48
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.36
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.98
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.63
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.59
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.32
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.61
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.43
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  399.70
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:42.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1397.21
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:00.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7238.34
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.55
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.46
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:02.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.27
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.85
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:44.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5098.87
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:29.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:20.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45839
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869839
  j =  1                              :        399908325
  j =  2                              :            45833
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:11.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45518
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869518
  j =  1                              :        399908966
  j =  2                              :            45514
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:27.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:19.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:46.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:58.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:35.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.85e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:34.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:34.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.56
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:49.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.59
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.05
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.32
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:48.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.67
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.86
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:45.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.93
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.23
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.50
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.15
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   10.73
p-value of test                       :  4.7e-3

-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.67
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17382.98
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.30
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.68
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.46
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.81
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.72
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.93
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.84
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.01
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.89
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.30
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.25
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.80
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  561.54
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.55
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.70
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.08
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.27
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.90
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.26
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.56
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.99
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.40
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5104.42
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.78
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.72
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.21
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  451.22
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4901.43
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.34
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.04
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.08
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -1.04
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:21.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.69
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:21.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.15e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 9.35e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.94
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.44
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.48
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:07.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:09.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9920.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9884.64
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:40.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.45
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:48.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4809.77
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4192.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.95
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11828.05
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:29.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11882.94
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:29.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.09
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999847217

Normal statistic for number of bits   :   -1.21
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.36
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999975647

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   0.071
p-value of test                       :    0.47

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:38.71

 All tests were passed




Server wird beendet - Lösche Semaphor 11042835.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:48.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1461
p-value of test                       :  4.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334581
  j =  1                              :        599997078
  j =  2                              :             1461
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1266
p-value of test                       :    0.9963

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334386
  j =  1                              :        599997468
  j =  2                              :             1266
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5405
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:57.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:41.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:58.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:05.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7135
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:06.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:56.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:00.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.24
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    2.56
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.39
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    2.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.95
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:13.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    3.73
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:41.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.79
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.03
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.13
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.85
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.00
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.89
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.07
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.06
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:43.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1393.93
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:01.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7117.10
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.57
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.84
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:02.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.28
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.24
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:34.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5166.42
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:12.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:02.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45849
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869849
  j =  1                              :        399908306
  j =  2                              :            45841
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45708
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869708
  j =  1                              :        399908585
  j =  2                              :            45706
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:28.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:20.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:46.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:00.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:55.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.14e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.46e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.59e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:27.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:21.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:38.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:37.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.52
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.18
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.94
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.01
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.35
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.94
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:38.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.88
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.04
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.41
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.39
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.93
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.39
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17123.19
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.52
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.76
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.50
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.25
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.15
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:39.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.89
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.45
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.57
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.43
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.35
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.06
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.60
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.59
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.79
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.18
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.99
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.54
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.04
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  101.06
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.18
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.07
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  448.31
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.42
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.56
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.22
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.71
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5110.77
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.05
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.24
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.26
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:23.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.34
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:22.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.78e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 4.77e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9973

-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.79
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.23
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.55
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:05.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:07.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10205.57
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  3.9e-3

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9786.80
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:42.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9971

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.72
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:50.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4150.88
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4025.24
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11584.71
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:28.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11913.00
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.66
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000016921

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.25
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999898199

Normal statistic for number of bits   :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:39.09

 All tests were passed




Server wird beendet - Lösche Semaphor 12058643.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:49.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5406
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:57.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:40.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:57.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:58.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:07.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7527
p-value of test                       :  7.7e-3


-----------------------------------------------
CPU time used                    :  00:03:07.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:56.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:04:01.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.30
p-value of test                       :  6.4e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     564
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:13.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.17
p-value of test                       :    0.9965


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.57
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:42.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.72
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.70
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.06
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.00
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.46
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.64
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.44
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.06
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.77
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:43.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1459.77
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:02.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7040.21
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:43.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.02
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.73
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:03.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.30
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:44.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5083.02
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:25.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46007
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870007
  j =  1                              :        399907986
  j =  2                              :            46007
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:13.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46039
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870039
  j =  1                              :        399907923
  j =  2                              :            46037
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:27.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:21.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:46.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:00.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:35.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 4.95e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 5.29e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.036
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:38.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:39.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.07
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.49
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.47
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.22
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.30
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:42.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.06
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.30
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   62.02
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.13
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.84
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17425.33
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.13
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.05
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.10
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.93
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.85
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.25
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.92
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.72
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.80
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.35
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.73
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.04
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.25
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.63
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   46.03
p-value of test                       :    0.9956


-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.80
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.17
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.48
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.58
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.77
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.38
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.18
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5060.24
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.21
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.40
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.14
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.06
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5034.86
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.85
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.37
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:34.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.81
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:22.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.80
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :   -0.51
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:21.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.04e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.37e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 7.58e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.53
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.78
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.65
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:07.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.88
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:08.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10077.95
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9805.06
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.77
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:55.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:47.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4795.28
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:48.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5009.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.60
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.68
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11667.12
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12043.78
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:30.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.45
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000052927

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.94
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000055018

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.93
p-value of test                       :    0.97

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:26.89

 All tests were passed




Server wird beendet - Lösche Semaphor 13107219.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5423
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:57.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4449
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:43.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:57.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:58.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:07.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:06.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:56.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:59.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.16
p-value of test                       :    0.9974


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     635
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.92
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:15.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.00
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:45.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.23
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.45
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.05
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.03
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.62
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  194.09
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.43
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:43.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1466.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:02.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7065.92
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.96
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.43
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:03.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.07
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.37
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:33.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5079.73
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:05.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45997
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869997
  j =  1                              :        399908011
  j =  2                              :            45987
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45952
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869952
  j =  1                              :        399908098
  j =  2                              :            45948
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:28.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :  8.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:19.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:47.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:03.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:54.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:35.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 3.19e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.20e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:37.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.047
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:36.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.20
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.36
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.77
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.88
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.22
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.08
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.40
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:43.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.49
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.67
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  165.07
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17194.21
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.91
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.92
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.41
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.99
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.04
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.96
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.25
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.59
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.17
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.72
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.91
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.29
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.25
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.50
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.91
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.78
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.12
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.88
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.77
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  479.45
p-value of test                       :  6.5e-4    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.18
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.82
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.29
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.89
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.32
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.34
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5312.90
p-value of test                       :  1.1e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.26
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.11
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.61
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :   -1.81
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:22.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.52
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :   0.066
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:23.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :  -0.022
p-value of test                       :    0.51

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 6.00e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 5.35e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.51
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.41
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:07.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.10
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:06.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10289.50
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10139.35
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:40.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4908.49
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:48.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4747.37
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:49.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4275.86
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4184.78
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11992.80
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11605.81
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:30.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.78
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999944153

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.56
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  7999921992

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :  -0.047
p-value of test                       :    0.52

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:58.48
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 H (L=10000, r=0)    6.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14123027.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9907


-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5342
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:55.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4538
p-value of test                       :  1.2e-3


-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7113
p-value of test                       :    0.9919


-----------------------------------------------
CPU time used                    :  00:02:42.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:57.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:00.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:06.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:06.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:55.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7472
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:00.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:48.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     647
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.75
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.94
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:15.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:41.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.91
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.62
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.57
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.79
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.44
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.84
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.34
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  366.40
p-value of test                       :    0.9919

-----------------------------------------------
CPU time used                    :  00:01:44.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1392.69
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:01.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6964.98
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:42.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.64
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.26
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:03.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.65
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.05
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:32.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5162.50
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:01.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45666
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869666
  j =  1                              :        399908669
  j =  2                              :            45664
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45686
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869686
  j =  1                              :        399908630
  j =  2                              :            45682
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:27.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:19.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:47.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:04.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:54.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:16.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:33.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.81e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.01
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:36.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.29
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.14
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.92
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.10
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.95
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:51.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.11
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:39.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.7e-3

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.61
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.62
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.23
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.51
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17562.23
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.59
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.53
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.42
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.47
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.36
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.78
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.09
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.78
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.39
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.42
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.03
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.02
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.63
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.09
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.98
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.88
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.40
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.21
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.83
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.69
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.01
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.83
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5137.66
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.58
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.03
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:34.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.08
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.25
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5074.74
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.85
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.49
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:34.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.54
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :   -0.98
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:21.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.36
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :   -0.96
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:23.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   0.027
p-value of test                       :    0.49

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.38e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 6.31e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:46.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.77e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.51
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.00
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.99
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:07.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.65
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:08.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10129.80
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10011.38
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:43.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5019.04
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4823.99
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:49.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.85
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.14
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11880.68
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11580.51
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.70
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999949130

Normal statistic for number of bits   :   -0.40
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.91
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000058486

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:54.72

 All tests were passed




Server wird beendet - Lösche Semaphor 15106067.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:50.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1470
p-value of test                       :  2.4e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334590
  j =  1                              :        599997060
  j =  2                              :             1470
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5437
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:58.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:43.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:45.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:01.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:03.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:11.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:11.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:04:04.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:04:08.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:49.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.52
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:14.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.57
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:45.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.54
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.01
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.34
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.25
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.09
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.99
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  364.20
p-value of test                       :    0.9936

-----------------------------------------------
CPU time used                    :  00:01:53.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1484.15
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:05.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7112.12
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.41
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:14.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.63
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.33
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:37.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5018.77
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:05.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45851
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869851
  j =  1                              :        399908301
  j =  2                              :            45845
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45642
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869642
  j =  1                              :        399908720
  j =  2                              :            45634
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:31.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:20.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:51.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:05.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:37.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 9.26e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.16e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:24.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.039
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:49.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:49.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.35
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.13
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.79
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.95
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.09
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.05
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.00
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.42
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.81
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.19
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.32
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:43.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17501.31
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:55.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.22
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.80
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.62
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.44
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   35.65
p-value of test                       :  5.1e-3


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.65
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   62.67
p-value of test                       :  2.8e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.55
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.99
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.89
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.70
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.26
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.35
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.45
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.50
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.82
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.49
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.65
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.43
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.12
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  440.72
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.21
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.15
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.44
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.34
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.09
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.46
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4931.57
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.64
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.03
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.43
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:24.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.28
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :   -1.51
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:26.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:11.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.40

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.10e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.08e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 6.83e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.37
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.02
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.73
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:05.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.36
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:06.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9899.25
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10033.09
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:04:27.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4846.81
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4844.97
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:57.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4123.72
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4006.07
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11883.60
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:33.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11974.49
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:34.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.28
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000074803

Normal statistic for number of bits   :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.15
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000031174

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:19.09

 All tests were passed




Server wird beendet - Lösche Semaphor 16121875.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:50.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1264
p-value of test                       :    0.9968

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334384
  j =  1                              :        599997472
  j =  2                              :             1264
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5582
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:04:00.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:43.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:46.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:01.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4513
p-value of test                       :  4.0e-3


-----------------------------------------------
CPU time used                    :  00:02:02.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7450
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:12.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:12.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:10.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:11.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.24
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     325
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    2.66
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:13.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.95
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:47.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.51
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.22
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.61
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.26
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:11.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.07
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.74
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.95
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.38
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:29.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  371.18
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:57.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1380.44
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:08.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7088.68
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.01
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.95
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:22.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.30
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:47.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.13
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:44.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4969.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:19.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46038
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870038
  j =  1                              :        399907929
  j =  2                              :            46028
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45354
p-value of test                       :    0.9930


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869354
  j =  1                              :        399909294
  j =  2                              :            45350
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:33.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:21.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:52.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:09.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:56.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:38.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.89e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.31e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 7.69e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:24.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:24.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.023
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:24.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:49.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:52.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.96
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.55
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.90
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.98
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.36
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.32
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:50.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.28
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.15
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.05
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.28
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17460.89
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:52.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.16
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.85
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.43
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.45
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.53
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:36.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.51
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.83
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.19
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.65
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.33
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.29
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.07
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.24
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.61
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.61
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.56
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.70
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.90
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.72
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.74
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.77
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.55
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5099.34
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.37
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.30
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.40
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.60
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4828.86
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.93
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.21
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.91
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :   0.052
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:23.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.98
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :   -1.18
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:22.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :  -0.065
p-value of test                       :    0.53

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 7.24e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.48e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.49
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.24
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.78
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:09.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.69
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:06.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10019.12
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10197.90
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:04:28.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.41
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:56.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.47
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4161.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11831.83
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:35.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11705.97
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:37.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.37
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999997280

Normal statistic for number of bits   :  -0.022
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   89.90
p-value of test                       :  1.6e-3


-----------------------------------------------
Total number of bits:  8000071020

Normal statistic for number of bits   :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.4e-3

Anderson-Darling statistic = A2       :    3.83
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.04
p-value of test                       :    0.02

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   0.092
p-value of test                       :    0.46

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :  -0.023
p-value of test                       :    0.51

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:33.11

 All tests were passed




Server wird beendet - Lösche Semaphor 17235987.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:48.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5358
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:57.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:43.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:58.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:58.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:05.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7554
p-value of test                       :  3.1e-3


-----------------------------------------------
CPU time used                    :  00:03:04.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:56.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:00.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.79
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:51.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.71
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.05
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    2.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:20.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.55
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    2.21
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     123
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:51.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.89
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:55.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.43
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.57
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.71
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.94
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.94
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.77
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:45.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1517.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:03.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6896.19
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:44.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.68
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.39
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:03.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.01
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.97
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:34.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5150.02
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:00.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46269
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870269
  j =  1                              :        399907463
  j =  2                              :            46267
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46040
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870040
  j =  1                              :        399907923
  j =  2                              :            46034
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9916


-----------------------------------------------
CPU time used                    :  00:02:28.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:18.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:44.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:58.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:33.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.99e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:22.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:38.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:38.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.42
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.83
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.38
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.47
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.85
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.45
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.02
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.99
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.55
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.80
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.25
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17781.68
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.42
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.18
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.32
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.62
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.44
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.71
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.70
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.02
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.29
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.28
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.13
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.02
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.49
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.23
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.20
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.59
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.48
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.61
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.13
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.19
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.34
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.40
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5136.29
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  425.59
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.38
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.94
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.26
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.25
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.40
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.07
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:24.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.50
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :  -0.082
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:26.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 2.20e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.01
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.60
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.58
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:06.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.39
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:06.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9790.24
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9822.65
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:55.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.36
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:49.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.52
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:50.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.21
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.21
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11808.94
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11975.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:29.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.79
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000190456

Normal statistic for number of bits   :    1.51
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.69
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000021370

Normal statistic for number of bits   :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    2.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    2.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.71

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:49.44

 All tests were passed




Server wird beendet - Lösche Semaphor 18448403.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:48.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5432
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:57.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4205
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:42.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:57.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:05.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7155
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:06.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:56.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:01.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:50.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    2.72
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     337
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:18.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:48.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.12
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.60
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.88
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.08
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  269.14
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.50
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:43.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1366.49
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:01.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7028.12
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.62
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:03.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.20
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.60
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:34.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5053.36
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:00.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45783
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869783
  j =  1                              :        399908437
  j =  2                              :            45777
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45752
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869752
  j =  1                              :        399908501
  j =  2                              :            45742
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:27.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :  2.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.75
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:19.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:46.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:55.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :  3.0e-3

Anderson-Darling statistic = A2       :    3.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:34.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:22.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.98e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:35.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.99
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.03
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:51.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.21
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.10
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.93
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:40.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.90
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.58
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.56
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17535.39
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.58
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.04
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.36
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.47
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.04
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.04
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.42
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.53
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.46
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.42
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.60
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.60
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.00
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.30
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.70
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.19
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.34
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  420.89
p-value of test                       :    0.9957


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.44
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.59
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  320.15
p-value of test                       :    0.9923


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.23
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.71
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.60
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.44
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.28
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.42
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.65
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  326.25
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.06
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.21
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:24.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.10
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :    0.14
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:25.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 4.29e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 3.55e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.67
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.74
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.40
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:06.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.91
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:07.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9785.96
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9932.37
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.83
p-value of test                       :  2.4e-3

-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:48.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4754.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:48.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5061.38
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:50.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4347.84
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.23
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12060.22
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12071.78
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:29.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.45
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000066703

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.27
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999921035

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.11

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:13.12

 All tests were passed




Server wird beendet - Lösche Semaphor 19464211.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:40.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5458
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:57.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:41.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:57.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:57.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:05.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:05.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7092
p-value of test                       :    0.9960


-----------------------------------------------
CPU time used                    :  00:03:56.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7068
p-value of test                       :    0.9983


-----------------------------------------------
CPU time used                    :  00:04:02.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    2.51
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:51.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9924

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:19.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.85
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:49.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.54
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.79
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.59
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.18
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.17
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.16
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  175.41
p-value of test                       :    0.9978

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.44
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:43.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1495.91
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:02.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7167.38
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.06
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.78
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:03.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.08
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.65
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4864.63
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:59.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46099
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870099
  j =  1                              :        399907805
  j =  2                              :            46093
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45504
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869504
  j =  1                              :        399908998
  j =  2                              :            45492
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:29.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:18.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  6.7e-3

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:45.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:00.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:34.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.82e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.41e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.51e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:21.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.097
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:36.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:36.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.26
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:49.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   40.42
p-value of test                       :    0.9958

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.00
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.58
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.32
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.50
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.01
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:45.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.72
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.28
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17351.03
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.78
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.95
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.86
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.85
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.06
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.46
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.68
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.90
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.78
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.62
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.96
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.14
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.06
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.39
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.22
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.64
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.11
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.29
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.94
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.17
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.68
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.44
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4919.39
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.66
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.45
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.21
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.75
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.82
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.96
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.29
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.91
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:26.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.66
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :   -0.51
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:26.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.20

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.80

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 2.39e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 5.87e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.01
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.80
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.04
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:05.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.12
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:04.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10109.47
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10180.31
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:35.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.04
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:41.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4991.37
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:43.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4233.89
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11997.61
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11958.12
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.79
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999965942

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.42
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000040678

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.79
p-value of test                       :    0.96

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:08.44

 All tests were passed




Server wird beendet - Lösche Semaphor 20447251.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5399
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:43.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:37.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:36.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:55.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:03.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7175
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:03.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:54.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:59.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.71
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.85
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:02.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:28.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.29
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.51
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.17
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.35
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:11.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.16
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.79
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.35
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.34
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.59
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:51.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.82
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:03.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6837.18
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:50.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.60
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.80
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   88.46
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:03:01.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.95
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.21
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:36.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5032.16
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:14.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46250
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870250
  j =  1                              :        399907505
  j =  2                              :            46240
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45704
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869704
  j =  1                              :        399908596
  j =  2                              :            45696
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:29.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 6.57e-3
p-value of test                       :    0.9921

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:18.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:44.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:59.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:53.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:34.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.97e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 2.41e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 7.67e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:37.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:36.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   96.84
p-value of test                       :  1.0e-2

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.81
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.58
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:50.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.33
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.91
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:43.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.59
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.02
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:31.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:29.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.43
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:40.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17806.06
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.27
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.72
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.04
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.22
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.97
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:40.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   55.67
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.90
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.73
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.45
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.46
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:40.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.67
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.23
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.05
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.46
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.25
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.91
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.10
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.27
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  103.16
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.18
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.19
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.77
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4902.52
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.90
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.40
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.13
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  301.70
p-value of test                       :    0.9993    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5108.16
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.48
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  158.31
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.09
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :   -1.39
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:17.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.00
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :   0.057
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:15.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.38

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:11.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.51e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 2.08e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.17
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.97
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.10
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:11.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.54
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:08.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9843.60
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10183.67
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:52.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5035.38
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.48
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:50.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4140.67
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4302.53
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11881.31
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11769.76
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   81.69
p-value of test                       :  8.8e-3


-----------------------------------------------
Total number of bits:  8000067975

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.59
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999998549

Normal statistic for number of bits   :  -0.011
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9960

Tests on the sum of all N observations
Standardized normal statistic         :  -0.046
p-value of test                       :    0.52

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:18:56.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 M (L=10000, r=15)   0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 786452.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5376
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:45.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:37.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7464
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:36.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:54.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:55.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:00.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:01.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:53.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:59.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:46.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:14.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:43.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.64
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.91
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.82
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.31
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.42
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.21
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.18
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.16
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.73
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:49.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1383.08
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:03.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6916.21
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:48.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.64
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:01.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.35
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.27
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:35.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5059.80
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:14.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46278
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870278
  j =  1                              :        399907448
  j =  2                              :            46270
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45471
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869471
  j =  1                              :        399909062
  j =  2                              :            45463
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:28.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:18.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:45.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:00.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:53.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:32.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.47e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.91e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:35.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:35.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.50
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.65
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.49
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.72
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.87
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.22
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:43.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.13
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.39
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.57
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:10.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17499.67
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.41
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.05
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.12
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.16
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.72
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.15
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.36
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.34
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.63
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.04
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.46
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.01
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.11
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.30
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.42
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.62
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.49
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.60
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.54
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.21
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.85
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.29
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.26
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.09
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.69
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.46
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.59
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4780.72
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.83
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.42
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.74
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :   -1.09
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:20.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.72
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:22.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.60

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:46.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.37e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.96
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:29.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.96
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.82
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:11.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.38
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:08.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9924.33
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9750.85
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:04:04.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4929.35
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:48.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4688.91
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:48.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.60
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11569.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11776.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:30.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.98
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999971159

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.57
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  7999999932

Normal statistic for number of bits   : -5.38e-4
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -2.03
p-value of test                       :    0.98

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    2.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :  -0.058
p-value of test                       :    0.52

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:11:04.04

 All tests were passed




Server wird beendet - Lösche Semaphor 1703956.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5604
p-value of test                       :  6.8e-3


-----------------------------------------------
CPU time used                    :  00:03:48.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:38.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:38.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4443
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:02.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:03.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:55.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:00.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.05
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    2.35
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:15.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:45.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.13
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.74
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.23
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.56
p-value of test                       :    0.9908

-----------------------------------------------
CPU time used                    :  00:01:11.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.67
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.43
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.56
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.26
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:47.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.33
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:01.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7038.68
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.20
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.63
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:00.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.54
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.15
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:35.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4830.96
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:12.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45676
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869676
  j =  1                              :        399908652
  j =  2                              :            45668
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46091
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870091
  j =  1                              :        399907821
  j =  2                              :            46085
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:29.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:18.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:45.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:00.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:54.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:33.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-5
p-value of test                       :    0.9956

Kolmogorov-Smirnov- statistic = D-    : 2.41e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:22.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.60e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:35.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.08
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.91
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.81
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.02
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.82
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.47
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:42.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.75
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.16
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:29.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:29.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.99
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17565.24
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.61
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.90
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.17
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.69
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.12
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.24
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.79
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.56
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.45
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  192.10
p-value of test                       :  6.3e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.16
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.73
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.25
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.21
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.97
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.41
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.40
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.40
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.54
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.06
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.68
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5026.13
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.42
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.05
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.89
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.68
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4965.82
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.18
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.51
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:34.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.97
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:23.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.85
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.78e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 5.48e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 8.54e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.57
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.06
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:08.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  257.09
p-value of test                       :  4.0e-3

-----------------------------------------------
CPU time used                    :  00:02:07.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9897.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.80
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.061
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:48.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4991.91
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:49.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4949.32
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:49.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4277.27
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4244.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12366.88
p-value of test                       :  2.5e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:28.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11726.13
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:30.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.54
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000031420

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.39
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999996113

Normal statistic for number of bits   :  -0.031
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:09.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   0.062
p-value of test                       :    0.48

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:28.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 99  HammingIndep, L=1200, r=0       2.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2818068.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5394
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:48.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:38.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:36.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:55.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:54.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:01.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:02.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:54.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:58.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.05
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.48
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.13
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:14.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:46.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.52
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.55
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.17
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.61
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:12.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.54
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.17
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.95
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.98
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.30
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1465.20
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:06.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7056.64
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:47.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.36
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9992    *****

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:08.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.20
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.34
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:37.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5107.27
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:13.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45619
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869619
  j =  1                              :        399908763
  j =  2                              :            45617
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45909
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869909
  j =  1                              :        399908183
  j =  2                              :            45907
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:29.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:18.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:02.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:56.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:36.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.04e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 9.48e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.024
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.92
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.57
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.21
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.75
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.28
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.48
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:47.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.16
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.66
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   62.39
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.67
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:29.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.88
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:30.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.94e-3
p-value of test                       :    0.9937

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  159.37
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17342.78
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.19
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.85
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.94
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.40
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.25
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.56
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.92
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.30
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.86
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.49
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.70
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.32
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.04
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.74
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.86
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.82
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.36
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.59
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.72
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.18
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.09
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4902.31
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.16
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.58
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.73
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.89
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.53
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.64
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.17
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.15
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :  -0.019
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:23.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.57
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :    1.12
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:25.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 2.95e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.69e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.16
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   41.00
p-value of test                       :  2.3e-3



-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.01
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:07.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.85
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:10.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10008.65
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9797.88
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:04:13.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4801.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:52.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.73
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:56.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4221.29
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4175.77
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11633.77
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:31.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11637.77
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:32.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.84
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999878705

Normal statistic for number of bits   :   -0.96
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.88
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000175285

Normal statistic for number of bits   :    1.39
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.83
p-value of test                       :    0.97

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:23.57

 All tests were passed




Server wird beendet - Lösche Semaphor 3768340.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:43.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:50.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:39.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:38.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:56.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:03.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:03.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:53.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:59.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:15.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:44.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.98
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.04
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.82
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.66
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.71
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.11
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:50.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1376.32
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:01.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7049.33
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:40.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.11
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:02.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.37
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.96
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:34.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5022.61
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:16.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46174
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870174
  j =  1                              :        399907656
  j =  2                              :            46166
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45919
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869919
  j =  1                              :        399908165
  j =  2                              :            45913
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:27.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :  6.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:18.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:45.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:55.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:34.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.60e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 7.24e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.69e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:33.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:34.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.89
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.01
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.61
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.80
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.40
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:41.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.50
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.22
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:29.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.06
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:18.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17442.38
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   58.01
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.67
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.40
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.64
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.92
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.70
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.07
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.28
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.67
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.68
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.60
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.09
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.31
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.43
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.42
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.78
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.57
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.49
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.66
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.60
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.89
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.98
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4893.57
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  320.87
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.13
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.07
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.48
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4906.11
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.34
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.42
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.65
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:24.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.24
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:25.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    2.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.09e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 6.02e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 8.84e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.77
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.64
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.12
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:07.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.88
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:08.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9840.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9919.13
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.69
p-value of test                       :    0.9964

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:43.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4990.69
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3991.25
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:20.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4193.66
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12039.05
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:28.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11802.90
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:29.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.51
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999988325

Normal statistic for number of bits   :  -0.092
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.09
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999986048

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.10

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:16.11

 All tests were passed




Server wird beendet - Lösche Semaphor 4947988.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5449
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:51.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:40.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:40.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4238
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:57.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:04.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:04.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:54.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:04:02.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.85
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     567
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.21
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:14.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.20
p-value of test                       :    0.9904

-----------------------------------------------
CPU time used                    :  00:02:43.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.76
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.46
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.58
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.46
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.52
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.45
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.54
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.63
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.28
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:45.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1414.90
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:03.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7167.41
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:40.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.41
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:01.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.06
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.05
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:35.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5111.22
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:13.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46050
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870050
  j =  1                              :        399907905
  j =  2                              :            46040
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45856
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869856
  j =  1                              :        399908291
  j =  2                              :            45850
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:28.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:18.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:46.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:01.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:54.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:34.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.41e-4
p-value of test                       :  9.6e-3

Kolmogorov-Smirnov- statistic = D-    : 8.29e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.83e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:21.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:21.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:32.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:33.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.01
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:48.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.25
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.84
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:38.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.95
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.96
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:28.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.19
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:38.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17407.80
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.50
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.91
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.11
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.48
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.68
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.58
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.07
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.39
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.79
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.00
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.76
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.68
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.67
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.79
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.79
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.23
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.66
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.70
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.02
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.21
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.34
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.30
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.45
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.31
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.93
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.98
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.75
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4788.47
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.45
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  240.52
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.26
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :    0.16
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:25.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.26
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:24.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   0.038
p-value of test                       :    0.48

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.91
p-value of test                       :    0.97

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.13e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 3.86e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.82e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.44
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.98
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:07.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.64
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:06.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.55
p-value of test                       :  1.1e-3

Anderson-Darling statistic = A2       :    6.06
p-value of test                       :  9.9e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10448.44
p-value of test                       :  8.8e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10046.88
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.07
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.061
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:55.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:51.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  6.9e-3

Anderson-Darling statistic = A2       :    4.34
p-value of test                       :  6.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5133.45
p-value of test                       :  7.6e-3

-----------------------------------------------
CPU time used                    :  00:01:49.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4832.76
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:49.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4351.85
p-value of test                       :  5.4e-3

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.75
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11794.48
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11907.20
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:30.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.40
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999964484

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.19
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000052264

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.04
p-value of test                       :    0.02

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:24.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 90  HammingWeight2, r = 0           8.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5832724.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5445
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:54.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4236
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:41.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4434
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:58.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:05.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:58.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:03.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.07
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    2.20
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:47.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.17
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    4.80
p-value of test                       :  3.6e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     347
p-value of test                       :  4.3e-3

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:13.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:40.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.48
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.90
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.62
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.95
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.13
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.96
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.76
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1369.13
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:02.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7322.84
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:48.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.27
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.02
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:09.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.04
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.05
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:36.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5139.88
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:05.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45815
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869815
  j =  1                              :        399908373
  j =  2                              :            45809
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45963
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869963
  j =  1                              :        399908078
  j =  2                              :            45955
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:30.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:18.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:46.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:03.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:55.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.71e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.94e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:44.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:43.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.52
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.94
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.38
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.16
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.70
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.57
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.89
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.21
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   15.94
p-value of test                       :  1.2e-3

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.37
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17083.75
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.38
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.93
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.85
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.90
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.15
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.77
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.57
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.96
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.12
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.56
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.86
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.84
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.68
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.65
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.99
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.35
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.49
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.78
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.06
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.51
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.09
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.79
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5076.51
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.12
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.45
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  455.56
p-value of test                       :  6.9e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.17
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4885.58
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.97
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.15
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.26
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:24.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.02
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :    0.69
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:26.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 6.73e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.10e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.09
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.36
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.49
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:06.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.19
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:06.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9892.61
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 5.36e-3
p-value of test                       :    0.9944

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9695.38
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.078
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:04:18.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5023.82
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:53.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5100.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:54.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.95
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11647.56
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:30.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12134.42
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.34
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999930362

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.15
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000092617

Normal statistic for number of bits   :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:57.45

 All tests were passed




Server wird beendet - Lösche Semaphor 6848532.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1262
p-value of test                       :    0.9973

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334382
  j =  1                              :        599997476
  j =  2                              :             1262
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5381
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:52.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:40.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:56.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:57.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:04.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:04.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7452
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:55.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:04:00.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    2.41
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     951
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    2.00
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:47.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.41
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    2.21
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     251
p-value of test                       :    0.9980

Stat. AD (mNP2)                       :    1.60
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:16.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:44.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   19.71
p-value of test                       :  6.2e-3

-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.77
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.73
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.14
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.92
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.03
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.47
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.74
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.97
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1438.53
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:02.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7316.06
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:45.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.64
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.72
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:01.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.12
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.06
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:34.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4977.95
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:05.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45520
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869520
  j =  1                              :        399908967
  j =  2                              :            45506
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46050
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870050
  j =  1                              :        399907903
  j =  2                              :            46044
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:28.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:19.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:45.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:58.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:55.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:34.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:21.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.00
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:36.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.10
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   35.72
p-value of test                       :    0.9994    *****

-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.77
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.00
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.20
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.92
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.07
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.08
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.13
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.96
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17547.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.42
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.12
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.58
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.30
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.93
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.49
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.07
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.14
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.88
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.50
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:38.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.54
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.45
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.90
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.48
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.53
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.54
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.42
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.64
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.70
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.47
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.20
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.41
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.93
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.87
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.44
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.85
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.02
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4872.89
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.13
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.20
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.95
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:22.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.41
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :   -2.40
p-value of test                       :    0.9918



-----------------------------------------------
CPU time used                    :  00:02:22.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.04e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.48
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.72
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.88
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:07.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.02
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:07.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9985.98
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9961.59
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.099
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:54.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4762.13
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4780.98
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:51.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.98
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.91
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11769.18
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12123.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:29.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.92
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999962042

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.91
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000154246

Normal statistic for number of bits   :    1.22
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    2.61
p-value of test                       :  5.1e-3

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:58.27
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 61  WeightDistrib, r = 28           0.9994 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7929876.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1263
p-value of test                       :    0.9971

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334383
  j =  1                              :        599997474
  j =  2                              :             1263
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5526
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:54.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4466
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7522
p-value of test                       :  9.0e-3


-----------------------------------------------
CPU time used                    :  00:02:40.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:57.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:57.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:05.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:04.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:55.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:04:00.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.18
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     867
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:14.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:41.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.84
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.06
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.46
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.00
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.36
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.66
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.22
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:45.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1651.26
p-value of test                       :  6.5e-5    *****

-----------------------------------------------
CPU time used                    :  00:02:05.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6969.08
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:46.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.64
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:03.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.52
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.74
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:34.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5203.00
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:59.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45594
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869594
  j =  1                              :        399908819
  j =  2                              :            45580
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45373
p-value of test                       :    0.9910


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869373
  j =  1                              :        399909258
  j =  2                              :            45365
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:28.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9993    *****

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:18.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:44.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:00.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:36.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.89e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 3.25e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:40.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.42
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.65
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.66
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.97
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.39
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.18
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.80
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:45.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.29e-3
p-value of test                       :    0.9966

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   65.02
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.40
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.55
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17678.78
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.77
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.39
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.85
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.29
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.26
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:38.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.78
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.91
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.04
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.77
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.53
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.24
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.02
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.13
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.66
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.98
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.92
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.11
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.27
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.81
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.68
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  317.60
p-value of test                       :    0.9942


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.53
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5236.86
p-value of test                       :  9.7e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.62
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.67
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.15
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.70
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4951.41
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.99
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.98
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.74
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :   0.016
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:25.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.34
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:25.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :  -0.076
p-value of test                       :    0.53

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.19
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.10
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.18
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:06.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    3.48
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.73
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:07.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9957.06
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9999.46
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:59.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:49.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.79
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:51.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3934.87
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4183.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11547.41
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11883.96
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:29.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.49
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000011443

Normal statistic for number of bits   :   0.090
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.64
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000002155

Normal statistic for number of bits   :   0.017
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:46.76
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 36  Gap, r = 0                      6.5e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8912916.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5412
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:58.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:45.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:02.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:02.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7110
p-value of test                       :    0.9926


-----------------------------------------------
CPU time used                    :  00:03:15.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:16.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:18.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:16.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9923

Test on the Nm values of W_{n,i}(mNP1):    2.30
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     828
p-value of test                       :    0.9920

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     645
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:13.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.84
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    2.08
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    3.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:38.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.45
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.40
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.93
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.46
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.72
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.60
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.65
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:34.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.59
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.02
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:07.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6842.40
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:12.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.79
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:13.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.34
p-value of test                       :    0.9969


-----------------------------------------------
CPU time used                    :  00:00:47.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.85
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:37.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5210.27
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:55.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46111
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870111
  j =  1                              :        399907780
  j =  2                              :            46107
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46036
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870036
  j =  1                              :        399907933
  j =  2                              :            46026
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:32.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:24.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:53.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:13.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:57.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:38.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.48e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:24.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:26.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:26.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:42.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:44.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.90
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.32
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.84
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.70
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   59.18
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.42
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:52.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.24
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.73
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.85
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:29.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.59
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:43.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17538.93
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.42
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.40
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.34
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.60
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.78
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:38.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.89
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.46
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.29
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.68
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.61
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.02
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.63
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.58
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.99
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.15
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.62
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.96
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.86
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.75
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.90
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.83
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.82
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.43
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.00
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.09
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.30
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.17
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5080.87
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  291.47
p-value of test                       :    0.9997    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.10
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.42
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :    1.06
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:25.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.80
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    1.17
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:26.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 5.48e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 8.38e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.67
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:38.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.15
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:33.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.76
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:22.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.80
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:23.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9928.19
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9804.91
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.96
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:04:13.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9916

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:54.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4773.02
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:58.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.49
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4267.00
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11692.15
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:33.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11968.62
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:34.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.34
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999988607

Normal statistic for number of bits   :  -0.090
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:16.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.12
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  8000026833

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:37.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :  -0.041
p-value of test                       :    0.52

Sample variance                       :    2.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:38.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:16:08.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 R (L=10000, r=15)   0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9895956.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5505
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:57.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:42.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:45.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:00.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4451
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:01.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:12.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7447
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:13.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:04:09.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:13.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.98
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:51.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:16.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.09
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:17.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.85
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     130
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:48.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.72
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.40
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.30
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.81
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.90
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.56
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.89
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.44
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.51
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:52.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1522.74
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:00.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7187.75
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:52.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.73
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.95
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:12.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.74
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.28
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:39.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5095.91
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:30.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:00.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45639
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869639
  j =  1                              :        399908723
  j =  2                              :            45637
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45843
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869843
  j =  1                              :        399908318
  j =  2                              :            45835
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:33.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:24.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:52.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :  1.4e-3

Anderson-Darling statistic = A2       :    5.00
p-value of test                       :  3.0e-3


-----------------------------------------------
CPU time used                    :  00:02:06.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:57.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:38.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.71e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.39e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.034
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:54.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.53
p-value of test                       :    0.9944

-----------------------------------------------
CPU time used                    :  00:01:52.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.78
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:51.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.85
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.29
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.86
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.05
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.11
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.20
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:54.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.52
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.09
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.50
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  100.74
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17027.60
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.67
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.38
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.64
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.49
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.16
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.63
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.57
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.72
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.17
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.45
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.08
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.10
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.24
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.77
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.67
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.49
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.48
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.86
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.25
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.67
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:43.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.27
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.59
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4848.78
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.02
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.15
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  449.08
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.59
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.15
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.32
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.01
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.96
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:23.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.60
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :    1.19
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:24.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    2.33
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.65e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 9.57e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.30e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.88
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.96
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:32.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:16.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.68
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:14.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10009.38
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9869.22
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:04:33.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4955.54
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:51.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9936

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4905.17
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:55.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.10
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4262.61
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11723.73
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:32.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11958.72
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:35.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.50
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000194479

Normal statistic for number of bits   :    1.54
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:10.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.24
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999953252

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.70
p-value of test                       :    0.96

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.15

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.17
p-value of test                       :    0.9968

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:08.82

 All tests were passed




Server wird beendet - Lösche Semaphor 11370516.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:57.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:42.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4181
p-value of test                       :    0.9911


-----------------------------------------------
CPU time used                    :  00:01:59.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:08.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:06.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7185
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:57.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:02.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:47.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     568
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.70
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:12.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.91
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:41.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.73
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.74
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.24
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.18
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.88
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.98
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.24
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  485.20
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:45.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1450.52
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:01.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7253.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:46.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.50
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   84.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:02.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.01
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.62
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:34.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4989.38
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:58.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45846
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869846
  j =  1                              :        399908313
  j =  2                              :            45836
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45761
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869761
  j =  1                              :        399908486
  j =  2                              :            45745
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:30.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:16.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:45.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:00.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:34.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.24e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 5.59e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:41.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:38.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.98
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.82
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.01
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.34
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.93
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:43.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.97
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.04
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.39
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17700.74
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.08
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.73
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.71
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.03
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.25
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.21
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.29
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.32
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.42
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.58
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  109.32
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.96
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.62
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.85
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.36
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.89
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.84
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.38
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.43
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.36
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.87
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.24
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.00
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.65
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.25
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.67
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.99
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4964.95
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.96
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.55
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.53
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :    1.30
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.67
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:22.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.83
p-value of test                       :    0.97

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.42e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.30e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 8.84e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.46
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.92
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.20
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:03.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.44
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:05.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10305.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10033.78
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:42.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:48.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4970.44
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:50.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4261.90
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.38
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12101.25
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11911.93
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.88
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000044791

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.48
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999829598

Normal statistic for number of bits   :   -1.35
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.43
p-value of test                       :    0.08

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:26.54

 All tests were passed




Server wird beendet - Lösche Semaphor 12582932.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5378
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:55.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7181
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:41.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:57.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:58.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:06.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7150
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:06.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:55.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:00.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.35
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     950
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.96
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     261
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:16.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.93
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:43.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.59
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.46
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.03
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.99
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.58
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.49
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:39.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.37
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:40.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:40.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  284.48
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.05
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1456.47
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:00.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7069.84
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:45.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.14
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  8.0e-3

Anderson-Darling statistic = A2       :    5.23
p-value of test                       :  2.4e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   98.35
p-value of test                       :  1.3e-3

-----------------------------------------------
CPU time used                    :  00:03:02.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.83
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.71
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:33.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4983.78
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:03.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45909
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869909
  j =  1                              :        399908185
  j =  2                              :            45903
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45896
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869896
  j =  1                              :        399908210
  j =  2                              :            45892
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:29.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:18.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:44.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:58.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:35.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 8.53e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.91e-4
p-value of test                       :  2.2e-3

Kolmogorov-Smirnov- statistic = D-    : 5.83e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    3.76
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:23.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:35.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:38.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.98
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.47
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.32
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.16
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.27
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.09
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:41.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.28
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.01
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.20
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.98
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.92
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.55
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17546.33
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.89
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.30
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.76
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.11
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.92
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.55
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.34
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.25
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.35
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.10
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.93
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.68
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.15
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.88
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.08
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.03
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.51
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.69
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.15
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.57
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.19
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.20
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4853.92
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.05
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.56
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.97
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.28
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4832.41
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.47
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:34.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.88
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   -2.03
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:22.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.35
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :    0.51
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:23.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.1e-3

Anderson-Darling statistic = A2       :    4.06
p-value of test                       :  8.5e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.56
p-value of test                       :  5.2e-3

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.56e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.41e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.85
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.84
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.51
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:05.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.93
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:06.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9944.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10122.20
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:39.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.19e-3
p-value of test                       :    0.9912

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5042.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:46.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.81
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:50.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4162.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11670.92
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12131.07
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.28
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999887789

Normal statistic for number of bits   :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.79
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999985337

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:10.55

 All tests were passed




Server wird beendet - Lösche Semaphor 13631508.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:38.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:49.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:58.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:42.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:44.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:01.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4175
p-value of test                       :    0.9931


-----------------------------------------------
CPU time used                    :  00:02:01.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:12.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:13.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:09.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:13.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.04
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    3.70
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     963
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:49.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:15.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:43.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.70
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.86
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.28
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.50
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:10.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.10
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.11
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.07
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.23
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.94
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.98
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:55.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.98
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:01.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7065.28
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:55.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.04
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.16
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:17.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.72
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:46.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.08
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:39.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5131.42
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:02.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45963
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869963
  j =  1                              :        399908076
  j =  2                              :            45959
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46102
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870102
  j =  1                              :        399907799
  j =  2                              :            46096
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:32.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:20.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:52.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:07.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9940

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:38.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.10e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.35e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 4.72e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:24.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:24.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:24.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:48.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.54
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.96
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.98
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.22
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.72
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.02
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.12
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:51.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.76
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.94
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.07
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.19
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17339.02
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.84
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.56
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.14
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.80
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.42
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.88
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.05
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.14
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.06
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.91
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  109.19
p-value of test                       :    0.9900


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.84
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.76
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.02
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.10
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.46
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.66
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.50
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.74
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.38
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.36
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.31
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.73
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  152.54
p-value of test                       :    0.9947


-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.20
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.84
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.11
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.54
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.81
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.90
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :    0.94
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:21.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.09
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:22.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.80e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 8.11e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.73e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 8.03e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.48
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.21
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.63
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:05.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.74
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:04.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9955.13
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10012.52
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:04:18.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4733.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:57.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.06
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:58.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4229.63
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.65
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11616.50
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:34.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12013.28
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:34.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.04
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  7999910517

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.75
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000023701

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    2.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 8.01e-3
p-value of test                       :    0.9914

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:05.37

 All tests were passed




Server wird beendet - Lösche Semaphor 14680084.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:38.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1219
p-value of test                       : 1 -  3.4e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334339
  j =  1                              :        599997562
  j =  2                              :             1219
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5329
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:58.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:43.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:46.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:01.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4239
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:03.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:14.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:14.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:11.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:15.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:49.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.31
p-value of test                       :  6.4e-3

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.61
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:15.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.23
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:43.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.35
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.54
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.76
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.15
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.05
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.76
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.33
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:28.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  501.23
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:56.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1422.60
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:01.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7058.58
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:56.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.17
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.74
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:16.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.11
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.04
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:43.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4947.85
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:02.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45968
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869968
  j =  1                              :        399908066
  j =  2                              :            45964
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45802
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869802
  j =  1                              :        399908397
  j =  2                              :            45800
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:33.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:21.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:53.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9972


-----------------------------------------------
CPU time used                    :  00:02:09.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:57.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:38.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.78e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:24.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:24.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.041
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:24.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:52.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:53.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.53
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.91
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.17
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.22
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.79
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.95
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.14
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:51.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.07
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.09
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.86
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.99
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17540.41
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:52.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.96
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.94
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.09
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.66
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.89
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.74
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.58
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.04
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.72
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.30
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.04
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.73
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.98
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.91
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.75
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.18
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.45
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.39
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  189.49
p-value of test                       :  1.7e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.94
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.45
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.40
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4933.02
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.91
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.64
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.10
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.96
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.72
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.89
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.96
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.48
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :    0.11
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:20.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.03
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:20.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.94
p-value of test                       :    0.03

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 6.62e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.76e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 8.49e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.51
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.93
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.34
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:05.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:06.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9857.35
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9954.65
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:04:23.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:57.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4812.44
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:01.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4162.13
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.28
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:30.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11803.74
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:37.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11665.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:38.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.62
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000100027

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.00
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000189511

Normal statistic for number of bits   :    1.50
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.71
p-value of test                       :    0.04

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.52e-3
p-value of test                       :    0.9908

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    2.06
p-value of test                       :    0.02

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:19.09
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21          1 -  3.4e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15761428.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5495
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:58.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:43.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:59.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:00.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:10.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:10.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:04:03.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:09.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.96
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.78
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.61
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    4.02
p-value of test                       :  8.5e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     330
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:13.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:43.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.34
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.40
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.79
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.87
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.17
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.34
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.96
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.08
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:53.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1536.57
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:01.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7148.74
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:49.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.66
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:08.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.93
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.57
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:37.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5064.23
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:02.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45828
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869828
  j =  1                              :        399908346
  j =  2                              :            45824
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46195
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870195
  j =  1                              :        399907612
  j =  2                              :            46191
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:30.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:24.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:54.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:12.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:57.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:37.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.24e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.71e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.76e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:24.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:40.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:41.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.24
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.88
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:50.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.94
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   17.99
p-value of test                       :    0.9964

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.14
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:46.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.94
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.70
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.65
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.29
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.28
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17326.20
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.17
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.68
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.76
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.85
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.53
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.16
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.16
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.01
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.09
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.76
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.38
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.53
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.07
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.94
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.77
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.58
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.31
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.13
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.05
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.80
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.53
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.53
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.36
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.49
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.31
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.91
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5107.26
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  438.15
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.17
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.62
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :   -1.15
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:21.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.89
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:21.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.66
p-value of test                       :    0.95

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   0.049
p-value of test                       :    0.48

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 7.09e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.39e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 9.47e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.74
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.74
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.50
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:04.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:04.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10121.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10017.24
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:04:06.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4758.30
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:52.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4821.29
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:53.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.54
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11287.99
p-value of test                       :    0.9998    *****

-----------------------------------------------
CPU time used                    :  00:01:30.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12202.17
p-value of test                       :  7.5e-3

-----------------------------------------------
CPU time used                    :  00:01:30.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.20
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999844316

Normal statistic for number of bits   :   -1.23
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.43
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000043810

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.64
p-value of test                       :    0.95

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :  -0.042
p-value of test                       :    0.52

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.38

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:06.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 99  HammingIndep, L=1200, r=0       0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16842772.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5392
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:04:01.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4418
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:43.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7450
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:45.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:01.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4454
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:02.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7160
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:12.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:13.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7462
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:09.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:13.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.89
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.60
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.17
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    2.30
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:14.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    6.00
p-value of test                       :  1.1e-3

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:45.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.32
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.51
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.39
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.17
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.94
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.21
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  373.80
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:55.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:04.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7004.20
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:55.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.24
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.09
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:18.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.30
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.40
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:39.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4911.48
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:06.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45890
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869890
  j =  1                              :        399908226
  j =  2                              :            45878
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45998
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869998
  j =  1                              :        399908007
  j =  2                              :            45992
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:36.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:27.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:57.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:14.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:55.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:37.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.67e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 4.85e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:24.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.19
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:24.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:42.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.42
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.57
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.64
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.46
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.31
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:51.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.89
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.87
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.28
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17726.50
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.71
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.73
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.68
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.20
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.07
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.25
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.38
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.52
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.38
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.77
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.16
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.24
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.82
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.02
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.35
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.55
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.44
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  568.13
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.16
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.55
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.20
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.64
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5185.79
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.71
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.08
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.61
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.82
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.42
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.46
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.49
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.83
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :   0.061
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:21.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.21
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :    0.86
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:19.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 4.52e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 8.97e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.39
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.13
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.12
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:02.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.53
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:03.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10124.47
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10285.01
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.085
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:04:21.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.41
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5007.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:58.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4228.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4078.10
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11934.24
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:35.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11885.06
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:36.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.59
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  7999914669

Normal statistic for number of bits   :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.37
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000109975

Normal statistic for number of bits   :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:16.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.81
p-value of test                       :    0.96

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:49.90

 All tests were passed




Server wird beendet - Lösche Semaphor 17891348.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1267
p-value of test                       :    0.9959

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334387
  j =  1                              :        599997466
  j =  2                              :             1267
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5262
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:56.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:41.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:56.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:59.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:06.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:06.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:56.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:00.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:49.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.81
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    2.96
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     329
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:15.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.15
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:47.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.70
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.69
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.37
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.54
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.46
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.18
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.12
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.80
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.94
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:42.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1446.93
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:00.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6882.94
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:42.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.17
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.64
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:03.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.46
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   87.10
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:32.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5005.15
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:23.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45832
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869832
  j =  1                              :        399908339
  j =  2                              :            45826
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45722
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869722
  j =  1                              :        399908563
  j =  2                              :            45708
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:30.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:24.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :  4.2e-3

Anderson-Darling statistic = A2       :    3.76
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:53.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :  3.4e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    5.09
p-value of test                       :  2.7e-3


-----------------------------------------------
CPU time used                    :  00:02:03.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:55.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:35.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.50e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:26.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:33.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:32.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.71
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.80
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.16
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.78
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.81
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   51.61
p-value of test                       :  6.0e-3

-----------------------------------------------
CPU time used                    :  00:02:01.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.38
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.02
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.84
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.46
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.17
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17603.03
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.07
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.89
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.57
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.99
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.75
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.65
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.73
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.02
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.00
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.50
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.03
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.04
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.88
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.60
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.26
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.71
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.24
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.18
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.76
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.45
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:42.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.68
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.36
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.00
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.91
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.45
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:34.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  458.00
p-value of test                       :  5.6e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.21
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4984.59
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.29
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.33
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   27.78
p-value of test                       :  5.9e-3


-----------------------------------------------
Normal statistic for number of jumps  :   -1.32
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:20.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.26
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :   -1.35
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:20.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.30e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.67
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.12
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.86
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:04.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.51
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:02.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10123.09
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9925.49
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.050
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:36.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4811.64
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:49.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.76
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:50.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4061.10
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4161.15
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11988.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11523.97
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.02
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000041569

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.00
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000023074

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 9.98e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:24.70

 All tests were passed




Server wird beendet - Lösche Semaphor 18939924.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5385
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:57.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:42.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:58.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:05.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:06.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:55.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:01.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.94
p-value of test                       :  9.5e-3

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.81
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:17.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:45.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.80
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.97
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.76
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.06
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.14
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.74
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.54
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.64
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  189.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  473.19
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:41.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1455.92
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:00.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6966.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:41.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.52
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:03.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.60
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  152.75
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:31.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5088.07
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:23.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46612
p-value of test                       :  3.3e-4    *****


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870612
  j =  1                              :        399906779
  j =  2                              :            46606
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45525
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869525
  j =  1                              :        399908953
  j =  2                              :            45519
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 8.19e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:30.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:24.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:52.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:07.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:56.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:35.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 5.92e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.013
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:30.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:31.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   96.35
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.51
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.99
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.43
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.69
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.43
p-value of test                       :    0.9954

-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.13
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:42.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.32
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.39
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.96
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.28
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:38.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17366.85
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:52.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.09
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.45
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.45
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.87
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.72
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.70
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.65
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.51
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.21
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.34
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.53
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.34
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.15
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.62
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.31
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.49
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.32
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.00
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.97
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:43.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.36
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.56
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4876.95
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.06
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.12
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.29
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.92
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.44
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.29
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.45
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:34.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.52
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :   0.083
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:20.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.06
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -0.63
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:21.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :  -0.022
p-value of test                       :    0.51

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.80

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.83e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 3.31e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.53
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.39
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.67
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:03.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.25
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:03.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.93
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.72
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:36.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4833.28
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:50.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4995.47
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.55
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4233.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11662.83
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11862.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.62
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000148204

Normal statistic for number of bits   :    1.17
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.71
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999909545

Normal statistic for number of bits   :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:05.51
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 44  CollisionPermut, r = 0          3.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19988500.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5385
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:59.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4456
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:43.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7131
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:44.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:00.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4247
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:01.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7444
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:09.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:09.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:04:02.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:06.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.36
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.97
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:48.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:16.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.43
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:46.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.19
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.07
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.02
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.37
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.60
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.00
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.83
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.32
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.51
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.71
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:49.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1393.25
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:01.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6673.51
p-value of test                       :    0.9993    *****

-----------------------------------------------
CPU time used                    :  00:01:48.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.99
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:05.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.34
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.23
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:32.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4970.15
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:50.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45836
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869836
  j =  1                              :        399908329
  j =  2                              :            45834
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46175
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870175
  j =  1                              :        399907652
  j =  2                              :            46171
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:22.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:13.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:49.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:31.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 2.67e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.66e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.34e-5
p-value of test                       :    0.9928

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:21.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.86
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.75
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.61
p-value of test                       :  8.5e-3

-----------------------------------------------
CPU time used                    :  00:00:47.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.67
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.20
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.69
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:44.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.61
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.06
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.30
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17429.69
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:47.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.46
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.50
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.56
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.31
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.53
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.14
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.32
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.05
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.78
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.46
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:34.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.15
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.70
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.81
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.29
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.59
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.26
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.59
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  414.20
p-value of test                       :    0.9979


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.33
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.48
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.59
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.03
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.55
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.20
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.11
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:31.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.56
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.59
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5044.22
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.32
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.41
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:31.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.24
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :  -0.046
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:07.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.89
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :    0.82
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:08.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 7.15e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:40.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.71e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 9.67e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:39.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.46
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.13
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.10
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:53.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.97
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:53.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9940.46
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  1.7e-3

Anderson-Darling statistic = A2       :    5.06
p-value of test                       :  2.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10359.57
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:49.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.075
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:15.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4926.32
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:39.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4850.98
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:41.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4218.58
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.28
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11834.51
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12010.65
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.58
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999997007

Normal statistic for number of bits   :  -0.024
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:58.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.38
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999991400

Normal statistic for number of bits   :  -0.068
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    2.48
p-value of test                       :  8.0e-3

-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   02:57:35.96
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 37  Gap, r = 20                     0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 21037076.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:20.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:23.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:16.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5419
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:42.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4222
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:36.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:35.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:55.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:55.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:02.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:02.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:54.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:04:00.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:52.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:10.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9911

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:30.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.79
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.54
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.63
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.44
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:11.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.63
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.67
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.31
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.74
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  370.11
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:51.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1444.18
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:03.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7085.30
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:51.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.51
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.46
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:01.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.74
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:46.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.17
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:36.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5138.24
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45998
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869998
  j =  1                              :        399908008
  j =  2                              :            45990
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45650
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869650
  j =  1                              :        399908704
  j =  2                              :            45642
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:14.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:27.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:18.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:44.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:59.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:52.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 6.67e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:22.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:35.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:36.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.93
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.75
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.98
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:51.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.60
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.22
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.27
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:44.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.88
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:31.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.66
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.52
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:39.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17205.10
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.09
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.69
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.88
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.32
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.22
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.21
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.86
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.19
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.25
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.53
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.26
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.64
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.25
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.22
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.45
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:46.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.25
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.42
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.08
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.79
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.71
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.76
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.22
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4935.98
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.82
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.07
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.26
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.18
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4892.89
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.75
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.35
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.42
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:19.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.21
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :   -1.88
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:15.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   0.049
p-value of test                       :    0.48

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.88e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 9.24e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-2
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 6.59e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.52
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.61
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.23
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:10.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.32
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:08.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9821.06
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9904.71
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.039
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:48.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.09
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:48.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.75
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:50.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4209.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.78
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11927.74
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12087.11
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:30.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.44
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000030280

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.51
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  8000055183

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.75e-3
p-value of test                       :    0.9928

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.75
p-value of test                       :    0.04

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.62
p-value of test                       :    0.05

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:18:32.56

 All tests were passed




Server wird beendet - Lösche Semaphor 819221.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:05.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:12.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5528
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:46.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:37.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7164
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:36.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:55.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:55.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:02.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:02.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:54.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:59.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.86
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:48.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.55
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:14.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.71
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:44.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.00
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.56
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.71
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.69
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:10.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.08
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  200.37
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.12
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:48.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1479.48
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:04.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7188.61
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   41.83
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:02.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.52
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.62
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5065.21
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:19.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45719
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869719
  j =  1                              :        399908566
  j =  2                              :            45711
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46136
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870136
  j =  1                              :        399907729
  j =  2                              :            46134
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:27.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:17.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:45.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:59.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:53.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :  4.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    3.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:33.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.033
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:34.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.60
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.33
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.71
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.83
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.65
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.16
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:44.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.87
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.54
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.06
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.85
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:30.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 9.49e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.37
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17325.03
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.99
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.61
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.18
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.49
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.47
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.59
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.35
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.76
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.15
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.95
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.33
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.18
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.90
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.41
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.63
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.84
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.91
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.68
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.16
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.20
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.79
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.47
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5026.65
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.33
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  439.69
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.62
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.07
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.03
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  242.01
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.77
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :    1.70
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:25.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.01
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :   -1.74
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:26.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.52
p-value of test                       :    0.94

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 6.54e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:47.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :  4.0e-3

Kolmogorov-Smirnov- statistic = D-    : 4.12e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.37
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:29.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.55
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.46
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:08.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:08.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10135.72
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9956.97
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.031
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:55.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4740.68
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4972.70
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4172.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.90
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11737.67
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11905.56
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:31.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.98
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000092059

Normal statistic for number of bits   :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.44
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999963932

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.87

Sample variance                       :    1.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:43.51

 All tests were passed




Server wird beendet - Lösche Semaphor 1671189.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5438
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:48.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:39.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:38.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:02.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:03.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:54.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:04:00.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    3.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:47.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.66
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.31
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     341
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:11.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:38.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.81
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.96
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.00
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.41
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.86
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.72
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.71
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.46
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.62
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.93
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:44.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1467.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7086.11
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.79
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.68
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:01.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.19
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.61
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:35.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5002.45
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:14.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45936
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869936
  j =  1                              :        399908132
  j =  2                              :            45928
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46105
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870105
  j =  1                              :        399907794
  j =  2                              :            46097
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :  6.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:28.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:17.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:44.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:00.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  1.4e-3

Anderson-Darling statistic = A2       :    3.42
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:54.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 2.70e-3
p-value of test                       :    0.9972

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:33.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.83
p-value of test                       :    0.9977

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.026
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:33.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:32.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.76
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.35
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.53
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.40
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.08
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.77
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.70
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:44.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.58
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.25
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.81
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.13
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17331.73
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.51
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.90
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.75
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.74
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.65
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.37
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.27
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.11
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.40
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.31
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.70
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.87
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.56
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.31
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.38
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.07
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.89
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.01
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   49.49
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.96
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.50
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5107.52
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.16
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.70
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.45
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.59
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4874.06
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.79
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.62
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.64
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :    2.12
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.53
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   -0.54
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:24.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :  -0.011
p-value of test                       :    0.50

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.91e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.97e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.24
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.58
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.77
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:10.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.3e-3

Anderson-Darling statistic = A2       :    3.94
p-value of test                       :  9.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  249.92
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:02:08.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10101.87
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9968.14
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:53.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4776.95
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4826.48
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:50.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.20
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4310.86
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11659.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:28.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11846.55
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:31.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.63
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999972746

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.84
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000018625

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.6e-3

Anderson-Darling statistic = A2       :    3.89
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.22
p-value of test                       :    0.01

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:52.70

 All tests were passed




Server wird beendet - Lösche Semaphor 2883605.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:41.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:52.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5335
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:49.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:38.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:37.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:55.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4237
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:55.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:02.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:03.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:54.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:58.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:48.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     644
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    3.86
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    2.31
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:14.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.17
p-value of test                       :  7.9e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     130
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    2.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:46.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.64
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.47
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.44
p-value of test                       :    0.9941

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.98
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.97
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.64
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.44
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.56
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.24
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:45.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1376.23
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:01.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7017.93
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.37
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:02.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.47
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.81
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:34.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4997.82
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:02.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46285
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870285
  j =  1                              :        399907433
  j =  2                              :            46279
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46217
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870217
  j =  1                              :        399907569
  j =  2                              :            46211
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:27.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:18.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:45.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:00.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:33.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:22.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:21.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:36.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:36.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.08
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.55
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.49
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:49.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.88
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   17.85
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   45.84
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.13
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.24
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17322.67
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.26
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.64
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.29
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.86
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.05
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.01
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.71
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.32
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.43
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.56
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.40
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.98
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.93
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.65
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.75
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.06
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.82
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.65
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.17
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.67
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.37
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.36
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.22
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.40
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  237.53
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.00
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.22
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5108.54
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.15
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.79
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.84
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   -1.23
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:22.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.17
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :    1.78
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:24.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 5.14e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 5.40e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.95
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.74
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.41
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:08.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.60
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:06.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9879.52
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10081.30
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:45.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.67
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:48.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5057.76
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:49.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.84
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.18
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11716.11
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:29.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12015.43
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:29.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.97
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999993101

Normal statistic for number of bits   :  -0.055
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.19
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000011287

Normal statistic for number of bits   :   0.089
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.32
p-value of test                       :    0.01

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:11.59

 All tests were passed




Server wird beendet - Lösche Semaphor 3801109.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1459
p-value of test                       :  5.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334579
  j =  1                              :        599997082
  j =  2                              :             1459
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5329
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:50.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4461
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:38.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7098
p-value of test                       :    0.9951


-----------------------------------------------
CPU time used                    :  00:02:38.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:55.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:03.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:03.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:54.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:04:00.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.75
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.77
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     865
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.92
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:11.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    3.42
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    2.05
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:40.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.79
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.78
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.29
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.80
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.58
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1452.63
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:01.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6883.00
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:44.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.27
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:17.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:02.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.56
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.69
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:35.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4978.54
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:01.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46194
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870194
  j =  1                              :        399907614
  j =  2                              :            46190
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45529
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869529
  j =  1                              :        399908943
  j =  2                              :            45527
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:28.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:18.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:45.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9924

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:01.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:55.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:33.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.75e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 2.79e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:21.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.19
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:21.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:32.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:34.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.19
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.91
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.08
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:48.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.42
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.54
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.39
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   62.93
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.66
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.22
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17698.42
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.15
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.90
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.83
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.51
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.19
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:39.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.87
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.53
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.98
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.29
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.82
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.97
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.77
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.15
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.85
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.53
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.32
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.98
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.25
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.63
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.07
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.05
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  460.75
p-value of test                       :  4.3e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4724.91
p-value of test                       :    0.9974


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.31
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.44
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.64
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.08
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4957.56
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.07
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.48
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.25
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:28.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.18
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:25.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.60
p-value of test                       :    0.95

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.09e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 9.14e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.06
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.53
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.11
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:07.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.15
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:07.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10082.80
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10014.38
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:43.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4962.62
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5033.11
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:49.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4272.19
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4173.37
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12045.25
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11567.47
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:29.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.07
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999973415

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.80
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000053785

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9903

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:33.67

 All tests were passed




Server wird beendet - Lösche Semaphor 4784149.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:39.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1461
p-value of test                       :  4.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334581
  j =  1                              :        599997078
  j =  2                              :             1461
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5438
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:52.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:39.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7528
p-value of test                       :  7.4e-3


-----------------------------------------------
CPU time used                    :  00:02:38.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4244
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:57.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7122
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:04.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:02.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:55.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:04:00.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.19
p-value of test                       :    0.9919

-----------------------------------------------
CPU time used                    :  00:01:46.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.13
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    2.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:11.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:43.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.40
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.57
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.88
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.36
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.98
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.39
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.85
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.08
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1416.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:59.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6947.77
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:46.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.27
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:02.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.21
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:33.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5056.46
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:56.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45989
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869989
  j =  1                              :        399908026
  j =  2                              :            45981
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45978
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869978
  j =  1                              :        399908047
  j =  2                              :            45972
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:28.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:18.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:45.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:58.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 7.07e-4
p-value of test                       :    0.9993    *****

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:55.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9935

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:33.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 5.05e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:37.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:43.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.62
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.84
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.41
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.99
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.99
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.35
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:40.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.26
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.04
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.67
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17635.24
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.31
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.38
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.58
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.29
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.81
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.38
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.08
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.79
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.11
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.60
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.85
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.04
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.52
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.13
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.36
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.64
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.25
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  434.73
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.96
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.86
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  325.31
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.80
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5109.75
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.18
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.28
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.57
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.08
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5181.79
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.55
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.61
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.60
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:24.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.62
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :   -0.92
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:23.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    0.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.95e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:46.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 2.69e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.45
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.11
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.03
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:07.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.41
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:10.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9885.86
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9939.08
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.94
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:43.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.59
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:48.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4714.02
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:50.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.46
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3897.18
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11798.14
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:29.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11839.72
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:30.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.11
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999832886

Normal statistic for number of bits   :   -1.32
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.64
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999961832

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.15
p-value of test                       :    0.98

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.19
p-value of test                       :    0.12

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.85
p-value of test                       :    0.97

Sample variance                       :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:09.27

 All tests were passed




Server wird beendet - Lösche Semaphor 5668885.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1261
p-value of test                       :    0.9975

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334381
  j =  1                              :        599997478
  j =  2                              :             1261
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5401
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:54.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:40.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:57.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:05.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:03.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:53.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:59.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    2.39
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     834
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    3.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:49.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.75
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.63
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     632
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:12.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:45.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.60
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.42
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.55
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.71
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.38
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.49
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.07
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  190.54
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  471.60
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:43.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1493.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:00.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6901.57
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:41.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.44
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.28
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:02.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.39
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  148.55
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:34.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4953.61
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:02.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45865
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869865
  j =  1                              :        399908274
  j =  2                              :            45857
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45873
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869873
  j =  1                              :        399908255
  j =  2                              :            45871
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 9.03e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:28.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:19.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:45.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:58.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:34.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:21.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:33.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.018
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:32.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.38
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.08
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.69
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:49.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.83
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.39
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.72
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:40.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.50
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.51
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.71
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.55
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17629.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.78
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.02
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.95
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.99
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.96
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.53
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.64
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.08
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.29
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.00
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.26
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.84
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.55
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.22
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.54
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.11
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.15
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  571.36
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.99
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.56
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.14
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.08
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4773.45
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.05
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.80
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.84
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.74
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4947.93
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.57
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  244.38
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.68
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :   -1.48
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:22.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.55
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :   -1.28
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:24.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 4.47e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 4.22e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.24
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.49
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.84
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:05.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.2e-3

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.83
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:06.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9721.89
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9836.35
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:44.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5019.76
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:48.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.08
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:51.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.73
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.03
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11939.04
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11476.12
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:29.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.31
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000147661

Normal statistic for number of bits   :    1.17
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.98
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000154630

Normal statistic for number of bits   :    1.22
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   0.089
p-value of test                       :    0.46

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:28.63

 All tests were passed




Server wird beendet - Lösche Semaphor 6651925.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:39.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5474
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:57.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7198
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:41.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:56.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:58.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:05.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:05.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:57.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:58.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    2.15
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     952
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:47.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    2.16
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:13.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:43.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.57
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.14
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.19
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.27
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.70
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.73
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:44.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.41
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:05.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6998.14
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:46.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.75
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:18.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.38
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.40
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:35.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5230.77
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:57.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45852
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869852
  j =  1                              :        399908298
  j =  2                              :            45848
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46073
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870073
  j =  1                              :        399907857
  j =  2                              :            46067
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:28.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:15.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:45.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:01.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:56.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.38e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.26e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 8.21e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:25.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:22.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:22.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:36.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.32
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:51.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.51
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.57
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   62.37
p-value of test                       :  5.6e-3

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.05
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.05
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:45.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.33
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.18
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.68
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.30
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.31
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17536.11
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.85
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.61
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.73
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.94
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.99
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:38.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.88
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.11
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.99
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.59
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.06
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.35
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.93
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.42
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.25
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.67
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.48
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.34
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.07
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.88
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.53
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.05
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.33
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4960.48
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.56
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.63
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.39
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.60
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4849.05
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.09
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.78
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.29
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:23.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.43
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:25.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 8.00e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 9.03e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.25
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.94
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.52
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:07.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.82
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:04.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10006.10
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9914.75
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.078
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:04:13.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.23
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:52.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5070.17
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:50.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.38
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.71
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11757.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11938.57
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:30.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.92
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000122272

Normal statistic for number of bits   :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.85
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999979124

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    2.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    2.71
p-value of test                       :  3.7e-3

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:04.29

 All tests were passed




Server wird beendet - Lösche Semaphor 7700501.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5475
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:58.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:42.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:57.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:57.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:04.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:04.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:54.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7116
p-value of test                       :    0.9911


-----------------------------------------------
CPU time used                    :  00:03:59.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.26
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.22
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     342
p-value of test                       :  9.3e-3

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:12.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.00
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.62
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:43.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.42
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   19.68
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.61
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.73
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.74
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.03
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.59
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.17
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  469.54
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:43.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.03
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:02.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6894.66
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:43.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.22
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   40.49
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:02.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.42
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.17
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:32.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5186.10
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:54.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45922
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869922
  j =  1                              :        399908160
  j =  2                              :            45914
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45725
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869725
  j =  1                              :        399908552
  j =  2                              :            45721
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:28.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:17.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:45.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:59.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:55.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:35.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.23e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 8.60e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.051
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:34.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:34.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.59
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:49.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.58
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.25
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.26
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.93
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.97
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.61
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:38.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.86
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.52
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.32
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.58
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17352.04
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.18
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.60
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.19
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.06
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.28
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.35
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.72
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.65
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.89
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.34
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.77
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  104.77
p-value of test                       :    0.9959


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.69
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.79
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.43
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.38
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.30
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.59
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.94
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.41
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.09
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.88
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5152.52
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.11
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  161.17
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.18
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.09
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.86
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.15
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.92
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.36
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:23.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.37
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:22.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 8.55e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 5.68e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.10
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.22
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.69
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:07.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.89
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:06.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9867.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10054.32
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:47.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4753.53
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:51.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.62e-3
p-value of test                       :    0.9907

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5050.26
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:50.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4180.22
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.01
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11796.59
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11682.83
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.89
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999996962

Normal statistic for number of bits   :  -0.024
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.19
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000146116

Normal statistic for number of bits   :    1.16
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9920

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:49.29

 All tests were passed




Server wird beendet - Lösche Semaphor 8716309.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:50.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5466
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:57.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:44.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7536
p-value of test                       :  5.7e-3


-----------------------------------------------
CPU time used                    :  00:02:43.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:59.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:58.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:06.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7509
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:05.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:54.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:59.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.11
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     946
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    2.65
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:49.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.83
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    5.26
p-value of test                       :  2.2e-3

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:13.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.69
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.82
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.39
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:15.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.89
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.47
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.90
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:43.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1389.78
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:01.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7028.00
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:42.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.00
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   87.53
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:03:01.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.10
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.60
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:33.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5030.88
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:54.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45760
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869760
  j =  1                              :        399908484
  j =  2                              :            45752
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45701
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869701
  j =  1                              :        399908599
  j =  2                              :            45699
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:26.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:18.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:46.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:00.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:55.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:35.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.33e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 1.40e-5
p-value of test                       :    0.9921

Anderson-Darling statistic = A2       :    3.94
p-value of test                       :  9.3e-3

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.49e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 3.06e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      : -6.78e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:34.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:34.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.56
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.67
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.21
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.38
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.69
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.61
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:38.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.25
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.18
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.53
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:16.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.5e-3

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.13
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17580.88
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.84
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.14
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.42
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.80
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.68
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.92
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.98
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.37
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.39
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.57
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:37.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.69
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.16
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.56
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.88
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.26
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.46
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.03
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.89
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.27
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.50
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.40
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.35
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.15
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.76
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.40
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.10
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.29
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.44
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.66
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.86
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.71
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :    0.57
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:23.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.12
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:23.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 7.22e-4
p-value of test                       :    0.9953

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 3.93e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.64
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.97
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.92e-3
p-value of test                       :    0.9938

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  243.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:06.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.71
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:07.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10034.62
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9718.57
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:41.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4804.98
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4954.67
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:49.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4204.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4179.31
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11802.76
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11751.50
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.56
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999982307

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.32
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000086995

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:04.54

 All tests were passed




Server wird beendet - Lösche Semaphor 9732117.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:51.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5323
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:00.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4241
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:44.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:00.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4441
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:00.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:08.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:07.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:54.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:01.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.19
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    2.67
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:51.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    2.74
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:18.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.61
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:47.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.51
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.62
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.75
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.72
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.77
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.04
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.34
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.09
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.78
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:44.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1542.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:02.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7069.42
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.76
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.32
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:02.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.87
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.29
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:33.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4954.61
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:04.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45911
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869911
  j =  1                              :        399908181
  j =  2                              :            45905
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45962
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869962
  j =  1                              :        399908077
  j =  2                              :            45960
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:27.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:18.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:45.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:59.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 4.96e-3
p-value of test                       :    0.9946

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.31e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 5.07e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.23
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:21.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:36.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.51
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:01:37.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   37.17
p-value of test                       :    0.9988

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.20
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.40
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.60
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.88
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.70
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.61
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.87
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.75
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.57
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17358.30
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.37
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.57
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.13
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.94
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.00
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.45
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.56
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.30
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.87
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.52
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.33
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.51
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.04
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.73
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.05
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.25
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.63
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.80
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  101.47
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.81
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.23
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4851.28
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.41
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.18
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.10
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.59
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.20
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.22
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.66
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.72
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :   -1.22
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:22.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.38
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   -1.90
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:22.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :  -0.043
p-value of test                       :    0.52

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:10.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 8.20e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.45e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.15
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.04
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.15
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:06.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.95
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:07.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9951.81
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10084.40
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.022
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:41.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4844.09
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.48
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:49.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4002.36
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.44
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11762.86
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11800.81
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:29.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.10
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000147319

Normal statistic for number of bits   :    1.16
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.97
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999992507

Normal statistic for number of bits   :  -0.059
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:06.13

 All tests were passed




Server wird beendet - Lösche Semaphor 10780693.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1459
p-value of test                       :  5.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334579
  j =  1                              :        599997082
  j =  2                              :             1459
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5481
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:04:00.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:43.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:47.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:59.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:01.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:11.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:11.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:04:03.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:05.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    2.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:50.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    3.99
p-value of test                       :  8.8e-3

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:14.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:45.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.94
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.82
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.44
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.61
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.59
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:11.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.49
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.13
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.54
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.38
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.66
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1303.13
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:02:05.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6936.81
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.77
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:08.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.62
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.64
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4962.49
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:06.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45978
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869978
  j =  1                              :        399908046
  j =  2                              :            45974
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45925
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869925
  j =  1                              :        399908152
  j =  2                              :            45921
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:29.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:18.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:02.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 7.46e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.64e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 8.03e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      : 5.01e-5
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.32
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:42.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.86
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:50.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.34
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.71
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.25
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.63
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.27
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.66
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.39
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.09
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.57
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.57
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17148.12
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.44
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.46
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.12
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.79
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.00
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.33
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.16
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.92
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.19
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.67
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  101.24
p-value of test                       :    0.9982


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.30
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.56
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.91
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.66
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  106.58
p-value of test                       :    0.9940


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.10
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.03
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.74
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.44
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.28
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.02
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5110.57
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  325.45
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.08
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  466.60
p-value of test                       :  2.4e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.43
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4906.26
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.91
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.39
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.12
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:23.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.04
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:22.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.72e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 7.99e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.47
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.97
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9936

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.56
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:06.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.81
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:07.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9914.89
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9829.71
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:04:16.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4793.90
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:53.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4867.88
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:53.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4016.85
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.14
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11931.47
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:30.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11864.66
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:31.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.16
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000001357

Normal statistic for number of bits   :   0.011
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.78
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999898025

Normal statistic for number of bits   :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:09.36

 All tests were passed




Server wird beendet - Lösche Semaphor 11862037.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5361
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:01.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:44.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:00.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:01.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:11.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:08.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:02.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:07.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    5.42
p-value of test                       :  1.8e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.72
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:15.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:42.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.76
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.36
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.31
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.66
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  267.78
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  393.68
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1387.40
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:05.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7114.79
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:50.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.46
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.56
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:07.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.28
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.45
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:36.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4970.54
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:12.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:06.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45887
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869887
  j =  1                              :        399908234
  j =  2                              :            45871
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45474
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869474
  j =  1                              :        399909057
  j =  2                              :            45464
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  9.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:29.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:19.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:47.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:05.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:36.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.03e-4
p-value of test                       :  1.5e-3

Kolmogorov-Smirnov- statistic = D-    : 2.94e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.77
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.72e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:44.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:45.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.70
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:50.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.69
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.50
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.22
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.87
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.27
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.29
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.13
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17355.64
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.85
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.38
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.83
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.46
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.51
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.99
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.01
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.11
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.06
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.83
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.33
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.56
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.62
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.17
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.21
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.52
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.35
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.45
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.39
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.27
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.20
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  448.89
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.96
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.74
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.11
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.07
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.85
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5092.11
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.56
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.73
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.41
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :    0.69
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:23.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.11
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:22.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.72
p-value of test                       :    0.96

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 2.55e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.92e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.60
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.73
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.91
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:03.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.94
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:06.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10195.52
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9802.18
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:04:19.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.43
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:52.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.80
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:54.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4029.47
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4029.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12093.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:31.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11871.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:31.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.56
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999916031

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.66
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000018298

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.55
p-value of test                       :    0.94

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    2.39
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:11.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:04.30

 All tests were passed




Server wird beendet - Lösche Semaphor 12943381.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5499
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:59.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:42.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:58.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:58.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:07.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:07.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:57.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:00.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:47.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.75
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     636
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    2.08
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9935

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:14.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:44.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   18.90
p-value of test                       :  8.5e-3

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.38
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.29
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.21
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.59
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.87
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.36
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.70
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.90
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:43.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1385.39
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:03.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7071.95
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.52
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.50
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:02.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.43
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:46.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.74
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:33.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4958.18
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:11.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:05.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46247
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870247
  j =  1                              :        399907509
  j =  2                              :            46241
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45739
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869739
  j =  1                              :        399908526
  j =  2                              :            45731
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:28.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:19.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:45.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:03.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:54.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:32.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 5.66e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.97
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:21.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:35.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.03
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.50
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   40.07
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.74
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.87
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.06
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:44.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.07
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.27
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:28.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 8.90e-3
p-value of test                       :    0.9904

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  102.02
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17629.12
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.92
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.24
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.85
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.49
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.94
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.31
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.25
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.21
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.68
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.98
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.48
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.42
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.53
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.51
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.76
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.80
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.51
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.66
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.70
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.72
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.57
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.92
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.78
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.56
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.97
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.79
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4921.10
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.51
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.37
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.03
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:22.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.74
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:23.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 4.56e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.93e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.55
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.68
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.89
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:06.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:06.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10083.49
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10142.75
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.070
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:47.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:48.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4910.52
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:49.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.46
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4281.88
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11719.30
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11868.31
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:29.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.15
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999980024

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.63
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999954236

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.51
p-value of test                       :    0.07

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   0.017
p-value of test                       :    0.49

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:35.72

 All tests were passed




Server wird beendet - Lösche Semaphor 14024725.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5466
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:58.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:42.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:57.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4453
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:58.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:08.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:07.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:57.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:04:00.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.08
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.77
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    2.53
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.02
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:14.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:42.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.74
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.66
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.33
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.01
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.70
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.43
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.23
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.51
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.44
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.89
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:44.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1492.18
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:02.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6996.95
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.73
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.97
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:03.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.69
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.43
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5086.32
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:04.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46173
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870173
  j =  1                              :        399907657
  j =  2                              :            46167
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45886
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869886
  j =  1                              :        399908235
  j =  2                              :            45872
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:27.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 5.79e-3
p-value of test                       :    0.9931

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:18.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:46.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9932


-----------------------------------------------
CPU time used                    :  00:02:00.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:33.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 7.92e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:32.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:33.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.44
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.31
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.14
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.06
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.39
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:38.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.67
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.32
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17255.57
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.75
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.07
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.73
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.63
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.03
p-value of test                       :    0.9930


-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.90
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.99
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.56
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.65
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.64
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.11
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.00
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.45
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.82
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.11
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.87
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.19
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.36
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.08
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.63
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.95
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.67
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5025.06
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.59
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.27
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.46
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.15
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.48
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.50
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.83
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.23
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:24.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.88
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:25.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.44e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 4.54e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:43.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.66
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.61
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.05
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:06.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.40
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:06.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10142.85
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9824.07
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:40.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5053.03
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4915.62
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:49.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4206.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.44
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11856.09
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11624.70
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.29
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000193516

Normal statistic for number of bits   :    1.53
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.10
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999954491

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:53.93

 All tests were passed




Server wird beendet - Lösche Semaphor 15040533.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5457
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:02.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:43.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:55.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4245
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:04.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:15.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:37.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:34.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:14.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:49.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:48.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.84
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:14.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:42.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.88
p-value of test                       :    0.9965

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.39
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.57
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.39
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.94
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.81
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.26
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.17
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.50
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:44.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1515.41
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:01.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7100.58
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.51
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:03.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.09
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.71
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4860.53
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:21.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45751
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869751
  j =  1                              :        399908501
  j =  2                              :            45745
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45903
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869903
  j =  1                              :        399908194
  j =  2                              :            45903
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:30.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:34.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:03.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:22.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:33.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 3.70e-4
p-value of test                       :  4.2e-3

Anderson-Darling statistic = A2       :    4.82
p-value of test                       :  3.5e-3

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.39
p-value of test                       :  8.4e-3

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:33.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.25
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.07
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:14.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.85
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.35
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.43
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   68.79
p-value of test                       :  1.2e-3

-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:38.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.06
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.28
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:15.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  167.62
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17215.77
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.85
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.56
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.65
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.90
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.67
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:38.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.36
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.11
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.74
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.97
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.03
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.22
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.89
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.73
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.30
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.78
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.80
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.66
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.89
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  102.64
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.49
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.36
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.19
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5157.98
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.66
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.07
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.09
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.24
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.20
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  427.33
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.12
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.96
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:22.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.07
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :  -0.033
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:24.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   0.033
p-value of test                       :    0.49

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.30e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 3.85e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9941

-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.16e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.81
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.54
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.14
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:08.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.75
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:07.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9963.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10046.37
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:55.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:39.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.08
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4971.24
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:49.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4255.16
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.50
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11687.23
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11774.50
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:29.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.70
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000096430

Normal statistic for number of bits   :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.38
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999809063

Normal statistic for number of bits   :   -1.51
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:57.65

 All tests were passed




Server wird beendet - Lösche Semaphor 16056341.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:50.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5483
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:58.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:42.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:43.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:58.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:59.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:08.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:07.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:56.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:00.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    2.17
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:48.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:14.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.81
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:44.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.89
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.03
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.43
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.40
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.93
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.23
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  383.91
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:44.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1476.65
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:02.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6948.85
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.64
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.67
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:04.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.30
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.39
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:33.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5110.20
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:02.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45917
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869917
  j =  1                              :        399908170
  j =  2                              :            45909
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45438
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869438
  j =  1                              :        399909129
  j =  2                              :            45428
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:28.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:24.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:53.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:08.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:55.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:35.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.29e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:21.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.79
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.59
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.59
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.34
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:40.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.91
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.15
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.25
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.15
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.51
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17356.63
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.33
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.85
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.13
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.82
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.28
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.97
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.36
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.43
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.65
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.90
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.92
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.44
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.35
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.60
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.72
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.30
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.24
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.86
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.29
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.41
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  325.00
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5108.76
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.25
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.58
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.11
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.41
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.61
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.08
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.71
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.57
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :    1.78
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.09
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:22.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.20e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.95e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 8.24e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.68
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.25
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.78
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:06.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.33
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:08.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10195.28
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:39.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.5e-3

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5071.68
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:47.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4787.74
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:49.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4133.53
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3960.40
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11700.90
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11837.47
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:31.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.04
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999983192

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.43
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000005947

Normal statistic for number of bits   :   0.047
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   0.067
p-value of test                       :    0.47

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:52.67

 All tests were passed




Server wird beendet - Lösche Semaphor 17104917.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1267
p-value of test                       :    0.9959

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334387
  j =  1                              :        599997466
  j =  2                              :             1267
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5361
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:58.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7466
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:43.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:59.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:01.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:09.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:09.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:57.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:00.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.23
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.10
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.90
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     261
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:16.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:44.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.27
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.71
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.80
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.48
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.80
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.83
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.68
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.39
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.16
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.39
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:43.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1380.29
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:02.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7221.67
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:44.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.66
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:24.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.67
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.78
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:33.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4968.70
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:59.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45893
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869893
  j =  1                              :        399908219
  j =  2                              :            45883
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45642
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869642
  j =  1                              :        399908718
  j =  2                              :            45638
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:28.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :  8.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:19.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:50.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:07.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:35.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:24.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.04e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:22.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:32.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:34.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.73
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.85
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.01
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.83
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.02
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.81
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:42.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.08
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.81
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.63
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.15
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.45
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17656.35
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.32
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.90
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.91
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.99
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.08
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.70
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.39
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.37
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.47
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.07
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:38.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.13
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.07
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.59
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.60
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.59
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.56
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.69
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.65
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.54
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.93
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.76
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.46
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5151.46
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.87
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.29
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.88
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.73
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.92
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.60
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.38
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.80
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.12
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:23.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.28e-3
p-value of test                       :    0.9956

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.36
p-value of test                       :  9.2e-3

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    2.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 5.00e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.12e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 9.51e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.84
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.32
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.67
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:07.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.17
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:06.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10203.34
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10162.99
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:56.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4809.89
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:48.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4964.73
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.09
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4244.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11849.90
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:29.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11677.51
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:31.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.67
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999998705

Normal statistic for number of bits   :  -0.010
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.28
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  7999972017

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.69
p-value of test                       :    0.05

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:16.69

 All tests were passed




Server wird beendet - Lösche Semaphor 18120725.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5463
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:58.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:42.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:58.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:08.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7077
p-value of test                       :    0.9977


-----------------------------------------------
CPU time used                    :  00:03:07.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:54.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:59.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.78
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:49.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     567
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:15.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:14.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:46.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.24
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.71
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.84
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.34
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.30
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   82.62
p-value of test                       :  7.3e-3

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.78
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.40
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.69
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:48.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1559.28
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:03.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7216.37
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:46.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.28
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:03.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.59
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.66
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4945.96
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:00.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45955
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869955
  j =  1                              :        399908094
  j =  2                              :            45947
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45923
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869923
  j =  1                              :        399908160
  j =  2                              :            45911
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:28.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:23.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:52.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:07.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:55.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:35.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 9.65e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:36.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:36.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.46
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.39
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.46
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.51
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.57
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.05
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.62
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.93e-3
p-value of test                       :    0.9937

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  167.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:40.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17668.31
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.96
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.13
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.48
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.32
p-value of test                       :    0.9931


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   34.97
p-value of test                       :  6.3e-3


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.87
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.19
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.66
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.90
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.17
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.10
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.18
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  440.52
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.73
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.91
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.36
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.19
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.30
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.35
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.98
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.18
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.41
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4890.47
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.53
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.98
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.51
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.68
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5025.46
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.38
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.30
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.28
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   -0.40
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:23.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.75
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:23.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 7.24e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.06e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 7.80e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.37
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.63
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:04.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:05.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9944.96
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10046.36
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:46.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4887.33
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4834.84
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:50.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4034.54
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.55
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11755.61
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11926.49
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:29.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.17
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000129637

Normal statistic for number of bits   :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.49
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000011761

Normal statistic for number of bits   :   0.093
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    2.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:09.12

 All tests were passed




Server wird beendet - Lösche Semaphor 19136533.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9961


-----------------------------------------------
CPU time used                    :  00:00:49.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5386
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:57.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:42.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:58.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:58.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:07.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:07.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:55.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:00.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.02
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.43
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    2.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:16.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.47
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    3.41
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    2.82
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:42.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.20
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.19
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.03
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.96
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.44
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.97
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.31
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.77
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  495.96
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:44.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1475.70
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:02.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7141.42
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:42.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.75
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.69
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:02.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.35
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.28
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:33.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5056.00
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:56.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46282
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870282
  j =  1                              :        399907439
  j =  2                              :            46276
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45983
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869983
  j =  1                              :        399908035
  j =  2                              :            45981
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:26.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:24.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:52.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 4.88e-3
p-value of test                       :    0.9946

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:08.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:55.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:35.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.06e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.050
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:33.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.96
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.06
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.39
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.55
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:51.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.67
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:38.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.57
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.18
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.97
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.85
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.26
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.29
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17252.08
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.47
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.58
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.78
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.53
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.27
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.87
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.92
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.45
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.57
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.34
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.35
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.38
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  450.79
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.33
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.52
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.32
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.27
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.73
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.69
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.48
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.90
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.00
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4993.45
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.12
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.47
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.95
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.72
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4892.49
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.08
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.04
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.63
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :  -0.078
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:22.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.03
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :    1.85
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:23.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 2.58e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 7.84e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.38
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.54
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.81
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:05.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.55
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:06.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9898.46
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10086.58
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.36
p-value of test                       :    0.9909

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:40.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4913.14
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:47.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.63
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:49.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.03
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.24
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11725.09
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.96
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:29.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.17
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999931409

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.44
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  7999992528

Normal statistic for number of bits   :  -0.059
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :  -0.011
p-value of test                       :    0.50

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.27

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 3.10e-3
p-value of test                       :    0.9968

Anderson-Darling statistic = A2       :    3.70
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.81
p-value of test                       :    0.9975

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:59.70

 All tests were passed




Server wird beendet - Lösche Semaphor 20185109.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:19.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:22.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:17.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5298
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:42.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:36.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:35.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:55.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:02.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:02.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:54.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:04:00.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.00
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:52.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.55
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.74
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:11.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:34.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.70
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.88
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.00
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.21
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.88
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.43
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.09
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.71
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.75
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:54.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1446.91
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:03.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7121.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:52.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.96
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.66
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:01.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.96
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.86
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:35.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4981.46
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:13.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45979
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869979
  j =  1                              :        399908046
  j =  2                              :            45971
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45937
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869937
  j =  1                              :        399908129
  j =  2                              :            45931
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:28.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:17.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:44.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:59.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:52.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:34.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.00e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.66e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 6.84e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:22.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:21.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:36.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:35.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.21
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:50.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.45
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.63
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.11
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.84
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.82
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:46.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.65
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:30.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.12
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:29.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17417.65
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   62.85
p-value of test                       :  3.7e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.37
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.43
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.17
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.12
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.58
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.63
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.59
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.41
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.29
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:39.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.19
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.83
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.66
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.97
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.24
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.30
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.25
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.89
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.88
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.64
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.48
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.44
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4882.48
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.17
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.28
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.28
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.35
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5197.22
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.22
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.79
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.72
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:16.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.41
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :  -0.055
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:18.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.06e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 5.35e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.05
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.79
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  162.31
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:10.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.42
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:09.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9877.00
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10000.15
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.06
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.29
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:45.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4841.25
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4832.40
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:49.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.90
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.71
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11827.10
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11704.91
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:30.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.93
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999964739

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.29
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999969377

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.65
p-value of test                       :    0.95

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.71
p-value of test                       :    0.96

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:18:50.12

 All tests were passed




Server wird beendet - Lösche Semaphor 851990.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:42.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5401
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:45.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:37.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:36.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4442
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:55.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:01.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:02.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7172
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:54.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:59.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.59
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:48.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    2.42
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:12.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.70
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     172
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:42.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.06
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.40
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.52
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.39
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.44
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:11.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.54
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.98
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.35
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.04
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.04
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1383.09
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:02.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7212.56
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:45.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.82
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.36
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:00.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.18
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.41
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:34.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4906.06
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:09.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45779
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869779
  j =  1                              :        399908444
  j =  2                              :            45775
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45995
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869995
  j =  1                              :        399908012
  j =  2                              :            45991
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 6.61e-3
p-value of test                       :    0.9915

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:28.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:17.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:45.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:58.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:53.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:34.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.98e-4
p-value of test                       :  1.8e-3

Kolmogorov-Smirnov- statistic = D-    : 4.11e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.63
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 2.49e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:31.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:31.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.15
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.14
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.77
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.66
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:48.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.00
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.70
p-value of test                       :  8.3e-3

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.41
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.47
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:30.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:10.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.94
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17325.91
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.10
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.66
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.75
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.93
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.42
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.77
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.78
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.79
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.65
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.55
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.33
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.07
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.33
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.65
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.68
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.82
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.91
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.53
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.75
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.63
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.96
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.14
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.63
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.61
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.52
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.48
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  441.68
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5062.95
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.50
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  246.90
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:34.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.87
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:25.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.79
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:20.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   0.049
p-value of test                       :    0.48

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.92e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.40
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.47
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.19
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:11.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.38
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:09.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9973.78
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9973.87
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:46.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4940.43
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:46.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4844.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:49.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.24
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.82
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11849.38
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11705.60
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:29.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.48
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999964793

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   30.03
p-value of test                       :    0.9966


-----------------------------------------------
Total number of bits:  8000084697

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.56
p-value of test                       :    0.94

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:28.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.11

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:31.07

 All tests were passed




Server wird beendet - Lösche Semaphor 1835030.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5353
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:46.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:38.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7508
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:37.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:55.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:02.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:03.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:54.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:59.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:45.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    2.10
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     642
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.57
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:14.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.59
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    2.52
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:45.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.87
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.49
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.46
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.34
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.33
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  356.04
p-value of test                       :    0.9975

-----------------------------------------------
CPU time used                    :  00:01:42.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.25
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:01.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7041.70
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:00.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.05
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.26
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:34.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4861.92
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:06.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46101
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870101
  j =  1                              :        399907802
  j =  2                              :            46093
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46220
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870220
  j =  1                              :        399907564
  j =  2                              :            46212
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:30.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:18.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:44.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :  4.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    4.66
p-value of test                       :  4.3e-3


-----------------------------------------------
CPU time used                    :  00:01:59.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:55.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.44e-4
p-value of test                       :    0.9990    *****

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:33.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 5.43e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:36.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:36.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.92
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.89
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.56
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.96
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.31
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.28
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.84
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:44.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.30
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.76
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:29.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.76
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17433.87
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.37
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.74
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.37
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.23
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.17
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.11
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.37
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.13
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.23
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.69
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.87
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.73
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.38
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.18
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.99
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.16
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.61
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.77
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.70
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.44
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.36
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4881.41
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.18
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.67
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.57
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.57
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5106.28
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.15
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.19
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.75
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :    1.33
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:27.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.84
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:25.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 4.50e-3
p-value of test                       :    0.9953

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.85
p-value of test                       :    0.97

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.96e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 7.43e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.61
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.73
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.56
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:09.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  159.81
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:09.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10196.22
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.99e-3
p-value of test                       :    0.9937

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10317.19
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:54.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4915.30
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:50.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5004.28
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:49.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4250.69
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11949.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12068.43
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.73
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999911546

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.18
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000118276

Normal statistic for number of bits   :    0.94
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   0.086
p-value of test                       :    0.47

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.066
p-value of test                       :    0.53

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:22.73

 All tests were passed




Server wird beendet - Lösche Semaphor 2523158.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:48.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:38.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:37.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:54.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:55.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:02.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:02.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:52.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:58.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    4.64
p-value of test                       :  4.3e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     858
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    2.01
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.13
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     269
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:16.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    4.15
p-value of test                       :  7.4e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     127
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:43.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.23
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.27
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.32
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.20
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.81
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.40
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.58
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.89
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:43.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1338.16
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:02.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6915.10
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.36
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.08
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:01.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.83
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.87
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:35.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5111.67
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:09.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45731
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869731
  j =  1                              :        399908541
  j =  2                              :            45725
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46542
p-value of test                       :  1.0e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870542
  j =  1                              :        399906919
  j =  2                              :            46536
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:29.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:18.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:45.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:00.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:55.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:33.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.33e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:37.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:39.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.33
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.87
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.33
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.83
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.21
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.31
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.72
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.36
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.25
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:18.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  164.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17596.72
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.04
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.42
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   10.87
p-value of test                       :    0.9935


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.04
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.90
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.90
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.06
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.44
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.72
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.14
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.36
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.55
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.99
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.80
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   48.05
p-value of test                       :    0.9917


-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.51
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.39
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.18
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.88
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.27
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.52
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.20
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5071.81
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.86
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.38
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:36.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.99
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.41
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.58
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.95
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.52
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.30
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :    1.26
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:24.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.86
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  : -1.49e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:23.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.22
p-value of test                       :    0.9914

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.70e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 9.36e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 7.30e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.28
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.09
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:09.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:10.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10073.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9978.96
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:04:06.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4768.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:48.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.13
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.18
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4290.42
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11606.31
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:29.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11708.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:31.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.83
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000162877

Normal statistic for number of bits   :    1.29
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.64
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999915869

Normal statistic for number of bits   :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.68e-3
p-value of test                       :    0.9962

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.60
p-value of test                       :    0.05

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:10.80

 All tests were passed




Server wird beendet - Lösche Semaphor 3538966.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:39.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:52.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5455
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:49.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:39.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:37.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:54.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:04.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:05.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:55.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:58.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:14.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.16
p-value of test                       :    0.9981

-----------------------------------------------
CPU time used                    :  00:02:13.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:38.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   18.15
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.67
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.60
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.79
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.38
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.21
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.30
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.05
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1475.00
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:09.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7016.43
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:50.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.61
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.08
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:08.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.94
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.98
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:36.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4920.28
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:19.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46166
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870166
  j =  1                              :        399907674
  j =  2                              :            46154
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45705
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869705
  j =  1                              :        399908592
  j =  2                              :            45701
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 3.26e-3
p-value of test                       :    0.9963

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:30.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:19.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:46.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:02.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:56.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:36.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 3.67e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:43.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:43.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.01
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.60
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.42
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.61
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.67
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.27
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.14
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17597.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.73
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.17
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.23
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   44.54
p-value of test                       :  6.6e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.46
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.35
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.11
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.28
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.14
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.35
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.82
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.89
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.61
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.00
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.57
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.73
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.85
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.86
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.70
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.48
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  320.29
p-value of test                       :    0.9921


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4934.50
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.14
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.59
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.51
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.35
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4846.08
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.87
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.44
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.46
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:23.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.04
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :    0.99
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:24.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.28
p-value of test                       :    0.99

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 6.70e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:46.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 4.54e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.37
p-value of test                       :    0.9947

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.83
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.01
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:07.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.24
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:09.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10031.61
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9962.93
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.087
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.28
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:04:19.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4833.18
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:54.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4784.01
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:57.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4217.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.89
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11827.75
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12125.32
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:31.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.16
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999875393

Normal statistic for number of bits   :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   33.69
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  7999967181

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    2.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:12.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:28.97

 All tests were passed




Server wird beendet - Lösche Semaphor 4554774.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:52.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:51.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:39.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:39.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:55.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:03.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7483
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:02.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:53.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:59.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.96
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     273
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:14.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:42.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.22
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.94
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.89
p-value of test                       :    0.9928

-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.44
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.40
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.72
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.86
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  469.35
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:43.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1446.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:02.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7015.76
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:42.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.26
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.89
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:01.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.82
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.26
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4984.12
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:12.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45944
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869944
  j =  1                              :        399908116
  j =  2                              :            45936
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46065
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870065
  j =  1                              :        399907875
  j =  2                              :            46055
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:28.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:17.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:45.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:00.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:54.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:34.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 4.68e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:21.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.083
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:33.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:33.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.06
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.25
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.61
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:48.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.23
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.20
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.34
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:41.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.91
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.28
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.29
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.29
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.17e-3
p-value of test                       :    0.9946

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  159.47
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17437.33
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.79
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.99
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.18
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.24
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.96
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.28
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.30
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.21
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.79
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.61
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:38.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.16
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.13
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.62
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.27
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.36
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.66
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.25
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  439.59
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.34
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.85
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.69
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.35
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4905.28
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.91
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.59
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.35
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.46
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5180.12
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.15
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.30
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.31
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:24.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.20
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:25.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.68
p-value of test                       :    0.05

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.06e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 9.87e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.46e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 8.89e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.93
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:28.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.87
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:05.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.27
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:08.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9956.97
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10009.84
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:04:02.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4725.12
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:49.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4788.89
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:50.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4159.56
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4034.28
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12116.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11919.71
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:29.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.37
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999821048

Normal statistic for number of bits   :   -1.41
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.76
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999998237

Normal statistic for number of bits   :  -0.014
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.68
p-value of test                       :    0.95

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.91

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:11.17

 All tests were passed




Server wird beendet - Lösche Semaphor 5898262.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5298
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:55.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4450
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:40.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4218
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:56.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7476
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:03.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:03.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:55.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7198
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:00.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:54.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    2.90
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     263
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:16.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:44.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.60
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.98
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.23
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.81
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:10.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.29
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.11
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.93
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.46
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  477.73
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:43.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1421.07
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:00.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6996.77
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:42.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.66
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.74
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:01.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.62
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.85
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:34.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4921.10
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9963


-----------------------------------------------
CPU time used                    :  00:03:00.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45927
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869927
  j =  1                              :        399908152
  j =  2                              :            45915
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45570
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869570
  j =  1                              :        399908861
  j =  2                              :            45568
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:28.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:19.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:45.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:58.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:55.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:33.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 8.79e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.58e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.081
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.51
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.22
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  105.31
p-value of test                       :  2.0e-3

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.64
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.40
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.43
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:43.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.34
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.44
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.59
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.87
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.9998    *****

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  173.88
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17115.80
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.50
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.94
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.12
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.29
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   35.20
p-value of test                       :  5.9e-3


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.06
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.11
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.30
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.76
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.20
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.10
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.16
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.78
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.43
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.17
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  106.10
p-value of test                       :    0.9946


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.30
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.86
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.39
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.62
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.48
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.24
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4961.93
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.36
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.77
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.60
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.75
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.08
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.56
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.50
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.28
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:23.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.39
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :   -0.40
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:24.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :  -0.027
p-value of test                       :    0.51

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.44e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.58e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.14
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.35
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:06.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.34
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:06.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10169.92
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9919.22
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:58.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.88
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:48.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4907.95
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:50.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.05
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.61
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12186.03
p-value of test                       :  9.9e-3

-----------------------------------------------
CPU time used                    :  00:01:28.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11707.90
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:28.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.62
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  7999953297

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.83
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  7999934883

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    2.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:49.88

 All tests were passed




Server wird beendet - Lösche Semaphor 6881302.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:40.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:51.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5438
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:55.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:56.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:04.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:04.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:58.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:00.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.92
p-value of test                       :  1.0e-2


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     272
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.69
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:14.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:42.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.72
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.79
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.48
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.56
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   87.01
p-value of test                       :  2.9e-3

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.06
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.53
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.74
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.39
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:44.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.67
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:01.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6861.15
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:40.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:01.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.61
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.69
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:33.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4977.54
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:01.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45683
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869683
  j =  1                              :        399908636
  j =  2                              :            45679
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45551
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869551
  j =  1                              :        399908901
  j =  2                              :            45545
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :  4.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:28.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:18.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:46.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:00.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:33.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:33.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:33.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.34
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.78
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.46
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.77
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:42.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.02
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.57
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.59
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17351.21
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:52.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   14.81
p-value of test                       :    0.9993    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.51
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.27
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.89
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.06
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.38
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.55
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.97
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.33
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.52
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.53
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.85
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.45
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.59
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.94
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.75
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.54
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.23
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  102.87
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.48
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.87
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  447.31
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4907.20
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.68
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.54
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.59
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.76
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5073.13
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.96
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.31
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.35
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:24.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.49
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :   -1.52
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:23.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.97e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.41e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 7.76e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.00
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.50
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.13
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:06.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.75
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:08.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9848.32
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9759.56
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.19
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:03:49.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5033.66
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:49.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4975.17
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:51.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3913.72
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4157.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11658.60
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:29.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.82
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:31.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.74
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999988934

Normal statistic for number of bits   :  -0.087
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.62
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999906350

Normal statistic for number of bits   :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:09.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    2.25
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:46.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 H (L=50, r=0)       0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7798806.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:39.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:50.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1232
p-value of test                       :    0.9999    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334352
  j =  1                              :        599997536
  j =  2                              :             1232
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5367
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:57.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4232
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:56.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:57.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:05.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:05.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7473
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:55.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:59.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    2.04
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:50.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.94
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:13.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.96
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.63
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:39.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.05
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.55
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.06
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.59
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.67
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.94
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.75
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:43.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1567.37
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:02:02.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6966.29
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:42.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.26
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   84.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:02.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.80
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:46.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.81
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4990.70
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:54.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45957
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869957
  j =  1                              :        399908089
  j =  2                              :            45951
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46381
p-value of test                       :  9.8e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870381
  j =  1                              :        399907241
  j =  2                              :            46375
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:27.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:17.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:43.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:58.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:55.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 3.64e-3
p-value of test                       :    0.9961

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:34.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.92e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 8.84e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.05e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.50e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:21.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:35.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:34.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.57
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.72
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.81
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:51.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.70
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:48.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.06
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.74
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:38.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.20
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.32
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.51
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.86
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17543.17
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.48
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.45
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.95
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.67
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.82
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.06
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.58
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.24
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.98
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.68
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.05
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.94
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.48
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.92
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.79
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.45
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.86
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.30
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.52
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.54
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.22
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.76
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4940.32
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.78
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.09
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.72
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.06
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.47
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.37
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.16
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.76
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :    0.99
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:22.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.40
p-value of test                       :    0.9920


-----------------------------------------------
Normal statistic for number of jumps  :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:22.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    0.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.68
p-value of test                       :    0.05

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 7.19e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.17e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.35
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.90
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:06.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.85
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:06.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9959.71
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.40e-3
p-value of test                       :    0.9986

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9723.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.060
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:55.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:46.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4905.96
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:50.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5001.18
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:49.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.46
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4291.53
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11915.32
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11768.17
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:29.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.30
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999773774

Normal statistic for number of bits   :   -1.79
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.88
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999871145

Normal statistic for number of bits   :   -1.02
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.96
p-value of test                       :    0.03

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:40.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           0.9999 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8781846.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:50.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5428
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:57.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:42.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:43.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:58.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:05.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:05.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:55.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7486
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:59.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.51
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.88
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:20.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.21
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:46.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.50
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.60
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.17
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.97
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.14
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.11
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.58
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.34
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:43.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1363.71
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:03.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6744.59
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:42.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.37
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:02.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.40
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.21
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:32.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4872.64
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:53.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45938
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869938
  j =  1                              :        399908127
  j =  2                              :            45932
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45712
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869712
  j =  1                              :        399908586
  j =  2                              :            45692
  j =  3                              :               10
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:26.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:18.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:45.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:00.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:55.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:35.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.70e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 8.10e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:36.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:36.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.40
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.69
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   59.17
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   50.96
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:01:38.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.71
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.73
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.41
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:16.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.00
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17230.73
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.85
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.77
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.48
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.57
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.45
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.19
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.28
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.88
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.04
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.64
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.10
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.70
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.96
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.05
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.73
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.01
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.50
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.12
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.10
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.50
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.74
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.50
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.05
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.69
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.60
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.30
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.14
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.74
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.09
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :   0.052
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:22.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.84
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:22.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    0.20
p-value of test                       :    0.9942

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 2.25e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.88e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.27
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.25
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.17
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:05.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.86
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:07.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10164.50
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9990.23
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:41.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4980.63
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:47.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.14e-3
p-value of test                       :    0.9989

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4662.36
p-value of test                       :    0.9901

-----------------------------------------------
CPU time used                    :  00:01:49.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4225.83
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4130.32
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12027.40
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11641.00
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.95
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999964355

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.19
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000051589

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:01.02

 All tests were passed




Server wird beendet - Lösche Semaphor 9764886.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9917


-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1264
p-value of test                       :    0.9968

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334384
  j =  1                              :        599997472
  j =  2                              :             1264
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5524
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:00.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:43.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7477
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:44.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4530
p-value of test                       :  1.8e-3


-----------------------------------------------
CPU time used                    :  00:02:00.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4240
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:00.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:08.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:07.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:54.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:01.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    2.17
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     840
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:53.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.96
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    2.35
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     649
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    6.57
p-value of test                       :  5.4e-4    *****

-----------------------------------------------
CPU time used                    :  00:02:18.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:45.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.95
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.45
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.00
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.68
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.69
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.71
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.34
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.61
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:43.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1365.51
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:02.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7192.28
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:42.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.67
p-value of test                       :  5.0e-3

Anderson-Darling statistic = A2       :    3.68
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   47.90
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.28
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:02.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.77
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.38
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:34.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5183.05
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:59.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45757
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869757
  j =  1                              :        399908489
  j =  2                              :            45751
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45808
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869808
  j =  1                              :        399908388
  j =  2                              :            45800
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:27.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:18.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:45.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:00.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:55.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:34.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 2.46e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:21.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:36.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:37.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.23
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.35
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.70
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   65.69
p-value of test                       :  2.5e-3

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.28
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:41.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.81
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.39
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.056
p-value of test                       :    0.9966

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.54
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17384.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.47
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.91
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.95
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.67
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.27
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.23
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   56.15
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.50
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.24
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    4.62
p-value of test                       :    0.9987


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.22
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.68
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  450.14
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.83
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.32
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.02
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.91
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.89
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.97
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.64
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.61
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.32
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.47
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.38
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.70
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.16
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  445.43
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5078.30
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.14
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.87
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.67
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:23.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.90
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:22.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.52e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.23e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 7.57e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.95
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.44
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.57
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:06.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.31
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:08.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10210.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9962.37
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:40.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4841.95
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4722.44
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:49.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4029.98
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.86
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11541.15
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11901.86
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.05
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000016162

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.44
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999951602

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.93

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.66
p-value of test                       :    0.95

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:37.67
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP2S, t = 9         5.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 10813462.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:50.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5309
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:01.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:44.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:47.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:01.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:02.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:12.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:13.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:06.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:07.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:51.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.14
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    2.60
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.14
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:02:19.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:50.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.04
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.31
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.68
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.95
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.57
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.86
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.14
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.44
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1489.17
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:04.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7033.65
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:52.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.27
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 8.07e-3
p-value of test                       :    0.9913

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   39.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:14.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.51
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   80.28
p-value of test                       :    0.9975


-----------------------------------------------
CPU time used                    :  00:01:37.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4860.33
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:58.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46145
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870145
  j =  1                              :        399907713
  j =  2                              :            46139
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45960
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869960
  j =  1                              :        399908086
  j =  2                              :            45948
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:30.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-3
p-value of test                       :    0.9983

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:19.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:06.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:36.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 7.11e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:24.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.29
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.10
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.79
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.99
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.44
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.74
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:49.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.56
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.26
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.58
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17300.61
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.42
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.71
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.69
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.46
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.71
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.85
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.70
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.21
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.89
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.42
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.17
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.23
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.99
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.23
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.00
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.42
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.56
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.74
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.95
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.46
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.88
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.62
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.56
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.31
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.88
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  329.71
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4839.84
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.99
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.98
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.26
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:23.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.11
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -1.05
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:23.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.23

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 9.54e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.97e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.90
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.36
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:07.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.04
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:07.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9796.72
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9861.51
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.096
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.097
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:04:24.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4902.56
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:55.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.94
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:56.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.61
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.72
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11551.19
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:33.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11996.07
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:33.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.80
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000094144

Normal statistic for number of bits   :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.19
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999986717

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         : 4.42e-3
p-value of test                       :    0.50

Sample variance                       :    2.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:00.76

 All tests were passed




Server wird beendet - Lösche Semaphor 11829270.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:50.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5431
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:56.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:42.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7147
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:43.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4189
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:58.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:07.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:06.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:56.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7464
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:02.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.86
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.85
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     959
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    2.62
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:50.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:17.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.94
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:49.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.88
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.74
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.19
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.37
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.01
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.41
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:44.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.78
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:02.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6970.47
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.12
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:03.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.89
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.32
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:34.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5134.91
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:55.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45718
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869718
  j =  1                              :        399908567
  j =  2                              :            45712
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46178
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870178
  j =  1                              :        399907645
  j =  2                              :            46176
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:27.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:17.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:45.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:00.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.63
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:55.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:33.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:21.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:35.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:35.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.56
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.05
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.03
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.05
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.98
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.16
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:42.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.29
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.97
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.80
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  151.82
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17157.29
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:52.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.50
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.75
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.25
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.56
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.21
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:36.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.90
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.43
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.69
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.36
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.34
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:37.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.83
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.60
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.98
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.91
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.90
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.75
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.46
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.92
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.14
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.00
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.09
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.05
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.42
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.52
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.81
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.29
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.88
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4926.28
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.66
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.01
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.26
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:24.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.27
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:25.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :  -0.054
p-value of test                       :    0.52

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 6.60e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.19e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.37
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.65
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.83
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:07.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.86
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:04.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10181.32
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9739.13
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:43.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4916.77
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5045.89
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:49.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.97
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.64
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11673.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11796.04
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.80
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000033703

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.97
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999998411

Normal statistic for number of bits   :  -0.013
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9930

Tests on the sum of all N observations
Standardized normal statistic         :  -0.094
p-value of test                       :    0.54

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9984

Tests on the sum of all N observations
Standardized normal statistic         :   0.066
p-value of test                       :    0.47

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:26.72

 All tests were passed




Server wird beendet - Lösche Semaphor 13008918.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:39.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1480
p-value of test                       :  1.0e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334600
  j =  1                              :        599997040
  j =  2                              :             1480
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1494
p-value of test                       :  2.8e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334614
  j =  1                              :        599997012
  j =  2                              :             1494
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5397
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:58.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4428
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:43.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:44.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:00.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:01.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7159
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:10.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7469
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:11.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:04:04.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:06.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.83
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    4.00
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:01:51.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    2.06
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    3.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9956

Stat. AD after spacings (mNP2-S)      :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:18.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.72
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:49.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.21
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:55.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.19
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.91
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.00
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.95
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.60
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.55
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  370.08
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:47.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1401.47
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:05.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7044.08
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.84
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.79
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:08.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.03
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.58
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:37.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5050.88
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:58.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45951
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869951
  j =  1                              :        399908102
  j =  2                              :            45943
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46097
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870097
  j =  1                              :        399907814
  j =  2                              :            46081
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:30.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:18.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:46.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:02.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 5.52e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.57e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.11
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:41.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:41.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.11
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.60
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.53
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.60
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.80
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.92
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:46.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.23
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.51
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.17
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.06
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.21
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17504.07
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.87
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.69
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.69
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.28
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.87
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.32
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.08
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.89
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.14
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.13
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.14
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.97
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  559.26
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.75
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.48
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.19
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.39
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.00
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.52
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.26
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.62
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.27
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4991.89
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.34
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.71
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.46
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.98
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4959.09
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  312.04
p-value of test                       :    0.9943


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.30
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.75
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :   0.034
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:21.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.63
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:23.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    2.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.49e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.20
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.85
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.33
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:06.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.67
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:06.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10007.53
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10288.70
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:04:19.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5010.39
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:52.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4805.53
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:53.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.72
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4224.96
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11614.31
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:31.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11913.15
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:31.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.59
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999859364

Normal statistic for number of bits   :   -1.11
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.05
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000016273

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.19
p-value of test                       :    0.12

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    2.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.036
p-value of test                       :    0.49

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:56.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 10  CollisionOver, t = 14           2.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13959190.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5376
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:56.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:42.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:57.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:59.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:07.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:07.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:56.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:00.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:51.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:18.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.90
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:48.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.63
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.94
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.16
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.58
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.43
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.66
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.09
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:43.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.54
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:02.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7154.38
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:42.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.93
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:03.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.16
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.34
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:33.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5113.40
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:58.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45779
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869779
  j =  1                              :        399908447
  j =  2                              :            45769
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46116
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870116
  j =  1                              :        399907774
  j =  2                              :            46104
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :  1.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.34
p-value of test                       :  6.1e-3


-----------------------------------------------
CPU time used                    :  00:02:26.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:20.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:46.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 9.60e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.28e-3
p-value of test                       :    0.9976

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:02.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:54.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:33.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 5.18e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.031
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:34.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.81
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.52
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   40.22
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.77
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.57
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.32
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:40.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.74
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17156.95
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.02
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.00
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.53
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.72
p-value of test                       :    0.9909


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.90
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.73
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.43
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.49
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.20
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.57
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:38.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.36
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.06
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.13
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  103.78
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.65
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.57
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  449.37
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.03
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.78
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.12
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.75
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.42
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.49
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.55
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.13
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.78
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5053.92
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.56
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.55
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :    1.51
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:21.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.16
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:22.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   0.033
p-value of test                       :    0.49

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    2.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.30e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 5.70e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.83e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.42
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.86
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  155.55
p-value of test                       :    0.9913

-----------------------------------------------
CPU time used                    :  00:02:07.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:09.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9997.99
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10235.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.052
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:44.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4826.61
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:48.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4867.48
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.51
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4226.34
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11781.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12090.56
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:29.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.46
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000013717

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.33
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000023020

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.60
p-value of test                       :    0.06

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:05.37

 All tests were passed




Server wird beendet - Lösche Semaphor 15073302.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:50.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5412
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:56.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4456
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:42.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:43.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:58.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4247
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:00.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:07.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:06.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:55.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7487
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:01.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:50.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.54
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:20.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:48.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.80
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.54
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.87
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.78
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.84
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.37
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  291.29
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.89
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:43.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1310.81
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:02:02.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7045.16
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.06
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.95
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:02.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.45
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.61
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5059.55
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:55.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45776
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869776
  j =  1                              :        399908451
  j =  2                              :            45770
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45767
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869767
  j =  1                              :        399908468
  j =  2                              :            45763
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:28.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.42
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9915


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.73
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:19.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:46.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:00.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:56.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:35.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:36.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.31
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.38
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.99
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.59
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.38
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.84
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.14
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:40.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.27
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.21
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.34
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.65
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17578.12
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.55
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   59.02
p-value of test                       :  6.8e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.79
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.07
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.28
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.39
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.07
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.62
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.90
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.25
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.40
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.27
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.06
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.53
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.12
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.76
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.06
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.07
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.72
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.76
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.97
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.22
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.78
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.52
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.30
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.36
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  445.82
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.93
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.50
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.69
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.20
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:24.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.23
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:25.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.65e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:46.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.41e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.14
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.21
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.70
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:06.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:07.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10072.36
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9768.49
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:42.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.50
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:47.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4960.18
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:50.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4015.48
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4272.49
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12110.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11783.76
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:29.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.81
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999861803

Normal statistic for number of bits   :   -1.09
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.41
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000144343

Normal statistic for number of bits   :    1.14
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.68
p-value of test                       :    0.95

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.87
p-value of test                       :    0.97

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.88
p-value of test                       :    0.97

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:15.88

 All tests were passed




Server wird beendet - Lösche Semaphor 16089110.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:50.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5423
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:58.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:43.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:43.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:58.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:00.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:06.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:07.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:56.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:04:00.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:50.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:16.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:18.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.92
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:52.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.01
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.93
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.33
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.90
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.48
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.00
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.09
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.00
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.90
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.88
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:43.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1388.14
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:02.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6883.91
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.65
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:03.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.86
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.16
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:34.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5100.66
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:58.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45978
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869978
  j =  1                              :        399908048
  j =  2                              :            45970
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46178
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870178
  j =  1                              :        399907652
  j =  2                              :            46162
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:28.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:19.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:46.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:00.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:35.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 7.00e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9924

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:35.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:35.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.36
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.53
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.11
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.52
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.12
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:40.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.13
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.28
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.46
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.04
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.17
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17408.57
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.07
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.74
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.99
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    8.93
p-value of test                       :    0.9977


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.06
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.12
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.13
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.07
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.47
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.66
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.98
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.35
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  554.92
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.17
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.95
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.02
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  195.96
p-value of test                       :  3.7e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  558.02
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.60
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.28
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.92
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.49
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.65
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.77
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.11
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.00
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.39
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.51
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.16
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.89
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.37
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :    1.97
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:24.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.05
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :   -0.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:25.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.89e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 5.05e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.42e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 7.99e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.11
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.21
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.68
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:06.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.03
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:07.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9846.72
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9969.14
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:39.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4801.53
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:48.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4952.18
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:49.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4118.38
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11976.18
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11759.80
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.54
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999961019

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.70
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000157270

Normal statistic for number of bits   :    1.24
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.51
p-value of test                       :    0.07

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.23
p-value of test                       :    0.9902

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9934

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.43

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:20.52

 All tests were passed




Server wird beendet - Lösche Semaphor 17137686.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5349
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:57.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:43.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:44.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4450
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:58.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:59.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:08.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:06.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7084
p-value of test                       :    0.9970


-----------------------------------------------
CPU time used                    :  00:03:55.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:04:01.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.9916

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:51.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:19.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     129
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    2.53
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:51.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.71
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.02
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.95
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.42
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.97
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.74
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  395.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:44.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1397.84
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:02.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7142.58
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.94
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.53
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:03.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.45
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.24
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:31.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5153.65
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:59.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45827
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869827
  j =  1                              :        399908349
  j =  2                              :            45821
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45753
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869753
  j =  1                              :        399908499
  j =  2                              :            45743
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 7.42e-3
p-value of test                       :    0.9901

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:27.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:18.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:45.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:01.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:55.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9913

-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 6.38e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:34.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:34.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.31
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.60
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.97
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.95
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:50.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.78
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.55
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:40.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.32
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.98
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.47
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.45
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17387.07
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.52
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.03
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.57
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.30
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.06
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.08
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.74
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.11
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.52
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.14
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.82
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.55
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.44
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.70
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.61
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.97
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.32
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.19
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.61
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.99
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.55
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.79
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.82
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.52
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.27
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.55
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.38
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.93
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.48
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.95
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.62
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:23.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.02
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:24.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.36e-3
p-value of test                       :    0.9933

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.73
p-value of test                       :    0.04

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 6.31e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.02e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.09
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.92
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.05
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:07.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:07.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10096.01
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10041.90
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.024
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:39.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.47
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.46
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:50.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.41
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4012.83
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11982.89
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11843.51
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:28.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.20
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000080566

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.57
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000123454

Normal statistic for number of bits   :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   0.043
p-value of test                       :    0.48

Sample variance                       :    2.44
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.77
p-value of test                       :    0.96

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         : -3.60e-3
p-value of test                       :    0.50

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:08.68

 All tests were passed




Server wird beendet - Lösche Semaphor 18153494.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5605
p-value of test                       :  6.6e-3


-----------------------------------------------
CPU time used                    :  00:03:58.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:44.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:00.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:01.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:11.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7511
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:08.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7063
p-value of test                       :    0.9986


-----------------------------------------------
CPU time used                    :  00:04:00.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:04:05.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:52.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     632
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:20.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:45.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.43
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.48
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.49
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.52
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.84
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.70
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.76
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  277.95
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  474.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:47.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1367.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:04.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7033.38
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:09.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.52
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.18
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4968.41
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:58.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46311
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870311
  j =  1                              :        399907384
  j =  2                              :            46299
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45823
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869823
  j =  1                              :        399908358
  j =  2                              :            45815
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:28.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:18.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:46.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:03.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:36.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 6.98e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:45.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.96
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:50.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.12
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.90
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.62
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.33
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.48
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.63
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.11
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.97
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.58
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:39.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17242.92
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.07
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.00
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.75
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.60
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.17
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.40
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.55
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.98
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.65
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.71
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.05
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.40
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  568.53
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.26
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.60
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.87
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.89
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.94
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.99
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.20
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.71
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.85
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4864.45
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.61
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.18
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.33
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.57
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.40
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.97
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  240.18
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.36
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :    1.35
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:24.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.94
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:23.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :  -0.092
p-value of test                       :    0.54

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.05e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 8.16e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9946

-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 5.46e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.33
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.74
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.39
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:05.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.83
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:06.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10093.09
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9855.25
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:04:21.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4826.84
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:53.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.66
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:54.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.14
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3996.41
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11788.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:31.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11907.25
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:31.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.33
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999974627

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.58
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999915305

Normal statistic for number of bits   :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.80e-3
p-value of test                       :    0.9928

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.72
p-value of test                       :    0.04

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   0.012
p-value of test                       :    0.50

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:50.15

 All tests were passed




Server wird beendet - Lösche Semaphor 19202070.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5478
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:57.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:43.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:58.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:06.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:05.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:56.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:00.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.92
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:49.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    3.44
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:12.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    3.91
p-value of test                       :  9.7e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     129
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:44.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.97
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.34
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.21
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.85
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.59
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.79
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.64
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.85
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:43.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1478.16
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:02.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6825.14
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.54
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.31
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:02.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.04
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.56
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:33.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5103.72
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:58.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45563
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869563
  j =  1                              :        399908877
  j =  2                              :            45557
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45748
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869748
  j =  1                              :        399908510
  j =  2                              :            45736
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:26.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:19.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 4.84e-3
p-value of test                       :    0.9947

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:46.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:58.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:35.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.79e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 3.65e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:35.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:34.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.20
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.65
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.26
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.07
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.58
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.36
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.34
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:01.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.52
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.28
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.24
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.51
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17145.32
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.81
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.19
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.31
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.01
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.91
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.84
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.58
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.37
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.71
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.22
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.73
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.52
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.80
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  172.33
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.44
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.40
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.75
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.71
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.16
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.55
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.60
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.58
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.12
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.06
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  248.30
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.61
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.73
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4756.18
p-value of test                       :    0.9933


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.15
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.09
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.02
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :   -1.47
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:23.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.84
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:23.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.12

Sample variance                       :    0.20
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.33e-3
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 3.40e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.77
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.07
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.91
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:05.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.16
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:06.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9800.14
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10176.93
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:46.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4966.90
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:47.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.60
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:49.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3981.96
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.80
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11500.07
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11867.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.66
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999982253

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.52
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000006184

Normal statistic for number of bits   :   0.049
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :  -0.014
p-value of test                       :    0.51

Sample variance                       :    1.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:47.26

 All tests were passed




Server wird beendet - Lösche Semaphor 20250646.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:18.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:19.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:14.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5350
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:42.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:36.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:34.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:55.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:55.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:02.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:01.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7177
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:54.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:59.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:52.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:10.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:34.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.64
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.50
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.38
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.27
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.88
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.70
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.16
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.95
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.54
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:54.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1510.81
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:03.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7036.30
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:52.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.25
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.99
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:01.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.79
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   91.02
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:35.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5103.49
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:14.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46111
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870111
  j =  1                              :        399907781
  j =  2                              :            46105
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45797
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869797
  j =  1                              :        399908406
  j =  2                              :            45797
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:28.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:18.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:45.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.64
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  5.4e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:57.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:37.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.47e-4
p-value of test                       :  8.1e-3

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:36.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:35.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.03
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.96
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.11
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.46
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.89
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:46.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:30.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:29.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:10.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:40.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17339.86
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.52
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.95
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.03
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.82
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.27
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.35
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.79
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.64
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.84
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.70
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.64
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.49
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.60
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.19
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.50
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.63
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.97
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.27
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.29
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.20
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.28
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.38
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4909.09
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.12
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.65
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:34.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.85
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.83
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.35
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.41
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.02
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:33.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.45
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :    2.36
p-value of test                       :  9.3e-3



-----------------------------------------------
CPU time used                    :  00:02:16.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.23
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :    1.80
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:19.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    2.45
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9993    *****

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:46.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.22e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 9.51e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.61
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.34
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:30.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.42
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:09.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.4e-3

Anderson-Darling statistic = A2       :    4.02
p-value of test                       :  8.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  252.45
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:02:08.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10028.67
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9828.58
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:47.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4845.61
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4787.97
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:49.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4197.65
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.62
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11653.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11896.49
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.07
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999949769

Normal statistic for number of bits   :   -0.40
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.79
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000031501

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:10.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:19:31.90

 All tests were passed




Server wird beendet - Lösche Semaphor 884759.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:43.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:55.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5385
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:45.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:37.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:36.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:54.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:54.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:01.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:02.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:54.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:59.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    2.40
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:48.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    2.27
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     637
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    2.45
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:14.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9951


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    3.35
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:44.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.61
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.82
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.72
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.48
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.28
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.65
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.47
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.78
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  470.80
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:45.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1421.91
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:03.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6949.24
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.71
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    3.61
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.97
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:02.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   14.80
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.77
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:35.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4994.01
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:15.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45851
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869851
  j =  1                              :        399908305
  j =  2                              :            45837
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46132
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870132
  j =  1                              :        399907740
  j =  2                              :            46124
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:28.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:17.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:45.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:59.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:53.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:33.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.56e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:22.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.90e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:21.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:21.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:33.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.21
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:48.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.93
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.65
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.62
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.56
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.51
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.98
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.20
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:30.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.13
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:33.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.29
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17599.98
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.92
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.43
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.72
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.86
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.64
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.54
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.71
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.87
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.13
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.64
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  105.07
p-value of test                       :    0.9957


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.66
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.07
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.46
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.95
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.20
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.30
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.27
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  171.12
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.88
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  312.32
p-value of test                       :    0.9970


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.89
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4991.31
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.37
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  143.68
p-value of test                       :    0.9990    *****


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.27
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.98
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5236.49
p-value of test                       :  9.8e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.80
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.65
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.06
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :    0.95
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:21.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.00
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :    1.13
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:22.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :  -0.011
p-value of test                       :    0.50

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.82e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.91e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 8.69e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.16
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.87
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.26
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  248.66
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:10.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.61
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:08.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9947.05
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9928.39
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.032
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:54.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4852.82
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:47.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4934.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:49.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4314.92
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4039.12
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12207.22
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11786.95
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:29.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.55
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999921458

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.06
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999805838

Normal statistic for number of bits   :   -1.53
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.67
p-value of test                       :    0.05

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:31.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 C (L=10000, r=0)    0.9990 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1867799.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5454
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:47.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:38.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:37.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4439
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:01.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:02.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:53.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:58.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    2.74
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     965
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:48.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.80
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.03
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:13.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:41.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.57
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.69
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.17
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.57
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.97
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.94
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.87
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.35
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:43.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1481.79
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:02.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6975.82
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.91
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:00.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.73
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  153.18
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:35.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5292.20
p-value of test                       :  6.4e-3


-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:20.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45581
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869581
  j =  1                              :        399908838
  j =  2                              :            45581
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46014
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870014
  j =  1                              :        399907977
  j =  2                              :            46004
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:29.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:18.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:46.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:01.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:54.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:33.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.97e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 8.85e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 2.06e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:22.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.022
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:34.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:34.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.30
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.24
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.73
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.01
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.58
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.92
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:42.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.86
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9918

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.43
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.59
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:30.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.61
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:29.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  156.64
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17470.10
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.28
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.52
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.42
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.60
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.38
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.67
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.30
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.60
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.87
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.44
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.36
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.83
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.38
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.66
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.69
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.57
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.13
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.52
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.95
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.51
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.73
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5104.04
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.85
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.11
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.89
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.27
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.40
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.33
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.58
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :    1.61
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:24.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.96
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:23.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.22
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.59
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.74
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:08.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:09.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9999.85
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9879.66
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:46.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4911.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:49.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4780.22
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:49.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.51
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4261.13
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11566.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11813.85
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:30.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.70
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000044548

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.03
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999984236

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:23.97

 All tests were passed




Server wird beendet - Lösche Semaphor 2654231.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  4.9e-3


-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5412
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:49.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:38.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:38.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:54.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4428
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:54.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:02.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:03.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7507
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:53.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:58.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:13.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.60
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.92
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:42.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.43
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.03
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.77
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.00
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.97
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.29
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:39.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.48
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:39.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  269.09
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:44.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1441.87
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:00.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7086.85
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:43.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.60
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.56
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:03.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.98
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.62
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:34.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5021.34
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:17.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45462
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869462
  j =  1                              :        399909078
  j =  2                              :            45458
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46200
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870200
  j =  1                              :        399907603
  j =  2                              :            46194
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  8.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    3.80
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:28.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:18.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:45.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:00.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:54.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:33.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.48e-4
p-value of test                       :  7.9e-3

Kolmogorov-Smirnov- statistic = D-    : 9.91e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.39e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 3.35e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:35.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.47
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:48.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.33
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.44
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.39
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   17.39
p-value of test                       :    0.9975

-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.99
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.57
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:40.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.57
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.62
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.11
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.50
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.77
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17678.31
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.17
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.49
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.83
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.16
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.61
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:38.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.47
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   55.22
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.25
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.96
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.10
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:39.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.82
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.30
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.67
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.86
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.62
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.01
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.99
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  596.09
p-value of test                       :  2.0e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.27
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.92
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.17
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.41
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5157.78
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.91
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.85
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.35
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.46
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5287.19
p-value of test                       :  2.4e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.09
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.10
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.30
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:23.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.69
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:23.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:12.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.16
p-value of test                       :    0.02

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.38e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 6.92e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.02e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 9.97e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.37
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.69
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 3.08e-3
p-value of test                       :    0.9968

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.90
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:09.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.47
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:08.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10106.42
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9972.53
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.044
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:50.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5042.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4966.12
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:49.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4070.07
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.75
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11669.95
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:29.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11672.21
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:30.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.79
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999977600

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.96
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999979343

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.029
p-value of test                       :    0.51

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:02.53

 All tests were passed




Server wird beendet - Lösche Semaphor 3670039.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:52.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1536
p-value of test                       :  2.7e-6    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334656
  j =  1                              :        599996928
  j =  2                              :             1536
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5494
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:50.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:39.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:37.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4485
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:55.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:56.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7506
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:02.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:03.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:54.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:58.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:49.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     648
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:14.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:41.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.71
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.64
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.79
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.96
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:10.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.68
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.90
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  471.26
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:50.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:00.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7003.21
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:42.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.88
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:17.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.71
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:01.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.88
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.36
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:34.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5001.68
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:02.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45890
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869890
  j =  1                              :        399908226
  j =  2                              :            45878
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45678
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869678
  j =  1                              :        399908648
  j =  2                              :            45670
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 7.11e-3
p-value of test                       :    0.9906

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:29.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9920


-----------------------------------------------
CPU time used                    :  00:02:18.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 3.70e-4
p-value of test                       :    0.9996    *****

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:00.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:55.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:34.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 7.72e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.80e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:22.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:31.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:35.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.95
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:48.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.04
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.90
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:48.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.62
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:37.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.61
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.84
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.96
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.73
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17382.20
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.92
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.76
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.86
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.33
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.49
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.76
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.69
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.54
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.98
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.08
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.31
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.27
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.29
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.41
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.27
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.91
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.48
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.96
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.14
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.95
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.08
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.15
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5093.05
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.74
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.02
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.24
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.75
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.11
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.10
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.13
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:36.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.19
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    0.86
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:26.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.07
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:25.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.74e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.84e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 5.37e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.76
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.54
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  240.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:06.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.08
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:07.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10275.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10066.71
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:48.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.88
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.29
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.58
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.43
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11718.82
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:28.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11634.78
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.05
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999976553

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.83
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999893150

Normal statistic for number of bits   :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.14

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.72

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:55.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  3  CollisionOver, t = 2            2.7e-6
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4587543.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:51.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5413
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:49.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:39.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7464
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:39.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4434
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:55.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:56.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:03.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:03.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:53.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7144
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:59.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:46.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    3.00
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:12.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.84
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:44.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.73
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.56
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.48
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.20
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.39
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.09
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.06
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.75
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.93
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.17
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:45.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.17
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:00.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6964.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:44.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.91
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:01.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.61
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.46
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:35.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5120.98
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:58.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46147
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870147
  j =  1                              :        399907711
  j =  2                              :            46137
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46024
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870024
  j =  1                              :        399907955
  j =  2                              :            46018
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9924

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:28.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:21.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 5.55e-3
p-value of test                       :    0.9938

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:59.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:33.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 9.92e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 6.47e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:21.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:34.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:35.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.08
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.28
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.43
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.91
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:41.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.2e-3

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.54
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  8.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.71
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.50
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.55
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:37.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17650.72
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.01
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.62
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.80
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.46
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.36
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.43
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.28
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.48
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.44
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.63
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.74
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.71
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.20
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.47
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.05
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.60
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.19
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.08
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.56
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.91
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.23
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.43
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.67
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.02
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.08
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.84
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.41
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.79
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.36
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.33
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.86
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :   -0.79
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:21.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.22
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :   -1.47
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:24.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.28e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.06
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.93
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.94
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:10.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.73
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:09.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10012.65
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9970.59
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:46.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4920.94
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:49.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4799.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:50.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.61
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4254.90
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12114.74
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:29.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12052.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.24
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999903629

Normal statistic for number of bits   :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.11
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999977060

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:50.38

 All tests were passed




Server wird beendet - Lösche Semaphor 5570583.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:51.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5349
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:56.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:43.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:59.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:01.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:10.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:10.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:04:08.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:12.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:48.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.88
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    3.09
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.66
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:17.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    5.50
p-value of test                       :  1.9e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    2.31
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:44.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.51
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.02
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:14.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.09
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:11.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.14
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   85.31
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.01
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:31.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.99
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:01.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1456.17
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:12.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7008.45
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.93
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.49
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:11.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.54
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:48.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  146.40
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:42.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4999.92
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:30.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:15.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46129
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870129
  j =  1                              :        399907743
  j =  2                              :            46127
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45520
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869520
  j =  1                              :        399908964
  j =  2                              :            45512
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:30.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:23.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:53.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:08.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:57.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 4.43e-3
p-value of test                       :    0.9952

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:39.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 7.10e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.09e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:24.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:51.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:50.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.07
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.50
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.44
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.20
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.83
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.10
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.15
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:51.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.85
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.25
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.91
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:28.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.31
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.16
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17240.44
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.17
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.86
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.00
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.86
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.56
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.52
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.40
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.55
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.53
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.36
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.10
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.62
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   98.97
p-value of test                       :    0.9928


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.29
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.37
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.56
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.72
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.87
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.61
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.29
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.91
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4835.56
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.23
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.08
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  463.58
p-value of test                       :  3.3e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.69
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4772.53
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.08
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.65
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.37
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :   -1.73
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:25.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.14
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:24.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.88e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 5.12e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.56
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.31
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:39.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.92
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:22.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.88
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:11.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10046.42
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9951.60
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:10.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:04:41.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.94
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:52.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5006.39
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.68
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.15
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11823.53
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:33.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11998.79
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:36.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.93
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  7999926789

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.88
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999971009

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:33.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9907

Tests on the sum of all N observations
Standardized normal statistic         :   0.048
p-value of test                       :    0.48

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:52.44

 All tests were passed




Server wird beendet - Lösche Semaphor 6750231.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1269
p-value of test                       :    0.9952

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334389
  j =  1                              :        599997462
  j =  2                              :             1269
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1466
p-value of test                       :  3.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334586
  j =  1                              :        599997068
  j =  2                              :             1466
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5526
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:54.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7452
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:41.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:59.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:59.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:07.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:10.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:03.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:05.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.32
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     959
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.95
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:14.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    2.47
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:15.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    3.99
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:02:41.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.53
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.63
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.23
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.47
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.03
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.01
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.81
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.26
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:53.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1438.69
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:01.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6936.06
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:54.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.43
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:13.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.09
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.37
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:49.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4936.10
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:13.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45436
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869436
  j =  1                              :        399909130
  j =  2                              :            45432
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45997
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869997
  j =  1                              :        399908010
  j =  2                              :            45989
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:31.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:19.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :  2.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    4.01
p-value of test                       :  8.8e-3


-----------------------------------------------
CPU time used                    :  00:01:48.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:05.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:56.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.51e-5
p-value of test                       : 1 -  1.5e-5    *****

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:37.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.44e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.75e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : -5.34e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.72
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:46.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.85
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.09
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.72
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:50.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.83
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.95
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.88
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:48.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.40
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.25
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:28.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.68
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17632.93
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.52
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.73
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.96
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.21
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.23
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   58.18
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.52
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.45
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.32
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.82
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.86
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.86
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.93
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  177.60
p-value of test                       :  9.6e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.35
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.19
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.81
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.62
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.49
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.40
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.42
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.91
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.71
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.28
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.49
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.52
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.83
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.43
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.92
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.54
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.47
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :    2.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:25.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.16
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:23.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.66
p-value of test                       :    0.95

Sample variance                       :    2.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.10
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.45e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.17e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 7.82e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.72
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.36
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:06.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.06
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:07.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10011.87
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10084.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.026
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:04:21.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4905.13
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:56.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4822.48
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:57.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3931.80
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4192.88
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11980.38
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:32.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11657.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:33.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.21
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999961355

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.46
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999859259

Normal statistic for number of bits   :   -1.11
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    1.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:12.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:51.12

 All tests were passed




Server wird beendet - Lösche Semaphor 8159255.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:50.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5449
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:53.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:41.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:57.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:57.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:05.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:05.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:54.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7486
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:00.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.69
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:46.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.53
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    2.88
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     552
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    2.38
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     334
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:13.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    2.38
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:42.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.74
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.51
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.57
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.61
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.45
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.57
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.21
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.21
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.28
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:43.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1411.09
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:00.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7007.46
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:44.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.22
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.40
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:02.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.89
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.48
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:35.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5155.47
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:54.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45975
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869975
  j =  1                              :        399908053
  j =  2                              :            45969
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45934
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869934
  j =  1                              :        399908135
  j =  2                              :            45928
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:27.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:17.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.99e-3
p-value of test                       :    0.9957

Anderson-Darling statistic = A2       :    3.60
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9954


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:44.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:59.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:35.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.68e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 4.70e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.90e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:24.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.12
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:22.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:22.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.080
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:35.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.25
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.78
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.35
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.20
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.98
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.01
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:46.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.17
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.70
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:29.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.52
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:29.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   93.48
p-value of test                       :    0.9934

-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17267.93
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.34
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.28
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.91
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.52
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.91
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.24
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.43
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.03
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.71
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.39
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.13
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.59
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.00
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.01
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.63
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.97
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.30
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.45
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.06
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.11
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.52
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.55
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5025.42
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.36
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.54
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.01
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  303.48
p-value of test                       :    0.9991    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.22
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  329.56
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.68
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.80
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:23.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.56
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :  -0.046
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:24.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :  -0.092
p-value of test                       :    0.54

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.11
p-value of test                       :    0.98

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.00e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.93e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 6.88e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.39
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.55
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.73
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:07.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.91
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:06.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10022.08
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9910.08
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.79
p-value of test                       :    0.9973

-----------------------------------------------
CPU time used                    :  00:03:46.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4735.81
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:48.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4795.61
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:49.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.85
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11887.72
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11900.53
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:29.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.05
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999838952

Normal statistic for number of bits   :   -1.27
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.64
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000123076

Normal statistic for number of bits   :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.81
p-value of test                       :    0.04

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:56.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 M (L=10000, r=15)   0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9306135.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5404
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:55.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:41.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:57.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:04.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:04.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:54.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:00.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.17
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.96
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:14.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:42.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.68
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.96
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.55
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.16
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.18
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.38
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.57
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:43.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1380.49
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:02.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6976.05
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:40.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.51
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.29
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:01.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.74
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.42
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:33.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4930.29
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:55.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45919
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869919
  j =  1                              :        399908170
  j =  2                              :            45903
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46144
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870144
  j =  1                              :        399907713
  j =  2                              :            46142
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:28.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:18.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.2e-3

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:45.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:59.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:57.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:35.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 5.73e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 6.80e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.062
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:21.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:34.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:34.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.98
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.81
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.73
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.49
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.66
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.13
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.06
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:29.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.19e-3
p-value of test                       :    0.9912

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  158.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17662.39
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.39
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.06
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.73
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.93
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.50
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.77
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.90
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.74
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.49
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.01
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.85
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.92
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.69
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.02
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.95
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.84
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.33
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.75
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.63
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.50
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.84
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.22
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5128.57
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  430.29
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.44
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.30
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.49
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4910.99
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.70
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.88
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.34
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:24.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.84
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:25.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.78

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.20e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 7.46e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 7.10e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.89
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.55
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.56
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:06.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.72
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:07.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9927.58
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10182.89
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.043
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:45.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4986.33
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.88
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:48.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4071.24
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.68
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12237.40
p-value of test                       :  4.0e-3

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11737.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.28
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999952355

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.77
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000095653

Normal statistic for number of bits   :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -2.08
p-value of test                       :    0.98

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   0.073
p-value of test                       :    0.47

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:50.45

 All tests were passed




Server wird beendet - Lösche Semaphor 10256407.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5496
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:58.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4455
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:43.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:44.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:00.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7148
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:11.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:10.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7131
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:04:06.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:10.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.05
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    1.94
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:46.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.70
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    2.69
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.15
p-value of test                       :    0.9988

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:15.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.77
p-value of test                       :  4.1e-3

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:45.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.52
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.23
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.19
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.45
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.55
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.48
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.42
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:28.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.51
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:55.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.99
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:03.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7184.94
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:54.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.29
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:16.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.00
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.76
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:38.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5073.12
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:01.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45828
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869828
  j =  1                              :        399908347
  j =  2                              :            45822
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46203
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870203
  j =  1                              :        399907596
  j =  2                              :            46199
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:33.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:19.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:51.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:07.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:56.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:38.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 5.40e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:49.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.49
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:50.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.46
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.69
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.47
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.52
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.27
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.08
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:49.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.75
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.34
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.60
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.32
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.35
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:43.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17205.35
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.53
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.88
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.31
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.43
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.88
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:36.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.45
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.42
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.35
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.23
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.76
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:36.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.49
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.44
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.72
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.84
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  110.07
p-value of test                       :  4.2e-3


-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.11
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.61
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.52
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.16
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.07
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.68
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.03
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.42
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.71
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.01
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.06
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.87
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.76
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.15
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.88
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.06
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :    1.55
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:23.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.25
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:24.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.97
p-value of test                       :    0.98

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.79e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 9.65e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.66e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.13
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.82
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.33
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:03.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.01
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:05.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.86
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10172.14
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.040
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:04:26.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5025.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:57.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4748.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:59.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4027.49
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4021.66
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11686.24
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:36.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11781.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:36.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.51
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999859124

Normal statistic for number of bits   :   -1.11
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.42
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999909881

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:15.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:30.22

 All tests were passed




Server wird beendet - Lösche Semaphor 11173911.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9982


-----------------------------------------------
CPU time used                    :  00:00:38.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:49.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5536
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:56.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:56.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4446
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:06.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:06.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:56.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:02.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:49.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    3.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:14.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:44.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.67
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.19
p-value of test                       :    0.9911

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.10
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.64
p-value of test                       :    0.9928

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.22
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.21
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.09
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.96
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.26
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:43.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1487.91
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:02.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6963.98
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:43.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.56
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.29
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:07.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.83
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.82
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:34.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4966.57
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:58.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46518
p-value of test                       :  1.5e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870518
  j =  1                              :        399906968
  j =  2                              :            46510
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45929
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869929
  j =  1                              :        399908142
  j =  2                              :            45929
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:27.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:17.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:44.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:58.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 6.05e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.36
p-value of test                       :    0.9909

-----------------------------------------------
CPU time used                    :  00:01:37.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:40.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.79
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.89
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.49
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.35
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.58
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.15
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.94
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:42.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.72
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.17
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.33
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17145.41
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.29
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.61
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.15
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.16
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.01
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   55.89
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.12
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.30
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.22
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.44
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.92
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.12
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.01
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.58
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.57
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.53
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.42
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.63
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.16
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.97
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.19
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.67
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.25
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.64
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.65
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.67
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.41
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4836.30
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.34
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.69
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.55
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:22.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.61
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   -1.58
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:24.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    2.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    2.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.60e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 4.44e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.30
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.18
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.69
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:08.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9915

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.14
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:07.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9744.18
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10121.48
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.016
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:40.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4936.64
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.05
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:49.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4068.99
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.91
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12245.60
p-value of test                       :  3.4e-3

-----------------------------------------------
CPU time used                    :  00:01:28.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12126.79
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:29.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.44
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999875573

Normal statistic for number of bits   :   -0.98
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.24
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999871127

Normal statistic for number of bits   :   -1.02
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :  -0.094
p-value of test                       :    0.54

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:06.45

 All tests were passed




Server wird beendet - Lösche Semaphor 12353559.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:49.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1467
p-value of test                       :  3.1e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334587
  j =  1                              :        599997066
  j =  2                              :             1467
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5462
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:58.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:42.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:42.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:58.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:00.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:08.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:07.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:04:00.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:04.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:49.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    2.85
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:15.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    2.92
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:44.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.04
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.11
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.49
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.12
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.20
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.05
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.24
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.77
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:50.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1484.09
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:04.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7092.98
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.93
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.77
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:08.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.69
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.45
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:36.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4909.23
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:02.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45839
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869839
  j =  1                              :        399908326
  j =  2                              :            45831
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46129
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870129
  j =  1                              :        399907744
  j =  2                              :            46125
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:30.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:20.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:06.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:57.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9952

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:37.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 8.48e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 5.16e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:46.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.77
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.38
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.42
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.64
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.69
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   56.95
p-value of test                       :  1.5e-3

-----------------------------------------------
CPU time used                    :  00:01:46.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.00
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9962

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.29
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.81
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17499.77
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.49
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.90
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.01
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.33
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.54
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:38.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.49
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.15
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.09
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.67
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.45
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.92
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  188.33
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.75
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.45
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.17
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:46.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.97
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.12
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.80
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.29
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.89
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.49
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.80
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.86
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.67
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.38
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.94
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.85
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4938.25
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.17
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.21
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.95
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:23.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.69
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :   -1.71
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:23.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 5.11e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 6.00e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.70
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.88
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.31
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:05.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.72
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:05.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10016.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9888.66
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:04:13.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4843.11
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:53.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.46
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:52.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.21
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4193.64
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11680.39
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11880.85
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:30.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.46
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999781853

Normal statistic for number of bits   :   -1.72
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.56
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000039826

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.4e-3

Anderson-Darling statistic = A2       :    3.39
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    1.94
p-value of test                       :    0.03

Sample variance                       :    0.18
p-value of test                       :    0.9962

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:11.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.57
p-value of test                       :    0.94

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:10.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:37.45

 All tests were passed




Server wird beendet - Lösche Semaphor 13336599.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5580
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:55.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:41.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:57.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:04.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:05.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:55.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:00.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.29
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:15.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.07
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    2.03
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:44.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.52
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.46
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.78
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.53
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.48
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.92
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  276.74
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  488.03
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:43.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1382.12
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:03.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7094.50
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.58
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.08
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:02.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.53
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.40
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:35.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5101.22
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:59.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45916
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869916
  j =  1                              :        399908169
  j =  2                              :            45914
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45621
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869621
  j =  1                              :        399908766
  j =  2                              :            45605
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:28.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:18.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:44.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:58.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:35.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.89e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.03e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.083
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:38.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.59
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.28
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.30
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.29
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.90
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:44.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.11
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.48
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.32
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.17
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17438.66
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.65
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.93
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.19
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.39
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.01
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.67
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   57.55
p-value of test                       :  9.5e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.26
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    7.95
p-value of test                       :    0.9991    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.36
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.51
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.25
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.79
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.38
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.43
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.17
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.39
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  616.44
p-value of test                       :  2.8e-4    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.96
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.30
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.48
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.21
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4903.18
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.91
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  159.34
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.47
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.32
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.50
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.70
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.16
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.71
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:25.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.75
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :    1.03
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:26.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 7.11e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:46.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.71e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 6.68e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.29
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.22
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:04.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.07
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:04.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9975.09
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10074.90
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:43.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4799.17
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:47.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4778.45
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:49.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.22
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.16
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12057.87
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11862.76
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:29.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.03
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000135505

Normal statistic for number of bits   :    1.07
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.70
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000163081

Normal statistic for number of bits   :    1.29
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.71
p-value of test                       :    0.04

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    2.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:01.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 75  RandomWalk1 R (L=50, r=25)      0.9991 
 77  RandomWalk1 J (L=1000, r=20)    2.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14450711.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5470
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:54.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:41.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:57.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:57.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:05.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:06.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:56.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:01.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    3.48
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     661
p-value of test                       :  7.4e-3

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    3.65
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:14.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    4.16
p-value of test                       :  7.3e-3

Stat. AD after spacings (mNP2-S)      :    2.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:44.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.07
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.84
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.59
p-value of test                       :    0.9932

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.64
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.54
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.17
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  202.62
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  495.72
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1509.80
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:03.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7012.79
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.58
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.40
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.51
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:02.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.94
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.09
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:34.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5097.50
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:00.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45911
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869911
  j =  1                              :        399908185
  j =  2                              :            45897
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45858
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869858
  j =  1                              :        399908288
  j =  2                              :            45850
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:27.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:19.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:00.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:57.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:35.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.81e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 6.17e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:22.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 7.37e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:38.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:38.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   94.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.91
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.71
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.62
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.76
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.44
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.67
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.39
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.49
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.05
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17532.24
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.42
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.71
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.62
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.04
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.12
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.68
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.85
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.80
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.91
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.19
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.08
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.64
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  445.28
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.03
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.11
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.03
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.46
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.88
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.58
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.52
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.74
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.79
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5044.66
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.42
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.96
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.31
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.18
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5178.29
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.51
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.94
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.47
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.87
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :   -1.32
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:24.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :  -0.092
p-value of test                       :    0.54

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.43
p-value of test                       :    0.08

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.11e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 9.56e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.42
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.64
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.58
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:05.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.23
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:08.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10222.19
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10025.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:41.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4929.90
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4824.27
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:49.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.45
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4157.85
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11757.00
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11620.69
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:29.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.46
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000039670

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.55
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999938966

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.59

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :  -0.056
p-value of test                       :    0.52

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    1.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:09.03

 All tests were passed




Server wird beendet - Lösche Semaphor 15466519.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  5.1e-3


-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5344
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:55.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7168
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:40.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:56.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:57.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:05.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:05.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:56.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:04:00.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     650
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.13
p-value of test                       :    0.9996    *****

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:15.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.84
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    2.44
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:42.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.68
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.09
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.31
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.71
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:10.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.61
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.94
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.17
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.61
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  485.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:43.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1467.06
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:02.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7208.12
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:42.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.21
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.58
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:02.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.01
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.76
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:34.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5077.65
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:00.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45716
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869716
  j =  1                              :        399908571
  j =  2                              :            45710
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45930
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869930
  j =  1                              :        399908143
  j =  2                              :            45924
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:27.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:18.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:45.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:00.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:36.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 7.91e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:42.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:40.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.67
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.06
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.21
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.16
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:49.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.11
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.62
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.81
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:45.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.19
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.31
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.78
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.07
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:28.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:18.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.08
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17448.66
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.44
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.23
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.60
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.30
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.93
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.53
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.40
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.04
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.29
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.63
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:37.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.23
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.11
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.40
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.26
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.00
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.23
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.73
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.42
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.63
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.33
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.54
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.44
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5110.03
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.80
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.50
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.39
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.16
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5034.67
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.16
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.70
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.80
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:23.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.66
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :   -1.29
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:23.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    1.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   0.043
p-value of test                       :    0.48

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 8.52e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 3.08e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.05
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.59
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.85
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:05.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.12
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:07.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10052.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9845.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.028
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.35
p-value of test                       :    0.9906

-----------------------------------------------
CPU time used                    :  00:03:44.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:46.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.62
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:50.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3914.44
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4147.71
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11731.00
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11555.61
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.31
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999967856

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.41
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000027997

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.15

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :  -0.052
p-value of test                       :    0.52

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:08.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs mNP2, t = 5          0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16547863.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:39.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:48.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5355
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:56.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:39.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:57.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:05.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:06.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:56.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:01.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     866
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     627
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    2.19
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.16
p-value of test                       :    0.9978


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.90
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     331
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:13.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    3.77
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:42.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.93
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.19
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.67
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.04
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.48
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.48
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.98
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.17
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.31
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.71
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:44.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1437.05
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:02.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6946.94
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:40.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.35
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.33
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:02.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.75
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  163.62
p-value of test                       :  4.2e-3


-----------------------------------------------
CPU time used                    :  00:01:32.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5055.31
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:59.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45841
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869841
  j =  1                              :        399908321
  j =  2                              :            45835
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45858
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869858
  j =  1                              :        399908286
  j =  2                              :            45854
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:28.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:18.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:00.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.68e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 3.04e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:35.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:36.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.10
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.21
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.14
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.31
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.01
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:38.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.55
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.04
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.56
p-value of test                       :  8.4e-3

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.44
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17145.80
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:54.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.80
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.23
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.17
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.59
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.81
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.10
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.74
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.62
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.30
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.38
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.26
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.04
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.36
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.49
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.03
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.50
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.64
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  556.34
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.20
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.63
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.81
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.50
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4978.90
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.13
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.42
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.65
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.85
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5114.32
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.08
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.34
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.07
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:21.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.72
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:25.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.27e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 8.28e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 4.67e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.74
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.58
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:05.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.80
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:05.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9877.37
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9936.89
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:43.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4822.13
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:47.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4979.65
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:51.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3987.80
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4210.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11622.94
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12009.71
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:29.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.25
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999992675

Normal statistic for number of bits   :  -0.058
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.46
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999970526

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.66
p-value of test                       :    0.05

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -2.08
p-value of test                       :    0.98

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.2e-3

Anderson-Darling statistic = A2       :    4.01
p-value of test                       :  9.0e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.12
p-value of test                       :    0.02

Sample variance                       :    0.18
p-value of test                       :    0.9964

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:22.87

 All tests were passed




Server wird beendet - Lösche Semaphor 17563671.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1270
p-value of test                       :    0.9948

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334390
  j =  1                              :        599997460
  j =  2                              :             1270
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5410
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:57.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:39.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:56.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7025
p-value of test                       :    0.9997    *****


-----------------------------------------------
CPU time used                    :  00:03:04.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:04.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:55.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:04:01.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:49.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:13.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:44.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.46
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.01
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.92
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.64
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.81
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.11
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.29
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.99
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.83
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:45.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1412.60
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:02.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7419.60
p-value of test                       :  9.7e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.56
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:15.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.13
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:02.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.34
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.28
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:34.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4976.84
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:58.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46010
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870010
  j =  1                              :        399907982
  j =  2                              :            46006
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46140
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870140
  j =  1                              :        399907726
  j =  2                              :            46128
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:27.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:17.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:44.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:00.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:35.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:33.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:37.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.24
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.36
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.55
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.15
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.08
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.52
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.11
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:38.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.58
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.15
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   17.10
p-value of test                       :  6.7e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  155.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17170.45
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.00
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.25
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.99
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.37
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.56
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.67
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.41
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.40
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.55
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.58
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.49
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.01
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.88
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.21
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.90
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.32
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.40
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.85
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.46
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.97
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.63
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.07
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  425.39
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.05
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.09
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.33
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5150.94
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.68
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.36
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.23
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :    2.37
p-value of test                       :  8.9e-3



-----------------------------------------------
CPU time used                    :  00:02:23.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.74
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:25.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.42e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.62e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 6.93e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.26
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.21
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.36
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:06.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.22
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:06.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9701.73
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9968.63
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    3.53
p-value of test                       :  2.0e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:44.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:47.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4914.21
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:50.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4184.89
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.84
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11941.27
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11519.35
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.56
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999977630

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.96
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000171715

Normal statistic for number of bits   :    1.36
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :  -0.075
p-value of test                       :    0.53

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.64
p-value of test                       :    0.95

Sample variance                       :    3.05
p-value of test                       :  1.2e-3

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:42.98
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 18  BirthdaySpacings, t = 8         0.9997 
 37  Gap, r = 20                     9.7e-4
 68  MatrixRank, L=1000, r=0         6.7e-4
 92  HammingCorr, L = 30             2.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18513943.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5290
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:56.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:56.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:57.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:05.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:05.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:54.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:01.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:48.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.86
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.93
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     564
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:14.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:43.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.99
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.59
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.25
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.69
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.98
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.30
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  192.77
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.61
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:44.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1410.79
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:02.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7024.66
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:41.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.83
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.27
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:02.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.62
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  148.18
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:32.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4953.12
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:00.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45990
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869990
  j =  1                              :        399908024
  j =  2                              :            45982
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45990
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869990
  j =  1                              :        399908023
  j =  2                              :            45984
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:28.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:19.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:59.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:55.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:35.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.04e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.95e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.62e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:38.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:37.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.66
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.62
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.39
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.66
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.06
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.71
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.28
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.64
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:28.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.43
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17305.11
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.01
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.82
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.32
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   43.11
p-value of test                       :  9.7e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.68
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.95
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.01
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.54
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.70
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.06
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.24
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.52
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.84
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.07
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.64
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.85
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.71
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.55
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.87
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.72
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.63
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.51
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.81
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.57
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.78
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.58
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.85
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4924.52
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.73
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.23
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.01
p-value of test                       :    0.9955


-----------------------------------------------
Normal statistic for number of jumps  :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:24.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.73
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :   -1.09
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:25.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.26

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.85e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.06e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.92
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.14
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.99
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:06.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.78
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:08.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9790.22
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10188.61
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:44.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4795.06
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4779.03
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:49.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.69
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4228.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12099.36
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11900.31
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.22
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000062335

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.96
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999980819

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.88e-3
p-value of test                       :    0.9904

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  2.8e-3

Anderson-Darling statistic = A2       :    3.43
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.43
p-value of test                       :  7.5e-3

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:02.15

 All tests were passed




Server wird beendet - Lösche Semaphor 19562519.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997355
  j =  2                              :             1321
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5338
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:57.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:41.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4474
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:57.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:05.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:05.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:55.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:00.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.84
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    2.91
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:15.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:46.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.48
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.33
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.39
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.73
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.50
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.16
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.69
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.88
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.32
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  484.30
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:44.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1481.95
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:03.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7050.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:41.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.88
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:15.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:01.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.08
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.18
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:31.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5069.61
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:00.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45689
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869689
  j =  1                              :        399908627
  j =  2                              :            45679
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45931
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869931
  j =  1                              :        399908142
  j =  2                              :            45923
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:28.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:18.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:45.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:58.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:55.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:37.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:36.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.02
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.39
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.02
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.80
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.98
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.33
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.22
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.05
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.52
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17457.67
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.91
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.14
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.95
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.87
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.96
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:36.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.54
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.87
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.59
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.92
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.46
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.39
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.40
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.20
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.15
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.97
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.75
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.62
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.45
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.93
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.56
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.23
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.50
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.80
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.59
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.83
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.75
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.25
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.46
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.77
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.16
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.28
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :    1.26
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:23.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.14
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:26.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 5.77e-3
p-value of test                       :    0.9939

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.78e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 7.97e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.15e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.15
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.25
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.16
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:02.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.13
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10082.77
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9895.38
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:31.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4946.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4915.40
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:42.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.73
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4202.08
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11922.99
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:15.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11837.58
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.48
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999854138

Normal statistic for number of bits   :   -1.15
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.45
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999956429

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.8e-3

Kolmogorov-Smirnov- statistic = D-    : 1.28e-3
p-value of test                       :    0.9987

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.42
p-value of test                       :    0.9923

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.78
p-value of test                       :    0.96

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:04.12

 All tests were passed




Server wird beendet - Lösche Semaphor 20611095.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:19.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:19.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:18.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5379
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:42.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4480
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:37.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:35.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:55.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:01.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:01.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:54.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:59.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     860
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:53.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.24
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:11.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    2.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:35.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.09
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.84
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.35
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:11.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.90
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.26
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  466.90
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1397.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:02.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7168.32
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:53.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.27
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:01.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.88
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.89
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5144.15
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:13.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45949
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869949
  j =  1                              :        399908104
  j =  2                              :            45945
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46288
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870288
  j =  1                              :        399907428
  j =  2                              :            46280
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:27.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:17.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:44.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 3.10e-4
p-value of test                       :    0.9997    *****

Anderson-Darling statistic = A2       :    3.27
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9965


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:59.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:52.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:33.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.75e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.048
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:35.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:35.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.83
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.84
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.63
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.36
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.96
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.45
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.64
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   64.12
p-value of test                       :  9.1e-3

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.23
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.75
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:29.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.56
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:29.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:11.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.08e-3
p-value of test                       :    0.9925

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  164.65
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:40.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17484.44
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:55.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.78
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.46
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.60
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.61
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.60
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:39.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.81
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.58
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.04
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.66
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.41
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.95
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.52
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.93
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.47
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.82
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.71
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.09
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.52
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.18
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.10
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.09
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.70
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4877.50
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.78
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.74
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.86
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.89
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.48
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  428.42
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.20
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.97
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:14.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.74
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:21.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.40e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 7.15e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 8.69e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.06
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.08
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.02
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:10.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.39
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:09.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9902.94
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10148.71
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:56.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:46.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4780.48
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:49.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4245.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4282.55
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11987.28
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11777.26
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:31.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.73
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999970220

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   85.27
p-value of test                       :  4.3e-3


-----------------------------------------------
Total number of bits:  7999950783

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:18:57.76

 All tests were passed




Server wird beendet - Lösche Semaphor 917528.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:55.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5597
p-value of test                       :  8.8e-3


-----------------------------------------------
CPU time used                    :  00:03:46.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:37.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7491
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:36.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4430
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:54.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:55.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:01.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:02.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:54.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:59.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     856
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:47.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.95
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:13.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:41.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.46
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.30
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.14
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.09
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.46
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.07
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.62
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:45.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1467.37
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:01.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6999.93
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:42.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.01
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:06.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.80
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:35.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4997.45
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:13.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45902
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869902
  j =  1                              :        399908196
  j =  2                              :            45902
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45922
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869922
  j =  1                              :        399908159
  j =  2                              :            45916
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:27.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:17.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:44.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:59.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:53.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:33.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.14e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:21.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:33.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:33.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   96.61
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:48.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.73
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.91
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.83
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.76
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.37
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   45.70
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:08.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.09
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.37
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.97
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:30.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:31.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.20
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.79
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17905.86
p-value of test                       :  5.7e-3



-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.70
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.46
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.93
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.03
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.52
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.94
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.19
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.58
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.41
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.03
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.02
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.33
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.85
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.12
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.91
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.86
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.03
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.79
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.74
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.33
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.53
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5054.39
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.75
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.70
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.98
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.03
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.88
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.77
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  148.88
p-value of test                       :    0.9973


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.47
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :    1.14
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:20.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.36
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :    2.55
p-value of test                       :  5.4e-3



-----------------------------------------------
CPU time used                    :  00:02:23.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:11.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 9.45e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:46.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.71e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 9.20e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.93
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.40
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.18
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:10.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.27
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:08.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10006.07
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9721.39
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:56.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4946.62
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.34
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:48.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4070.18
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3949.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11744.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11863.97
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:30.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.43
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999954299

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.49
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999939287

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:10.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:59.96

 All tests were passed




Server wird beendet - Lösche Semaphor 1900568.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1266
p-value of test                       :    0.9963

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334386
  j =  1                              :        599997468
  j =  2                              :             1266
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5361
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:50.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:40.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:41.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:58.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4190
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:00.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:11.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:11.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:08.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:15.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.91
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.15
p-value of test                       :    0.9987

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:49.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.83
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.27
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:16.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:46.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.03
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.95
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.51
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.28
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.86
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.44
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.14
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  390.39
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:58.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1420.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:02.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6969.98
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:52.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.36
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:18.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.71
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.04
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:43.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4984.09
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:05.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46060
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870060
  j =  1                              :        399907882
  j =  2                              :            46056
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46136
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870136
  j =  1                              :        399907732
  j =  2                              :            46128
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9906


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:30.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:20.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:57.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 9.87e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:12.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:59.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:39.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.23e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 2.24e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.88
p-value of test                       :  1.0e-2

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.91e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:25.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:25.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.77
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:51.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.60
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.37
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.65
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.23
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.66
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.96
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:53.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.08
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.21
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.14
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:29.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.91
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:29.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.77
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17582.36
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.35
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.37
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.44
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.95
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.06
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.44
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.28
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.62
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.69
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.86
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.49
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.67
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.19
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.52
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.89
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.00
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.82
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.21
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.23
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.46
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.27
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.47
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4902.60
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.49
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.32
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.48
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.85
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4908.01
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.89
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.48
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.59
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :   -2.16
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:26.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.12
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :   -2.25
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:02:26.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.46e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:46.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 5.15e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.00
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.52
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.97
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:09.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.41
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:08.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10170.96
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.54
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9667.55
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:04:42.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.18
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:52.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5042.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:54.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4130.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.44
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11530.06
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:33.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11881.30
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:35.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.22
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000123142

Normal statistic for number of bits   :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.01
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999980279

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   0.039
p-value of test                       :    0.48

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:15:02.37

 All tests were passed




Server wird beendet - Lösche Semaphor 2785304.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1269
p-value of test                       :    0.9952

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334389
  j =  1                              :        599997462
  j =  2                              :             1269
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5439
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:55.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:50.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:02.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:12.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:32.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:35.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:04:13.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:54.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.62
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    2.54
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     256
p-value of test                       :    0.9949

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    2.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:15.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:42.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.64
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.41
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.49
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.73
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.99
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.46
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.74
p-value of test                       :    0.9902

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.09
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.10
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:48.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1571.98
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:02:01.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6924.06
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:48.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.62
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.42
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.78
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:06.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.28
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.40
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:36.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5031.53
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:12.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:56.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45731
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869731
  j =  1                              :        399908540
  j =  2                              :            45727
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45888
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869888
  j =  1                              :        399908229
  j =  2                              :            45878
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :  4.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.29
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:34.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:32.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:03.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:23.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:56.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:36.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 9.97e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:44.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.98
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.60
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.71
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:55.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.93
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.22
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.48
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.89
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.92
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.48
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:29.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:18.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17277.89
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.23
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.25
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.71
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.51
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.35
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   58.24
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.06
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.89
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.38
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.65
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:39.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.72
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.54
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.40
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.92
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.18
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.94
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.45
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.50
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.86
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.57
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.80
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.81
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4940.93
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.39
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.37
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.58
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.07
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.45
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.91
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.68
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.59
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:24.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.16
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :   -1.04
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:25.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 7.55e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 5.02e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.52
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.92
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:07.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.32
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:08.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9936.36
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10116.26
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.043
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:04:01.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4783.14
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4849.96
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:50.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4195.80
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4263.92
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11782.60
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11790.79
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.26
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000126091

Normal statistic for number of bits   :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.48
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999934403

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.79
p-value of test                       :    0.04

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         : -2.48e-3
p-value of test                       :    0.50

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:13.23

 All tests were passed




Server wird beendet - Lösche Semaphor 4227096.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:39.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:50.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5527
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:52.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:40.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:42.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:59.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:12.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:13.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:10.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:04:13.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:48.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     559
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    2.07
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:13.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:42.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.00
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.14
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   34.06
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.70
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.47
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.06
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.85
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:56.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1372.30
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:02.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7158.14
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:56.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.36
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.08
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:21.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.23
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.73
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5047.06
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:59.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46020
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870020
  j =  1                              :        399907962
  j =  2                              :            46016
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45564
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869564
  j =  1                              :        399908876
  j =  2                              :            45556
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:33.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:20.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:50.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:09.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:37.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.17e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:24.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:24.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:24.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:47.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:47.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.85
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.77
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.18
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.32
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:50.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.56
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.08
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.79
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:50.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.83
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.64
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.93
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17600.03
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.93
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.66
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.74
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.39
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.77
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.11
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.37
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.66
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.68
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.00
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.38
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.28
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  188.45
p-value of test                       :  2.0e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.14
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.43
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.53
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.23
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.81
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.47
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.37
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.57
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4938.10
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.80
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.22
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.25
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.30
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4909.01
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.54
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.08
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.33
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:26.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.61
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :   0.021
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:25.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   0.011
p-value of test                       :    0.50

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.75e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:46.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.89
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.14
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.89
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:06.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.36
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:06.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9912.73
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10079.26
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:04:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.40
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:54.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5025.92
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:57.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4179.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3936.59
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11525.57
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:32.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12235.43
p-value of test                       :  4.1e-3

-----------------------------------------------
CPU time used                    :  00:01:33.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.48
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999935474

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.62
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000071854

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :  -0.034
p-value of test                       :    0.51

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:02.15

 All tests were passed




Server wird beendet - Lösche Semaphor 5210136.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5530
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:55.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:40.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:41.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:56.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:58.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:06.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:06.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:55.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7463
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:01.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:15.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:43.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.25
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.85
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.60
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.79
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.61
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.43
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.49
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:42.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1388.64
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:00.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7204.59
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.52
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:00.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.85
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.31
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:32.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5132.29
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:54.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45470
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869470
  j =  1                              :        399909065
  j =  2                              :            45460
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46096
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870096
  j =  1                              :        399907814
  j =  2                              :            46084
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:27.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:16.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:44.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:58.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:36.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:35.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.75
p-value of test                       :  2.9e-3

-----------------------------------------------
CPU time used                    :  00:01:33.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.64
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.88
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.98
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.04
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.02
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.33
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:43.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.07
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:29.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.04
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 5.06e-3
p-value of test                       :    0.9947

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17058.72
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.65
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.39
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.95
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.70
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.65
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.62
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.85
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.64
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.50
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.14
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  187.20
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.11
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.29
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.79
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.60
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.73
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.82
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.47
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.69
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.06
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.34
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.76
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.51
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.60
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.17
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.59
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  441.24
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4948.74
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.70
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.22
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.76
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :   -1.52
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:25.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.86
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    1.39
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:25.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.44e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.35e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 5.93e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.79
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.50
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.98
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:06.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.55
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:07.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10157.93
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10067.06
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.040
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:43.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4946.11
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.63
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:49.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4029.55
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.38
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11910.37
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11769.99
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.13
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000056038

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.40
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999886937

Normal statistic for number of bits   :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.71
p-value of test                       :    0.96

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :  -0.044
p-value of test                       :    0.52

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:07.42

 All tests were passed




Server wird beendet - Lösche Semaphor 6291480.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997322
  j =  2                              :             1336
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5389
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:55.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:41.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:56.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4223
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:58.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:06.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:05.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:55.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7515
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:59.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:48.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.96
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    2.39
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:17.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:46.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.90
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.66
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.40
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.06
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.83
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.27
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.58
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.49
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  202.61
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.59
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1446.82
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:57.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7073.67
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:42.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.80
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.66
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:02.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.19
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  149.51
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5242.98
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:12.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:58.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45572
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869572
  j =  1                              :        399908859
  j =  2                              :            45566
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45764
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869764
  j =  1                              :        399908472
  j =  2                              :            45764
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:28.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:18.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:43.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:59.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:36.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.02e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.84e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.70e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:38.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.078
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:35.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.70
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.83
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.36
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.40
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   50.97
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:01:43.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.22
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.59
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:29.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.41
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:31.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17196.29
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.77
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.09
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.23
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.83
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.18
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.30
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.46
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.73
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.62
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.26
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.20
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.41
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.48
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.31
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.07
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.37
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.71
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  453.06
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.10
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.32
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.63
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.14
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5145.66
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  431.05
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.43
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:36.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.23
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.27
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4873.85
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.05
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.23
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.44
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:24.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.20
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :   -1.99
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:25.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.0e-3

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.30
p-value of test                       :    0.01

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 9.41e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.82e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 2.35e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.00
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.55
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.42
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:05.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.23
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:06.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9952.95
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9871.62
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.015
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:55.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:44.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4690.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:46.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.28
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3953.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12045.26
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11629.38
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.79
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000119614

Normal statistic for number of bits   :    0.95
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.90
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000066484

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.44
p-value of test                       :    0.07

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.15

Sample variance                       :    0.16
p-value of test                       :    0.9976

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:36.45

 All tests were passed




Server wird beendet - Lösche Semaphor 7274520.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1464
p-value of test                       :  3.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334584
  j =  1                              :        599997073
  j =  2                              :             1462
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5338
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:56.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:57.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4427
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:58.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:05.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:05.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:54.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:04:00.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.37
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    2.35
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     988
p-value of test                       :  2.0e-3

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:46.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.24
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:14.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.60
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    2.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:44.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.53
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.74
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.14
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.53
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   83.06
p-value of test                       :  6.7e-3

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.41
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.98
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   82.36
p-value of test                       :  7.7e-3

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  273.33
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  492.36
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:43.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1441.41
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:01.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6875.59
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:43.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.17
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.85
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:03.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.70
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   93.54
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:35.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5112.73
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9985


-----------------------------------------------
CPU time used                    :  00:02:56.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45649
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869649
  j =  1                              :        399908707
  j =  2                              :            45639
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45658
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869658
  j =  1                              :        399908688
  j =  2                              :            45650
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :  5.1e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:27.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:19.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:44.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 9.14e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:59.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:57.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.00e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:38.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:38.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.45
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.08
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.28
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.84
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.52
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.73
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.00
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.09
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:29.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.66
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.18
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17570.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.74
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.68
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.74
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.66
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.62
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.72
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.25
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.24
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.23
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.42
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.54
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.40
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.07
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.85
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.12
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  104.24
p-value of test                       :    0.9964


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  438.72
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.74
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.00
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.05
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.50
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5116.07
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.17
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.70
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.21
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.61
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.80
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.14
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.25
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.12
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:23.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.41
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:23.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.87

Sample variance                       :    2.31
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.75e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 7.59e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.11
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.03
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.48
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:05.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:07.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10040.22
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:50.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.91
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:49.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5012.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:49.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4178.12
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.45
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11959.19
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11768.08
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:28.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.78
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999964283

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.17
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999919250

Normal statistic for number of bits   :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.50
p-value of test                       :    0.07

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.71

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.57

Sample variance                       :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:12.84

 All tests were passed




Server wird beendet - Lösche Semaphor 8257560.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:50.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5320
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:53.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:40.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:41.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:56.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:57.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:05.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:05.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:55.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:01.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.90
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.71
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.83
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:15.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:43.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.18
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.22
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   34.76
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.55
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.25
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.74
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.10
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  304.93
p-value of test                       :  9.2e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.50
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:43.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1402.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:00.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7222.31
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:42.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.46
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:02.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.77
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:31.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5074.15
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:57.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45867
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869867
  j =  1                              :        399908267
  j =  2                              :            45865
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45769
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869769
  j =  1                              :        399908466
  j =  2                              :            45761
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:27.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:17.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:44.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  8.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:00.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:55.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:01:33.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.61e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.086
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:36.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.22
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.10
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.02
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:49.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.35
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.89
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:42.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.44
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.04
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.66
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:28.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:37.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17434.73
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.48
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.66
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.31
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.49
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.12
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.43
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.73
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.11
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.50
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.24
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.23
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.30
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.47
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.13
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.37
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.98
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.29
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  450.38
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.41
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.41
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.45
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.23
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5073.90
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.92
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.43
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:34.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.99
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.87
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4930.28
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.48
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.39
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:34.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.60
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:22.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.68
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :    0.69
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:24.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.02e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.54e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 8.10e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.48
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.69
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.50
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:06.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.96
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:06.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9896.85
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9940.84
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:45.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4799.04
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9908

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4908.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:50.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4021.72
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4003.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11587.43
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11706.28
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.27
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999950252

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.16
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999973616

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.35
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.35
p-value of test                       :  9.4e-3

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :  -0.029
p-value of test                       :    0.51

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    4.34
p-value of test                       :  6.2e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.76
p-value of test                       :  2.9e-3

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:29.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 34  Gap, r = 0                      9.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9273368.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:50.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5450
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:55.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:41.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:56.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:57.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7193
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:04.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:04.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:54.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:01.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    2.97
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.12
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     632
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.51
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:13.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:42.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.01
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.07
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.05
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:10.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.26
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.98
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.62
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  271.37
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.55
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:43.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1408.45
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:00.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7099.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.32
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.43
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:00.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.96
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.89
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:33.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5126.10
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:58.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46001
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870001
  j =  1                              :        399908002
  j =  2                              :            45993
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45824
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869824
  j =  1                              :        399908355
  j =  2                              :            45818
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:28.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:17.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:44.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 6.17e-3
p-value of test                       :    0.9931

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  8.2e-3

Anderson-Darling statistic = A2       :    3.30
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  7.7e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:00.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:34.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 6.02e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.068
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.10
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:34.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:34.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.85
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:48.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.76
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.44
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:51.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.36
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.85
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:51.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   48.87
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.02
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.15
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.38
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.32
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.98
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  156.92
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:37.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17466.78
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:54.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.47
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.95
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.01
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.85
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.18
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.23
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.81
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.77
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.68
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.82
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.90
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.54
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.54
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.08
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.59
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.41
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.58
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.71
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.35
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.84
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.54
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.89
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.80
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.76
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  262.85
p-value of test                       :  1.9e-3


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.21
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.97
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5068.70
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.68
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.18
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.08
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :    1.66
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:26.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.96
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :   -1.45
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:26.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.31e-3
p-value of test                       :    0.9966

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.64
p-value of test                       :    0.05

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.20e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 8.52e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.10e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 8.66e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.34
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.26
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.21
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:05.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.31
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:07.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9926.06
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10270.46
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:42.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4971.29
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:49.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4212.83
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3991.16
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11930.78
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11654.92
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.86
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000108643

Normal statistic for number of bits   :    0.86
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.23
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000110455

Normal statistic for number of bits   :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   0.018
p-value of test                       :    0.49

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:05.98

 All tests were passed




Server wird beendet - Lösche Semaphor 10190872.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5322
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:56.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:44.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4450
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:58.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:07.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:07.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:58.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7171
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:04:05.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    2.28
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:46.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:13.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.91
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    3.23
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:39.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.23
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.38
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.20
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.32
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.50
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.70
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.19
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.17
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1461.59
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:03.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6862.17
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.83
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.49
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:07.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.49
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.17
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:50.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5040.43
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:31.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:21.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46168
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870168
  j =  1                              :        399907667
  j =  2                              :            46162
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46061
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870061
  j =  1                              :        399907882
  j =  2                              :            46053
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:31.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9904


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:18.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:03.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:37.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 3.59e-4
p-value of test                       :  5.8e-3

Anderson-Darling statistic = A2       :    4.24
p-value of test                       :  6.7e-3

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:45.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:45.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.08
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.23
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.90
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.15
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.38
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:46.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.00
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.61
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.54
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.77
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17507.38
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.18
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.46
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.31
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.58
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.78
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.65
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.40
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.74
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.50
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.99
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.19
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.46
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.07
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  189.36
p-value of test                       :  9.1e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.64
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.30
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.35
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.79
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.28
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.56
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4778.16
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  441.29
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.27
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.11
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.13
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4853.32
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.29
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.40
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:34.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.57
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:23.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.75
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:24.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.5e-3

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.62
p-value of test                       :    0.05

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.55e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 4.99e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.01
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.98
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.80
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:05.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.09
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:07.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10015.39
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9813.74
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:04:16.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.09
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:53.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 5.36e-3
p-value of test                       :    0.9944

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4637.97
p-value of test                       :    0.9952

-----------------------------------------------
CPU time used                    :  00:01:53.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.69
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4123.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11896.52
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:32.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11552.49
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:31.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.86
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999992903

Normal statistic for number of bits   :  -0.056
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.13
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  7999877244

Normal statistic for number of bits   :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   0.097
p-value of test                       :    0.46

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:51.75

 All tests were passed




Server wird beendet - Lösche Semaphor 11141144.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5486
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:57.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4433
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7185
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:41.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:57.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:04.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:05.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7152
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:55.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:04:00.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    2.16
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    2.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     546
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    2.06
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:14.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     265
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    3.51
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:15.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:44.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.04
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.81
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.57
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.07
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.45
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.70
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.00
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.70
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  274.24
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.96
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:44.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1504.60
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:01.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7068.67
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:40.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.70
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.39
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.61
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.39
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:32.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5104.81
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:03.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46118
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870118
  j =  1                              :        399907770
  j =  2                              :            46106
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45948
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869948
  j =  1                              :        399908109
  j =  2                              :            45938
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:28.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:19.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:58.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:57.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.83e-4
p-value of test                       :  8.9e-5    *****

Kolmogorov-Smirnov- statistic = D-    : 6.38e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    5.08
p-value of test                       :  2.6e-3

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:34.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:34.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.65
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.68
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.45
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.53
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.13
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.71
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:43.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.49
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.56
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.81
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17426.30
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.30
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.22
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.96
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.38
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.12
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.74
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.66
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.38
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.52
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.58
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.75
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.66
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.32
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.72
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.76
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.86
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.65
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.67
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.69
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.20
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.78
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.87
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5084.47
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.37
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.37
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  439.35
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.33
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.35
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.99
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.55
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.15
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :   -1.52
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:24.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.54
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :  -0.046
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:23.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :  -0.033
p-value of test                       :    0.51

Sample variance                       :    0.96
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 2.17e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.43e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.64
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.67
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  240.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:04.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 5.87e-3
p-value of test                       :    0.9938

Anderson-Darling statistic = A2       :    4.20
p-value of test                       :  7.3e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  151.03
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:02:06.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10165.28
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10224.50
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:44.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  8.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.55
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4651.28
p-value of test                       :    0.9928

-----------------------------------------------
CPU time used                    :  00:01:48.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4809.14
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:50.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.20
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11971.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11848.43
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:29.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.46
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  8000108451

Normal statistic for number of bits   :    0.86
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.64
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  8000125704

Normal statistic for number of bits   :    0.99
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.55
p-value of test                       :    0.06

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.56
p-value of test                       :    0.06

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:33.87

 All tests were passed




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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:57.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4232
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:41.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:58.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:05.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:05.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:55.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:00.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.14
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     863
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     627
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    2.01
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.59
p-value of test                       :  4.7e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     329
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:12.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    4.03
p-value of test                       :  8.4e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     128
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:45.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.88
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.89
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.65
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.80
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.89
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.04
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.14
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  393.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:43.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1497.69
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:01.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7053.70
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:42.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.01
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.93
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:04.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.23
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:46.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.65
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:33.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4909.75
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:12.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:58.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45726
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869726
  j =  1                              :        399908555
  j =  2                              :            45712
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46056
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870056
  j =  1                              :        399907892
  j =  2                              :            46048
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:28.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:18.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    3.63
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:44.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:57.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:36.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 7.37e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.32e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:26.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:41.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:40.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.83
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.45
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.07
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.92
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.65
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:44.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.31
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.03
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:28.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.14
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:28.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.95
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 6.25e-3
p-value of test                       :    0.9934

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  102.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17283.82
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.89
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.05
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.88
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.53
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.82
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.30
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.12
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.78
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.47
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.68
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.56
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.77
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.21
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.03
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.90
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.59
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.84
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.88
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.29
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  102.02
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:43.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.03
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.69
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.30
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  324.47
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.74
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:34.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.79
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.55
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5071.58
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.87
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.31
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:34.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.81
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :   0.070
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:24.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.10
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:23.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    1.07
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.27
p-value of test                       :    0.01

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 5.85e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.05
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.50
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.37
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:05.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.42
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  241.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:06.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9802.23
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9803.85
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.027
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:47.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.19
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:47.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4786.99
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:51.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.62
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.34
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11766.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11984.52
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:29.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.29
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000143080

Normal statistic for number of bits   :    1.13
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.14
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000083263

Normal statistic for number of bits   :    0.66
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.90

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:02.98

 All tests were passed




Server wird beendet - Lösche Semaphor 13238296.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5349
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:58.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:43.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4244
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:00.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:02.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:12.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:11.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:04:08.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:11.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:49.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.29
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:15.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:45.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.77
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.15
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.21
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.01
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:10.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.20
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.05
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.78
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.57
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.10
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:55.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1427.90
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:03.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6958.52
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.65
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.31
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:15.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.17
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.05
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:40.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5082.34
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:16.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45736
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869736
  j =  1                              :        399908531
  j =  2                              :            45730
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45879
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869879
  j =  1                              :        399908243
  j =  2                              :            45877
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:33.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:21.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9959

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:53.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:11.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:58.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 2.44e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.89e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:24.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.12
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:24.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:47.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.022
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:47.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.58
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.57
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.73
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.45
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.66
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:48.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.41
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.12
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.12
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.80
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17355.89
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.67
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.38
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.24
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.58
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.03
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.11
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.23
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.78
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.58
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.57
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.33
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.63
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.74
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.16
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.57
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.21
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.73
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.39
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.41
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.19
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.44
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.54
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5053.86
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.25
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  247.74
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.48
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  441.84
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5058.53
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.22
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  157.22
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.19
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :    1.27
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:23.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.75
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:22.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.88

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.62e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 8.95e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.02e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 9.72e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.20
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.70
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:07.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.03
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:09.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9946.95
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10071.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:04:22.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5000.82
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:55.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.37
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:59.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4244.76
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4243.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11785.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:34.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11705.16
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:35.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.40
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000104443

Normal statistic for number of bits   :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.99
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000030046

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :  -0.061
p-value of test                       :    0.52

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :  -0.054
p-value of test                       :    0.52

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.050
p-value of test                       :    0.48

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:16.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:53.03

 All tests were passed




Server wird beendet - Lösche Semaphor 14286872.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:40.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:50.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5427
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:55.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:40.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:59.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7170
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:05.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:05.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7173
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:55.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:00.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.40
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    2.07
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     554
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:14.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:45.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.43
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.61
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.54
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.43
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:10.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.65
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.94
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.45
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.23
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.18
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:43.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1476.72
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:02.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6969.11
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.57
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.77
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:02.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.90
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:46.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.08
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5036.52
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:13.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45301
p-value of test                       :    0.9966


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869301
  j =  1                              :        399909399
  j =  2                              :            45299
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45795
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869795
  j =  1                              :        399908412
  j =  2                              :            45791
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 4.75e-3
p-value of test                       :    0.9943

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:29.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:18.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:46.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:00.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.28e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 7.90e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:22.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:34.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:35.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.02
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.48
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.13
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.62
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.03
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.05
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:45.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.02
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.51
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.15
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17502.05
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.97
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.32
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.50
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.95
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.90
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.05
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.27
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.72
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.71
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.71
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.87
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.08
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  441.09
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.67
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.13
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.99
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.58
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.24
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.32
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.60
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.73
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.42
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4981.28
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.45
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.63
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.19
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.89
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5085.82
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.76
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.83
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.31
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:24.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.36
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:24.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   0.098
p-value of test                       :    0.46

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 7.17e-4
p-value of test                       :    0.9953

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.47e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.30
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.12
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.45
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:06.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.76
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:05.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9940.64
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10045.39
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:45.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 6.93e-3
p-value of test                       :    0.9926

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4680.35
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:47.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5004.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.12
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4174.38
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12079.05
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11770.32
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:30.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.57
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999957701

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.40
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000022225

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.60
p-value of test                       :    0.05

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:32.78

 All tests were passed




Server wird beendet - Lösche Semaphor 15433752.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:39.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5339
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:56.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:41.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4436
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:57.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:05.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:05.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:57.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:01.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    2.27
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     971
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.11
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     334
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    2.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:13.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    3.27
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     118
p-value of test                       :    0.9961

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:43.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.08
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.10
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:10.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.44
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.88
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.61
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:44.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1462.43
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:03.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7136.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:45.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.97
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.92
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:03.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.51
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:35.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4897.56
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:12.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46142
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870142
  j =  1                              :        399907727
  j =  2                              :            46120
  j =  3                              :               11
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45880
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869880
  j =  1                              :        399908245
  j =  2                              :            45870
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:30.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:20.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:44.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:00.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:35.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.19e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.38e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:39.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.37
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:50.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.71
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.19
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.23
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.68
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.95
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.17
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:45.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.69
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.03
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.84
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:37.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17410.10
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.17
p-value of test                       :    0.9903


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.66
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.31
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.40
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.82
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.63
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.14
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.06
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.69
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.79
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.76
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  555.14
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.51
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.97
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.57
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.34
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.18
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  101.23
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.95
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.52
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.47
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.54
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.72
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.95
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  439.34
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.91
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.67
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.79
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.54
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.68
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:24.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.09
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:24.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :  -0.092
p-value of test                       :    0.54

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 5.66e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.11e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.55
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.51
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.50
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:04.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:05.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9808.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9983

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10006.62
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:51.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4798.68
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:48.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.73
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:51.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4193.33
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.47
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11877.91
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12000.03
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:29.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.52
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999927608

Normal statistic for number of bits   :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.10
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000038980

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.20
p-value of test                       :    0.99

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:10.71

 All tests were passed




Server wird beendet - Lösche Semaphor 16482328.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:39.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5397
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:59.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4415
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7092
p-value of test                       :    0.9960


-----------------------------------------------
CPU time used                    :  00:02:45.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:57.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:01.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:11.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:13.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:04.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:04:08.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     335
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:13.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.45
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:44.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.36
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.94
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.86
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   82.33
p-value of test                       :  7.8e-3

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.37
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.94
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.92
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:32.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.68
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:48.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1468.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:25.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6941.16
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:49.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.78
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.26
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:08.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.62
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.08
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:36.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5126.10
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:00.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45606
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869606
  j =  1                              :        399908790
  j =  2                              :            45602
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46403
p-value of test                       :  7.4e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870403
  j =  1                              :        399907200
  j =  2                              :            46391
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:30.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:19.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:47.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:05.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:36.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.02e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 2.93e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:40.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.03
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.85
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.74
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.69
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.31
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.72
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.27
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:46.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.70
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.57
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:29.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.21
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.92
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17522.34
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:55.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.93
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.91
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.11
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.92
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.46
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.32
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.65
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.39
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.58
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.99
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.05
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.00
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.71
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.84
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.39
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.37
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.79
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.63
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.98
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.04
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  446.17
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.85
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5182.49
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.33
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.17
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.47
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.27
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4876.35
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.60
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.29
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.22
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:23.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.02
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:21.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 2.05e-3
p-value of test                       :    0.9979

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.53
p-value of test                       :    0.9943

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 8.35e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 5.86e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.75
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.75
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:07.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.31
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:09.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9938.91
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9935.67
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:04:08.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.54
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:53.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.35
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:52.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4133.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.64
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11856.25
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:30.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11831.96
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:30.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.20
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999782576

Normal statistic for number of bits   :   -1.72
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.65
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000068890

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:24.89

 All tests were passed




Server wird beendet - Lösche Semaphor 17498136.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:50.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:53.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:41.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:57.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:59.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7503
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:08.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7459
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:09.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:03.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:06.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:51.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:19.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:51.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.69
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.03
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.31
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.18
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.04
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.86
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.22
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.02
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.72
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.40
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:01.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6909.84
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:50.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.59
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 5.83e-3
p-value of test                       :    0.9940

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.92
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.11
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:10.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.56
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.70
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:36.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5345.78
p-value of test                       :  1.3e-3


-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:10.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46168
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870168
  j =  1                              :        399907668
  j =  2                              :            46160
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45814
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869814
  j =  1                              :        399908375
  j =  2                              :            45808
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:30.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:20.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:47.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:04.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:56.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:36.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.86e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.44e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.12e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:24.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:40.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:43.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.92
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.29
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.12
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.93
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.63
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.26
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:16.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.30
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.69
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.54
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.96
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:39.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17432.85
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.72
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.46
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.20
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.46
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.97
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.07
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.26
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.22
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.32
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.28
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.44
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.81
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  557.81
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.14
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.16
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.48
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.15
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.53
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.28
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.46
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.20
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.19
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5073.78
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.12
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.54
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.59
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.28
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.48
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.32
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.87
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.08
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:24.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.61
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :    0.11
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:23.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.038
p-value of test                       :    0.52

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.44e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 4.86e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.02
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.79
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.90
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:07.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.41
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:06.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10113.96
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9693.12
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:04:12.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.34
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:52.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5012.91
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:54.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4287.56
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3939.50
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11855.36
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:31.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12004.34
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:30.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.92
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  7999971720

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.70
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999828878

Normal statistic for number of bits   :   -1.35
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.82e-3
p-value of test                       :    0.9950

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.31
p-value of test                       :    0.99

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:43.20

 All tests were passed




Server wird beendet - Lösche Semaphor 18677784.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5359
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:58.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4486
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:45.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:57.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:01.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:11.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:12.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:59.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:05.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    2.66
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:52.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:20.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:50.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.09
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.30
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.19
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.80
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.50
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.96
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.72
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.92
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:29.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.70
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:42.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1403.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:19.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7189.13
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.40
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.95
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:01.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.59
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.32
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:33.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4980.31
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9978


-----------------------------------------------
CPU time used                    :  00:02:58.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45890
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869890
  j =  1                              :        399908222
  j =  2                              :            45886
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46306
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870306
  j =  1                              :        399907391
  j =  2                              :            46300
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:28.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:20.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:46.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9988

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:00.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.30e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.14e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:37.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:39.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.72
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:49.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.23
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.48
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.00
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.35
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.64
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:46.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.69
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.27
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.66
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.35
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17537.26
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.89
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.85
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.16
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.98
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.98
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.73
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.86
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.11
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.16
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.38
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.78
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.86
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.08
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.20
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.07
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.92
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.88
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  602.46
p-value of test                       :  1.1e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.34
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.18
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.95
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.59
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5174.30
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.33
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.08
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.89
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.90
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.49
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.34
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.66
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.05
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:26.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.41
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:25.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 3.10e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.02e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 5.94e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.19
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.11
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.54
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:07.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.39
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:06.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10014.55
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9957.94
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:39.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5025.71
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4756.60
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:49.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4183.47
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3994.38
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11492.74
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12067.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.52
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000092155

Normal statistic for number of bits   :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.80
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000032641

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.88
p-value of test                       :    0.97

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:46.70

 All tests were passed




Server wird beendet - Lösche Semaphor 19726360.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5397
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:55.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:41.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:58.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7184
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:06.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:06.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:56.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:01.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:49.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.05
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.02
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:13.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    2.04
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:51.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.99
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.69
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.18
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.87
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.17
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.97
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.69
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.06
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:42.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.50
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:01.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6918.79
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.77
p-value of test                       :  6.6e-4    *****

Anderson-Darling statistic = A2       :    4.34
p-value of test                       :  6.6e-3

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   47.56
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.52
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:01.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.25
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   90.32
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:32.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5096.90
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:11.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:58.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46016
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870016
  j =  1                              :        399907970
  j =  2                              :            46012
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45371
p-value of test                       :    0.9912


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869371
  j =  1                              :        399909259
  j =  2                              :            45369
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:27.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:20.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:46.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 7.60e-3
p-value of test                       :    0.9912

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:59.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:55.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:36.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 7.11e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:22.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:38.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:37.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.95
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:49.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.34
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.16
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.84
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.31
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.45
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:41.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.27
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.97
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.74
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17243.43
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:51.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.44
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.28
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.13
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.13
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.22
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.54
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.77
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.72
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.54
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.37
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.31
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  440.23
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.19
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.62
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.15
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.98
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.63
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.54
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.01
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.05
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.52
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5110.51
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.64
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.59
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:34.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.29
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.11
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4893.58
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.62
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.96
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:33.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.45
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:20.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.80
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:19.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.82e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 8.83e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 6.84e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.52
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.10
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.34
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:58.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.12
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:59.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9962.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10014.95
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:22.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5077.37
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:38.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.37
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.89
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:13.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3970.09
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11863.52
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11964.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.29
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000079804

Normal statistic for number of bits   :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.37
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000027142

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    2.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    2.62
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   02:58:36.65

 All tests were passed




Server wird beendet - Lösche Semaphor 20774936.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:18.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1506
p-value of test                       :  8.3e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334626
  j =  1                              :        599996988
  j =  2                              :             1506
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:20.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:17.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5401
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:42.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4247
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:36.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:35.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:55.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4478
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:55.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:01.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:02.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:54.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:04:00.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.42
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    3.27
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:52.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.57
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.41
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.23
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:09.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:36.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.94
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.19
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.47
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.73
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.15
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:12.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.33
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.10
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.66
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.80
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:56.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1550.36
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:02.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7087.88
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:54.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.69
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.45
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:01.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.05
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.56
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:36.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4942.74
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:15.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46153
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870153
  j =  1                              :        399907698
  j =  2                              :            46145
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45851
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869851
  j =  1                              :        399908302
  j =  2                              :            45843
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 3.34e-3
p-value of test                       :    0.9962

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:27.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:17.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:44.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:59.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:53.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:15.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:33.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.69e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 3.30e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.19
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.065
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:34.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.62
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.61
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.21
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   14.90
p-value of test                       :    0.9995    *****

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   45.38
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.23
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.94
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.68
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:29.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:29.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  170.77
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:00:40.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17243.38
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.85
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.56
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.09
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.89
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.41
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.21
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.13
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.83
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.78
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.47
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.58
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.43
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.73
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.48
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.57
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.83
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.96
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.68
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.94
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.02
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.86
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.47
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4884.58
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.42
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.16
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:33.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.58
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.65
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.58
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.52
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.80
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:33.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.53
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :   -1.32
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:15.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.75
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :  -0.010
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:22.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :  -0.054
p-value of test                       :    0.52

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 4.57e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 6.75e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.06
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:30.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    0.86
p-value of test                       :    0.9990    *****

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.58
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:09.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.62
p-value of test                       :  4.6e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  266.70
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:02:09.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9943.58
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10149.82
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:49.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4820.78
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.77
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4090.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11886.94
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11717.00
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:31.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.77
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999916682

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.98
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000024913

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:10.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.55
p-value of test                       :    0.06

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9955

Tests on the sum of all N observations
Standardized normal statistic         :  -0.081
p-value of test                       :    0.53

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:19:09.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14           8.3e-5
 63  WeightDistrib, r = 10           0.9995 
 87  LongestHeadRun, r = 27          0.9990 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 950297.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:56.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5376
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:46.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:37.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:36.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4441
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:55.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7105
p-value of test                       :    0.9938


-----------------------------------------------
CPU time used                    :  00:03:01.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7141
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:02.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:55.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:59.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:48.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:14.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:45.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.56
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.91
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.89
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.59
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.86
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:11.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.14
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.60
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  200.66
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.00
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1550.43
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:02.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7034.98
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:43.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.65
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.49
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:01.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.72
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.52
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:35.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5022.57
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:14.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45613
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869613
  j =  1                              :        399908777
  j =  2                              :            45607
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45709
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869709
  j =  1                              :        399908584
  j =  2                              :            45705
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:28.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:17.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:44.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:53.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:34.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-5
p-value of test                       :    0.9947

Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 5.79e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.072
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:21.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:32.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:32.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   96.37
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.29
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.21
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.28
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.56
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:42.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.98
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.18
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.90
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.36
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:30.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.84
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17328.12
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.62
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.73
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.58
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.32
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.32
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.93
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.78
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.31
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.65
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.86
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.65
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  189.44
p-value of test                       :  9.0e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.25
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.46
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.48
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.30
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.83
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.29
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.42
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.02
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.96
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.11
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.22
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.11
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.08
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.29
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.34
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.01
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.46
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.01
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.15
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:21.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.41
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :   -1.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:22.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   0.011
p-value of test                       :    0.50

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.54e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.35
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.25
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.97
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:10.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:08.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9991.22
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9691.74
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:47.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.50e-3
p-value of test                       :    0.9974

Kolmogorov-Smirnov- statistic = D-    :    0.61
p-value of test                       :  1.8e-4    *****

Anderson-Darling statistic = A2       :    6.14
p-value of test                       :  9.0e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5241.34
p-value of test                       :  2.5e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:46.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.46
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:49.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.96
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.70
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11948.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11549.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:29.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.87
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000026470

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.33
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999933767

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.56
p-value of test                       :    0.06

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.50
p-value of test                       :    0.07

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:32.19
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 95  HammingIndep, L=30, r=0         2.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1966105.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9972


-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5480
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:47.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:38.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:38.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:55.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4451
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:02.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:03.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:53.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:59.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.84
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    2.38
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    3.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:13.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:49.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.09
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.35
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.20
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.67
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.65
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.17
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.79
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:42.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1347.12
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:01.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6927.77
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:42.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.97
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 3.28e-3
p-value of test                       :    0.9966

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.31
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:08.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.70
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:35.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4919.54
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:06.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45826
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869826
  j =  1                              :        399908351
  j =  2                              :            45820
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45752
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869752
  j =  1                              :        399908497
  j =  2                              :            45750
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:29.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  6.4e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    4.66
p-value of test                       :  4.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9952


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:19.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:03.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:54.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:32.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 7.10e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.97e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 4.60e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.078
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:35.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.92
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.43
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.51
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:48.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.20
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.41
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:43.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.71
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.80
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.21
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.22
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:29.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.70
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17453.69
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.30
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.87
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.72
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.69
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    4.72
p-value of test                       :    0.9985


-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.01
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.58
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.12
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.59
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.18
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.63
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.76
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.27
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.58
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.22
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.90
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.22
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.53
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.39
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.79
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.92
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  457.92
p-value of test                       :  5.6e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4918.44
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.90
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.27
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.74
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.04
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5025.90
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.53
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.00
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.98
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :  -0.095
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:23.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.80
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :    1.25
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:23.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    2.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.11e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 6.17e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.48e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.75
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.64
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.70
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:09.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:08.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9807.16
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10129.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:04:01.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.98
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:49.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.56
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:50.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4222.72
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4226.54
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11808.55
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:28.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12023.00
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:31.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.90
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999934379

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.11
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999857750

Normal statistic for number of bits   :   -1.12
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   0.067
p-value of test                       :    0.47

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:04.70

 All tests were passed




Server wird beendet - Lösche Semaphor 2687001.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5531
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:49.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:38.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7178
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:37.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:55.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:54.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:02.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:02.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:53.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:58.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.95
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.69
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:05.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.99
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:33.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.15
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.75
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.24
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.20
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.35
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.59
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.76
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.34
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.26
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.89
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:43.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1411.80
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:03.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6983.60
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.22
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.53
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:02.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.17
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:43.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.50
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:35.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5118.23
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:58.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46409
p-value of test                       :  6.8e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870409
  j =  1                              :        399907185
  j =  2                              :            46403
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45773
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869773
  j =  1                              :        399908460
  j =  2                              :            45761
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:29.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:19.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:59.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.26e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 7.26e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.38e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 6.18e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:22.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.80
p-value of test                       :    0.9974

-----------------------------------------------
CPU time used                    :  00:01:34.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:35.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.58
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.74
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.63
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.62
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.86
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.35
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:44.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.76
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.78
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.06
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17090.38
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.55
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.80
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.46
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.98
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.93
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.34
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.22
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.06
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.63
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.47
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:38.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.02
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.31
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.86
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.10
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.93
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.47
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.94
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.43
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.97
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.28
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.28
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.54
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.15
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.23
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.39
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.95
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.46
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5152.86
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.80
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.62
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:34.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.38
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:23.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.71
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:24.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 6.34e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.76e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 5.41e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.63
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.74
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.71
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:10.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.34
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:07.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10188.38
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9958.72
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:04:06.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.66
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:49.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4808.20
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:50.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4038.31
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4182.03
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11740.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:29.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11812.08
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:30.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.89
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000009022

Normal statistic for number of bits   :   0.071
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.01
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999993653

Normal statistic for number of bits   :  -0.050
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.58
p-value of test                       :  4.6e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    6.12
p-value of test                       :  9.2e-4    *****

Tests on the sum of all N observations
Standardized normal statistic         :   -2.99
p-value of test                       :    0.9986

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    1.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:56.87

 All tests were passed




Server wird beendet - Lösche Semaphor 3702809.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5345
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:50.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:38.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:38.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4440
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:54.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:55.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:03.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:03.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7478
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:53.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:58.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9909

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    2.05
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:11.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:44.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.58
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.34
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.80
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.56
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.96
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.54
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.93
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.43
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  384.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:44.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1456.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:04.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7189.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:46.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.77
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:04.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.23
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.08
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5086.34
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:02.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45725
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869725
  j =  1                              :        399908554
  j =  2                              :            45717
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45838
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869838
  j =  1                              :        399908326
  j =  2                              :            45834
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:29.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:19.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:45.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:01.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.12
p-value of test                       :    0.9998    *****

-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:34.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.21e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.65e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.26e-5
p-value of test                       :    0.9937

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:22.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:36.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.07
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.59
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.27
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:51.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.87
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.64
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:54.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.10
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:45.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.06
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.18
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.55
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.56
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17834.17
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.11
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.59
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.67
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.00
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.68
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.92
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.31
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.92
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.92
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.10
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.53
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.74
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.29
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  174.24
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.79
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.05
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.06
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.94
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.13
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.51
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.56
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.45
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.76
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.64
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.46
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.75
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.98
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.17
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.66
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.54
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.59
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:23.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.57
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:23.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.78
p-value of test                       :    0.04

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.48e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 7.78e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:46.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 3.16e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.38
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.73
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.97
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:07.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.70
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:08.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9742.37
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9714.33
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:04:05.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4845.33
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:50.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4790.17
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:51.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4018.51
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.34
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11767.55
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12005.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.89
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999933590

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.30
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999939902

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:20.72
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 50  SampleProd, t = 8               0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 4816921.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5315
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:50.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:39.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:39.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:55.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:56.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:02.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:03.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:53.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:59.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:50.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.77
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:17.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    2.08
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:44.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.88
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.68
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.16
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.55
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.03
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.78
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:42.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1491.86
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:03.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7095.70
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:44.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.25
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.73
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:01.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.40
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.91
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5149.41
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:57.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46077
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870077
  j =  1                              :        399907849
  j =  2                              :            46071
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45701
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869701
  j =  1                              :        399908600
  j =  2                              :            45697
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:28.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:17.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.76
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:44.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:59.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:55.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:33.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.19e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:35.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.15
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.61
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.91
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.31
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.81
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.45
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:42.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.16
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.86
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.18
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.71
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   12.74
p-value of test                       :  1.7e-3

-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  100.60
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17628.36
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.13
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.02
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.02
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.51
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.63
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.89
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.68
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.27
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.40
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.21
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :   93.25
p-value of test                       :    0.9998    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.87
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.16
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.08
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.18
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.65
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.25
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.55
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.10
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.40
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.44
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5168.99
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.86
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.98
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.56
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.44
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.82
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.92
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.23
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:36.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.55
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :   0.021
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:25.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.09
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :    1.12
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:25.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.71

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 6.01e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.05e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 7.71e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.69
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.52
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.91
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:07.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.97
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:06.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9941.31
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10221.99
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:04:00.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4698.75
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:50.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5060.11
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.28
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4129.94
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11792.26
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11848.40
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.44
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000056311

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.07
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000021910

Normal statistic for number of bits   :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    0.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :  -0.067
p-value of test                       :    0.53

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:43.25
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 M (L=1000, r=0)     0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5799961.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1266
p-value of test                       :    0.9963

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334386
  j =  1                              :        599997468
  j =  2                              :             1266
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5427
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:54.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:40.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:58.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:03.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:03.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:54.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:59.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.80
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:51.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.02
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:15.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    2.16
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:42.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.64
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.66
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.94
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.09
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:10.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.25
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.78
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.43
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.36
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:48.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.62
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:02.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7123.85
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:41.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.86
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.15
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:00.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.83
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.52
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:34.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5074.46
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:02.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45780
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869780
  j =  1                              :        399908445
  j =  2                              :            45770
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45928
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869928
  j =  1                              :        399908147
  j =  2                              :            45922
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:28.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:18.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:44.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:58.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:55.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 7.81e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:34.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:32.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.62
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.40
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.99
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:49.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.47
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.08
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:38.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9971

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.40
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.50
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.02
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17714.75
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:52.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.87
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.93
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.50
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.35
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.07
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:36.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.49
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.84
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.51
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.20
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.11
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.79
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.93
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.31
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.08
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.62
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.32
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.78
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.87
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.06
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.84
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.95
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.01
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5091.37
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.14
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.89
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.62
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  448.86
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.75
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.12
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  158.43
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.00
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:23.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.88
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   -1.00
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:23.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    3.23
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -1.81
p-value of test                       :    0.96

Sample variance                       :    0.18
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 4.89e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.50e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.23
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.48
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.99
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:06.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.17
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:07.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10087.98
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10247.56
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:43.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4723.91
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:50.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.67
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:49.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.93
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4008.42
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11656.55
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12203.16
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:01:29.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.57
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999917654

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.11
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999967679

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    2.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:49.96

 All tests were passed




Server wird beendet - Lösche Semaphor 6783001.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:40.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:51.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:56.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:43.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:00.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:00.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:10.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:10.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:05.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:04:08.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     948
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.97
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    3.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:14.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:42.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.63
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.86
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.75
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:11.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.00
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.31
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.36
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  285.10
p-value of test                       :  9.9e-3

-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.94
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1509.72
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:06.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6920.14
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:55.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.31
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.75
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:18.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.56
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:46.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  164.51
p-value of test                       :  3.7e-3


-----------------------------------------------
CPU time used                    :  00:01:38.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4988.92
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:59.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45763
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869763
  j =  1                              :        399908477
  j =  2                              :            45757
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45807
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869807
  j =  1                              :        399908389
  j =  2                              :            45801
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:32.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:20.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :  2.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    4.06
p-value of test                       :  8.4e-3


-----------------------------------------------
CPU time used                    :  00:01:50.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:07.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:56.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:38.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.28
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.060
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.063
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:44.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:44.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.97
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.12
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   94.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.18
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.37
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:50.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.36
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.05
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.06
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.97
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17330.49
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.68
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   13.64
p-value of test                       :    0.9996    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.53
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.49
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.47
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.19
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.56
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.36
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.32
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.33
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.73
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.59
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.93
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.44
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.11
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.82
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.51
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.96
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.79
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.84
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.21
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.63
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.81
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.69
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.76
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.97
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.71
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4894.61
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.40
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.87
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.38
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:23.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.50
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:23.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.92e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.34e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.41
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.81
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:07.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.31
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:06.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10063.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.41
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:10.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:04:26.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.04
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:56.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4995.61
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:59.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3963.84
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.73
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11795.01
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:35.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12003.04
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:36.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.80
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999900953

Normal statistic for number of bits   :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.17
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999973409

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:06.28
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 M (L=50, r=0)       0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7733273.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5417
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:56.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7464
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:41.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:57.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:59.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7452
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:07.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:07.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:59.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:05.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:47.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.24
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:16.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:41.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.82
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.42
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.62
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.38
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.92
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.63
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.83
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.85
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:51.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1517.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:11.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7192.80
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:53.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.58
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    3.54
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.58
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.76
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:09.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.10
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  144.64
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:37.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5065.70
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:56.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46128
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870128
  j =  1                              :        399907748
  j =  2                              :            46120
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45752
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869752
  j =  1                              :        399908499
  j =  2                              :            45746
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:29.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:18.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:46.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:05.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.42e-3
p-value of test                       :    0.9928

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:36.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.40e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 6.33e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.68e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 5.45e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:39.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:40.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.18
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.07
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.77
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.87
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.51
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.73
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:46.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.80
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.38
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.16
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.42
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:39.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17407.56
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:52.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.86
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.03
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.90
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.46
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.49
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.66
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.82
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.62
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.01
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.73
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.61
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.76
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.37
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.37
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  110.19
p-value of test                       :  4.1e-3


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  108.76
p-value of test                       :    0.9908


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  107.74
p-value of test                       :    0.9925


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.57
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.95
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.91
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.36
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.97
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.27
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.19
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.89
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.57
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  443.57
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4988.28
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.18
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.38
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.75
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:22.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.40
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :   0.025
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:25.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 5.86e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.01
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.86
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.44
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:07.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.25
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:05.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9885.20
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9875.97
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.052
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:04:23.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4963.39
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:53.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5052.70
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:53.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.61
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4205.75
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11787.68
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:32.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11986.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:32.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.34
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999957098

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.99
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999986255

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.84
p-value of test                       :    0.97

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:07.75

 All tests were passed




Server wird beendet - Lösche Semaphor 9011225.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5369
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:53.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:40.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7136
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:41.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:58.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:06.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:06.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:54.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7173
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:04:02.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:47.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:13.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9917

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:42.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.65
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.17
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.05
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.26
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.21
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.08
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.47
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.58
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1481.94
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7152.77
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:40.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.35
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.96
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:04.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.83
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.04
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:34.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4966.71
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:53.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46058
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870058
  j =  1                              :        399907891
  j =  2                              :            46044
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45839
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869839
  j =  1                              :        399908328
  j =  2                              :            45827
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:28.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:17.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:45.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-3
p-value of test                       :    0.9983

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:59.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:35.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 6.73e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:32.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:33.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.67
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.90
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.73
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.65
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.56
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.75
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:41.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.16
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.70
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.23
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.40
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.84
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.75
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:38.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17222.81
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.41
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.18
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.08
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.96
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.21
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   65.75
p-value of test                       :  1.8e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   60.18
p-value of test                       :  5.1e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.13
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.58
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.66
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.34
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.62
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.54
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.69
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.09
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.62
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.80
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  568.35
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.35
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.80
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.14
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.21
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.58
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.72
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.39
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.78
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.06
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5039.18
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.40
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.95
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.41
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   0.079
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:24.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.68
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:24.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    2.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.99e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 4.50e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.14e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.08
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.62
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.80
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:07.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.65
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:07.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9991.50
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10027.76
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.047
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:55.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:42.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4964.21
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.95
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:49.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3983.18
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4215.92
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11673.36
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11849.12
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:29.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.28
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000086983

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.67
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999944117

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   0.082
p-value of test                       :    0.47

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.87
p-value of test                       :    0.03

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:50.12

 All tests were passed




Server wird beendet - Lösche Semaphor 10027033.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:49.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5526
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:57.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:42.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:58.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:58.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:06.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:06.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:55.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:04:00.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    3.26
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:14.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:44.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.00
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.87
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.75
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.59
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.74
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.91
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.73
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  261.22
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  477.67
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:45.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1522.94
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:00.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6931.28
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:44.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.48
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.36
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:02.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.32
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.90
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:33.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4948.69
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:00.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45759
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869759
  j =  1                              :        399908484
  j =  2                              :            45755
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46335
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870335
  j =  1                              :        399907334
  j =  2                              :            46327
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:28.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:18.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:00.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:36.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.16e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 6.12e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:35.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.64
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.91
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.08
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.82
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.05
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.38
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.38
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:45.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.38
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.65
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.71
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.36
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17734.09
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.32
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.05
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.83
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.66
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.75
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.65
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.49
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.16
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.12
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.51
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.51
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.16
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.00
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.92
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.55
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.73
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.91
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.45
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.82
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   50.59
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.45
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.36
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4915.78
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.91
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.33
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  450.09
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.48
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.78
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.06
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.67
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.77
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:22.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.24
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :    2.41
p-value of test                       :  8.0e-3



-----------------------------------------------
CPU time used                    :  00:02:22.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 6.91e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.73e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 8.29e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.61
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.50
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.07
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:05.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.52
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:07.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9912.79
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10139.90
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:44.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4973.10
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4824.39
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4137.44
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.48
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11954.95
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12027.82
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:30.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.99
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  7999850913

Normal statistic for number of bits   :   -1.18
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.43
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000010600

Normal statistic for number of bits   :   0.084
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.50
p-value of test                       :    0.07

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.22
p-value of test                       :  7.1e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.70
p-value of test                       :    0.9965

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:13.95

 All tests were passed




Server wird beendet - Lösche Semaphor 10977305.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:48.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5335
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:57.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4193
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:42.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4430
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:57.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7146
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:06.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:06.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:55.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:59.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    2.79
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:13.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.28
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:41.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.73
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.32
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.97
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.64
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.52
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.66
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  475.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:43.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.20
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:02.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7004.65
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:41.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.76
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:02.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.96
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:35.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4922.67
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:59.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45851
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869851
  j =  1                              :        399908301
  j =  2                              :            45845
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46045
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870045
  j =  1                              :        399907912
  j =  2                              :            46041
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:27.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:19.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:45.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:00.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.35e-3
p-value of test                       :    0.9941

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:36.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.21e-5
p-value of test                       :    0.9942

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.28e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.030
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:35.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:34.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.80
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.89
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.31
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.21
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.72
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.27
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.45
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:39.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.58
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9945

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.63
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.72
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.10
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.75
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17385.06
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.33
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.24
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.65
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.12
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.15
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.38
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.43
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.19
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.92
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.42
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.66
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.20
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.39
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.00
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.26
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  196.73
p-value of test                       :  3.3e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.60
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.64
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.85
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.70
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  444.70
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4868.31
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  445.01
p-value of test                       :  9.9e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.41
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.93
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.42
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.21
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.49
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.65
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.30
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:24.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.59
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:23.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.20e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 6.98e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.97
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.58
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.98
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:05.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.51
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:07.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10109.25
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9865.17
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:40.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:48.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4768.08
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:51.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4180.43
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.54
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11790.32
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11569.07
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:31.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.17
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000199771

Normal statistic for number of bits   :    1.58
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.87
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  7999903329

Normal statistic for number of bits   :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:21.45

 All tests were passed




Server wird beendet - Lösche Semaphor 12025881.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:49.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1274
p-value of test                       :    0.9929

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334394
  j =  1                              :        599997452
  j =  2                              :             1274
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5318
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:00.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:44.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:44.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4228
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:01.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:02.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:13.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:13.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:04:09.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:04:13.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.99
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:49.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    2.71
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.96
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:13.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:43.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.30
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.49
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.64
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.97
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.95
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.66
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.33
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.42
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.07
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:56.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.34
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:06.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7171.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:56.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.14
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.94
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:20.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.68
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:46.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.99
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5027.33
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:00.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45818
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869818
  j =  1                              :        399908366
  j =  2                              :            45814
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45748
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869748
  j =  1                              :        399908504
  j =  2                              :            45748
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:32.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:21.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:51.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :  2.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    5.06
p-value of test                       :  2.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9982


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:12.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:58.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 9.22e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:37.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.48e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:41.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.096
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:50.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.82
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.55
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.07
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.79
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.76
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.09
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:51.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.24
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.28
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.68
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17505.46
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   67.75
p-value of test                       :  1.1e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.52
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.80
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.12
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.01
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.74
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.17
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.28
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.78
p-value of test                       :    0.9905


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.96
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.03
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.33
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.18
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.27
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.14
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.94
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.68
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.42
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.36
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.18
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.96
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.76
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5064.61
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.02
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.10
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.35
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.02
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5220.25
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.92
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.49
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.56
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :  -0.064
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:25.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.87
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :    1.03
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:27.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.10e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.12e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.93
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.56
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.60
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:05.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.57
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9845.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9912.26
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.021
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:04:28.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4780.58
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:55.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:00.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.33
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.18
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11650.33
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:35.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11673.17
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:38.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   32.09
p-value of test                       :    0.9923


-----------------------------------------------
Total number of bits:  7999958142

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.13
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000070408

Normal statistic for number of bits   :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   0.074
p-value of test                       :    0.47

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.75
p-value of test                       :    0.04

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.05
p-value of test                       :    0.02

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:58.60

 All tests were passed




Server wird beendet - Lösche Semaphor 13041689.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5384
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:00.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:43.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:59.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:08.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:08.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:04:01.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:04.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     855
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:14.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:44.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.10
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.76
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.80
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:12.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.56
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.63
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.60
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  263.46
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.91
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:48.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1437.71
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:04.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7129.89
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:50.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.02
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:09.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.31
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.16
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:37.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5064.59
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:58.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45483
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869483
  j =  1                              :        399909034
  j =  2                              :            45483
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45590
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869590
  j =  1                              :        399908825
  j =  2                              :            45580
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:30.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:19.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:47.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:03.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:56.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:36.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 2.89e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.039
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:40.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.02
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.10
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.44
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.47
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.13
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.35
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.77
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:45.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.17
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.51
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.41
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.96
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17411.41
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.59
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.37
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.47
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.05
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.72
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.54
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.96
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.29
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.92
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.28
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:39.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.24
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.15
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.14
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.37
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.27
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.87
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.84
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.57
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.17
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.59
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.62
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.90
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5026.02
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.88
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.54
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.08
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.33
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.50
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  326.76
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.22
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.00
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :   -1.54
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:23.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.79
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :    1.55
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:25.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   0.076
p-value of test                       :    0.47

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 6.41e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.89e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.42
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.54
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:05.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.52
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:06.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9809.66
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9765.01
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:04:16.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4820.67
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:52.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4928.94
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:54.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4137.85
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.09
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11676.02
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:31.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11800.96
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:31.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.59
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000079465

Normal statistic for number of bits   :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.32
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000085642

Normal statistic for number of bits   :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    2.30
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:11.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.93
p-value of test                       :    0.97

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:12.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:36.70

 All tests were passed




Server wird beendet - Lösche Semaphor 14254105.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:49.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5339
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:57.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4458
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7465
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:43.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4241
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:58.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4495
p-value of test                       :  8.6e-3


-----------------------------------------------
CPU time used                    :  00:01:59.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:06.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:08.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:04:01.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:04.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.74
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.9905

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:49.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.25
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.33
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:16.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.72
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.51
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:46.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.84
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.47
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.38
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.35
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.17
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.19
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.77
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:49.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.29
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:02.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7111.96
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:49.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.34
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.36e-3
p-value of test                       :    0.9921

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   85.85
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:08.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.79
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.30
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:36.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5035.58
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:59.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45977
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869977
  j =  1                              :        399908048
  j =  2                              :            45973
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45998
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869998
  j =  1                              :        399908009
  j =  2                              :            45988
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:30.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:19.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:05.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:36.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:24.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.48e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 7.77e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:26.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.03
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.57
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.91
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.99
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.59
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.90
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.73
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.35
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:46.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.95
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.58
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.82
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:40.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17529.57
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.62
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.88
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.45
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.47
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.73
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.90
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.94
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.43
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.90
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.84
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.51
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.03
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.50
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.46
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.60
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.18
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.74
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.16
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.99
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.71
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.64
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.55
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4935.94
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.92
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.72
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.68
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.33
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5177.01
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.41
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.91
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.83
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:25.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.09
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:24.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    2.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 3.40e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:46.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.40e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.68
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.91
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.05
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:04.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.73
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:06.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10064.68
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10002.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:04:18.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4718.54
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:54.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4931.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:53.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4042.19
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4059.78
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11941.53
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:30.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11853.87
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:31.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.62
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000001102

Normal statistic for number of bits   : 8.71e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.30
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  7999912821

Normal statistic for number of bits   :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 2.23e-3
p-value of test                       :    0.9977

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.90
p-value of test                       :    0.97

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:11.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:12.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:37.79

 All tests were passed




Server wird beendet - Lösche Semaphor 15335449.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:49.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5499
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:57.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4192
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:57.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4168
p-value of test                       :    0.9949


-----------------------------------------------
CPU time used                    :  00:01:57.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:05.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:05.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7500
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:56.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:01.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.68
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     843
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.98
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:53.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:18.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:43.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.62
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.88
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.79
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.30
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.28
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.32
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.63
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:43.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1458.05
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:02.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6988.99
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:42.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.41
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.02
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:02.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.70
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.24
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:32.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4977.75
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:59.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45579
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869579
  j =  1                              :        399908848
  j =  2                              :            45567
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45839
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869839
  j =  1                              :        399908324
  j =  2                              :            45835
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:28.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:18.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:45.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:58.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :  6.3e-3

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:55.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:35.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.54e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:42.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.10
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.64
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.50
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.26
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.03
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:44.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.25
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.80
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.93
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.19
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.50
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.55
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:37.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17552.81
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.98
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.34
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.66
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.82
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.33
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.48
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.58
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.16
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.26
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.94
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.01
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.87
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.39
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.75
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.30
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.53
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.00
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.28
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.49
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.66
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.48
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  302.42
p-value of test                       :    0.9992    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4855.75
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.15
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.85
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.98
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.03
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.66
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.13
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.94
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.39
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:25.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.94
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:25.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.61
p-value of test                       :    0.05

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 4.44e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 8.80e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.37
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.19
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.20
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:04.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.77
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:04.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9829.13
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.47
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:49.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4973.48
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:49.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4842.15
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:49.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.84
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.25
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12162.14
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12222.64
p-value of test                       :  5.2e-3

-----------------------------------------------
CPU time used                    :  00:01:29.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.93
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000044068

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.76
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999998459

Normal statistic for number of bits   :  -0.012
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.068
p-value of test                       :    0.53

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.69
p-value of test                       :    0.05

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:59.51
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 M (L=10000, r=0)    0.9992 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16416793.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1461
p-value of test                       :  4.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334581
  j =  1                              :        599997078
  j =  2                              :             1461
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5477
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:02.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:44.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:47.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4443
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:03.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:04.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:17.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:18.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:20.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:25.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:49.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.92
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    2.64
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    3.00
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.14
p-value of test                       :    0.9992    *****

Stat. AD after spacings (mNP2-S)      :    3.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:15.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.73
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:43.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.90
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.67
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.19
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.69
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.21
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.38
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.53
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:30.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.73
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:36.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  475.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:05.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1509.41
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:06.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7250.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:05.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.11
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:32.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.60
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:27.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.58
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.77
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:49.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5115.76
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:05.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46112
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870112
  j =  1                              :        399907782
  j =  2                              :            46100
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46161
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870161
  j =  1                              :        399907681
  j =  2                              :            46155
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:36.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:33.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:12.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:57.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:38.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 9.72e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:25.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:55.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.034
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:54.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.86
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.35
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.19
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.88
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.60
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.65
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.21
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:57.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.26
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.98
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.70
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:48.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17492.21
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.22
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.52
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.93
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.06
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.69
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.88
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.68
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.64
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.11
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.91
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.51
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.20
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  445.14
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.75
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.23
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.37
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.37
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.72
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.14
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.09
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.30
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.20
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5192.74
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.52
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.85
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.08
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.29
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.87
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.29
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.89
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:34.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.77
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :    0.72
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:24.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.91
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:25.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :  -0.071
p-value of test                       :    0.53

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.90e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 5.97e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.75e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 7.51e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.57
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.14
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.91
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:06.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9984

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:05.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10032.74
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9703.15
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.65
p-value of test                       :    0.9959

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:04:52.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5014.38
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:02.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5017.88
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:05.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4218.67
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:33.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11845.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:40.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11879.53
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:43.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.65
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999981635

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.01
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000035875

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:15:57.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP2, t = 9          0.9992 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17465369.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:40.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5499
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:55.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:41.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:56.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4433
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:58.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:07.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:07.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:55.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7192
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:04:00.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.27
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:06.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.75
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     263
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    2.69
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:18.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:47.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.91
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.15
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.29
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.51
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.59
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.48
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  193.77
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.98
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:43.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1470.79
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:00.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7060.37
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:43.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.04
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.25
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:01.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.26
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.13
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5054.20
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:02.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45760
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869760
  j =  1                              :        399908486
  j =  2                              :            45748
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45935
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869935
  j =  1                              :        399908134
  j =  2                              :            45927
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:29.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:19.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:46.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:01.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:56.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.60
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:35.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.74e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 7.74e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:22.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:34.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:34.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   41.60
p-value of test                       :    0.9937

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.47
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.79
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.17
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.21
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.61
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:42.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.62
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.30
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.62
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  103.07
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17490.29
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.84
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.02
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.50
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.14
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.84
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.77
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.90
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.59
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.79
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.59
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.90
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.15
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.66
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.86
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.05
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.34
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.86
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.58
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.15
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.03
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.64
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.80
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5135.11
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.55
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.78
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.92
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.58
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4864.12
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.16
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.80
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:34.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.82
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:20.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.36
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :   -2.05
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:20.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.04e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 6.38e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.80e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 9.15e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.02
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.71
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.94
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:05.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.81
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:05.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10090.85
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10177.07
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.028
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:04:17.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:46.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5015.73
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:51.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.55
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3978.75
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11724.76
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11982.30
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:29.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.07
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999930278

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.29
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999980657

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  1.7e-3

Kolmogorov-Smirnov- statistic = D-    : 7.82e-3
p-value of test                       :    0.9916

Anderson-Darling statistic = A2       :    4.24
p-value of test                       :  7.0e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.81
p-value of test                       :    0.9975

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:17.84

 All tests were passed




Server wird beendet - Lösche Semaphor 18907161.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5456
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:57.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:44.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:01.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:02.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:13.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:13.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:09.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7179
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:12.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.20
p-value of test                       :  7.1e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:50.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.83
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:16.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:44.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.52
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.93
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.71
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.05
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.43
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.93
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.01
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.98
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:54.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1355.81
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:01.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7248.25
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:54.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.65
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.40
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:16.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.10
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.66
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:37.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4893.44
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:02.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45909
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869909
  j =  1                              :        399908183
  j =  2                              :            45907
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45852
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869852
  j =  1                              :        399908298
  j =  2                              :            45848
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:33.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  3.9e-4    *****

Anderson-Darling statistic = A2       :    5.12
p-value of test                       :  2.6e-3


-----------------------------------------------
CPU time used                    :  00:02:21.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:54.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:10.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.24e-3
p-value of test                       :    0.9904

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:58.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:38.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.30e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.81e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:49.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.47
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.70
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.49
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:51.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.84
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.19
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.25
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:50.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.9998    *****

Anderson-Darling statistic = A2       :    3.31
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.03
p-value of test                       :    0.9906

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.55
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17525.65
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:52.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.59
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.49
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.68
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.45
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.04
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.27
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.56
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.40
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.64
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.50
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.29
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.48
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.80
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.90
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.08
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.54
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.13
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.46
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.07
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.05
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.16
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.97
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.66
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.70
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.51
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.72
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  465.14
p-value of test                       :  2.8e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4834.82
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.97
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.47
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.82
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:22.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.07
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :   -1.15
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:22.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.47
p-value of test                       :    0.07

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:16.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 8.51e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.61e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 9.95e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.26
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.36
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:02.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.14
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:03.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10027.98
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9900.92
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.90
p-value of test                       :    0.9981

-----------------------------------------------
CPU time used                    :  00:04:16.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4779.82
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:55.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4811.33
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:58.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.95
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4011.12
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11832.58
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11830.40
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:34.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.36
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000010528

Normal statistic for number of bits   :   0.083
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.94
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999950765

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.87
p-value of test                       :    0.03

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:45.42

 All tests were passed




Server wird beendet - Lösche Semaphor 19955737.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9973


-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:49.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1474
p-value of test                       :  1.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334594
  j =  1                              :        599997052
  j =  2                              :             1474
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5410
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:00.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:44.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:45.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:03.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:04.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:17.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:13.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:04:09.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:04:11.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    4.23
p-value of test                       :  6.7e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     857
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:50.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:17.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    2.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:45.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.51
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.55
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.46
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.00
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.79
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.85
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.52
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.96
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:31.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.65
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:54.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1423.18
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:08.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7149.06
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:58.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.73
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:11.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.22
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:48.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.93
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5077.64
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:50.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45836
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869836
  j =  1                              :        399908332
  j =  2                              :            45828
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46111
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870111
  j =  1                              :        399907781
  j =  2                              :            46105
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:25.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:16.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9910


-----------------------------------------------
CPU time used                    :  00:01:48.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:03.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:49.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:33.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.02e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 7.86e-6
p-value of test                       :    0.9975

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:43.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:43.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.97
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:49.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.22
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.64
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.22
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.31
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.15
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:42.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.50
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.28
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.70
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17827.54
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:47.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.38
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.72
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.35
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.93
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.13
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.90
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.48
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.53
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.02
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.58
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:32.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.10
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.21
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.85
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.68
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.90
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.20
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.77
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.00
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.13
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.80
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.13
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.16
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4945.24
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.04
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.35
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:31.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.70
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.31
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5093.82
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.51
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.86
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:31.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.78
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  :   -0.14
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:08.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.41
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :    1.07
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:09.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.61
p-value of test                       :  2.2e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    5.31
p-value of test                       :  2.2e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.72
p-value of test                       :    0.9967

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.43
p-value of test                       :    0.08

Sample variance                       :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.37e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 4.36e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.83e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 9.27e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.97
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.24
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:52.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  2.8e-3

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:51.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9915.82
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10035.76
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.06
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:04:09.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4717.02
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:48.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4823.56
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:51.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4065.00
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4286.53
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11975.12
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11735.26
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:31.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.57
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999910982

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.10
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000070996

Normal statistic for number of bits   :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9997    *****

Tests on the sum of all N observations
Standardized normal statistic         :  -0.085
p-value of test                       :    0.53

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:11.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:40.09

 All tests were passed




Server wird beendet - Lösche Semaphor 21004313.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1255
p-value of test                       :    0.9986

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334375
  j =  1                              :        599997490
  j =  2                              :             1255
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:19.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:21.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:17.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1462
p-value of test                       :  4.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334582
  j =  1                              :        599997076
  j =  2                              :             1462
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5430
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:42.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:36.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:34.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:55.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7456
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:01.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:01.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:54.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:04:00.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     866
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:51.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.49
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:12.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.38
p-value of test                       :  6.3e-3

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:36.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.51
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.19
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.16
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.16
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.24
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.84
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.03
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.77
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.58
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.13
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:46.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1566.33
p-value of test                       :  9.2e-3

-----------------------------------------------
CPU time used                    :  00:02:03.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6950.74
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:45.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.58
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.59
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.33
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:01.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.42
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   93.60
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5249.78
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:15.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:01.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45594
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869594
  j =  1                              :        399908815
  j =  2                              :            45588
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45867
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869867
  j =  1                              :        399908269
  j =  2                              :            45861
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:13.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:28.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9940

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:18.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:44.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:00.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:53.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:34.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:22.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:34.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:34.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.69
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:48.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.59
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.81
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:49.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.92
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.67
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.74
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.02
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.98
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.09
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:31.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   13.62
p-value of test                       :  3.5e-3

-----------------------------------------------
CPU time used                    :  00:01:31.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.29
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  101.28
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17220.69
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.29
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.08
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.59
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.95
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.30
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.58
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.29
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.10
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.38
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.77
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.37
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.65
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.59
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.52
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.23
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:46.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.12
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.82
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.68
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.24
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.69
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:46.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.95
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.84
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4887.95
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.67
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.17
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  318.47
p-value of test                       :    0.9936


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.14
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4920.92
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.56
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.67
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.80
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :   -1.19
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:27.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.25
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :   -1.26
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:19.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.70e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.21e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.00
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.04
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 6.37e-4
p-value of test                       :    0.9994    *****

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.54
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:11.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.60
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:10.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10026.37
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9818.68
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.083
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:49.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4811.39
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 2.74e-3
p-value of test                       :    0.9972

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4723.29
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:49.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3945.34
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4208.47
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11706.20
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11940.02
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:29.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.65
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999983273

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.62
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999936164

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   0.074
p-value of test                       :    0.47

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:29.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:17:38.37

 All tests were passed




Server wird beendet - Lösche Semaphor 983066.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5343
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:43.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:37.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:36.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4434
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:54.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:55.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:02.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7157
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:03.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:53.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:59.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.39
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:46.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.90
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     656
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     343
p-value of test                       :  8.0e-3

Stat. AD (mNP2)                       :    2.43
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:10.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    7.27
p-value of test                       :  2.9e-4    *****


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.30
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:39.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.55
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.45
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.86
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.63
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.04
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.07
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.95
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.29
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.64
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1465.42
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:02.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7114.09
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:00.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.76
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.11
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:33.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5036.06
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:04.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45742
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869742
  j =  1                              :        399908526
  j =  2                              :            45722
  j =  3                              :               10
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46077
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870077
  j =  1                              :        399907848
  j =  2                              :            46073
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:32.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:18.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:02.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:55.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:15.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:34.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.41e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:32.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.95
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:48.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.03
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.14
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.81
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.28
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.79
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.31
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:29.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:30.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.65
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17199.90
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:55.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.75
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.76
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.27
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.52
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.39
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.68
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.60
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.40
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.20
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:39.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.59
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.62
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.31
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  180.31
p-value of test                       :  6.6e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  108.88
p-value of test                       :  5.2e-3


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.72
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.62
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.08
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.40
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.46
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.62
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.92
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4934.05
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.62
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.74
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:36.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.22
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.16
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5094.80
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.96
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.97
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.54
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:25.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.96
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:26.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   0.049
p-value of test                       :    0.48

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    6.13
p-value of test                       :  9.2e-4    *****

Tests on the sum of all N observations
Standardized normal statistic         :   -3.35
p-value of test                       :    0.9996    *****

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.75e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 8.00e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 4.70e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.93
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.78
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.74
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:10.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.80
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:11.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10042.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10047.24
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:04:02.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4973.62
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5024.84
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:49.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4123.41
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.29
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11891.72
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11771.06
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:28.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.51
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999945023

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.76
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000051607

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.56
p-value of test                       :    0.94

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    3.87
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.30
p-value of test                       :    0.99

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:29.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:46.84
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs NP, t = 16           2.9e-4
 83  LempelZiv, r = 15               0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1376282.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:48.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5464
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:43.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:37.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:36.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:55.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:55.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:02.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:02.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:53.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:59.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     849
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:45.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:12.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:41.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.74
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.62
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.79
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.71
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:10.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.85
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.95
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.85
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  267.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.66
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1507.40
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:01.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7097.77
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:42.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.89
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.82
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:00.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.69
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.89
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5170.39
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:01.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45413
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869413
  j =  1                              :        399909176
  j =  2                              :            45409
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45921
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869921
  j =  1                              :        399908162
  j =  2                              :            45913
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:31.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:18.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:45.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:01.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:55.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.11
p-value of test                       : 1 -  8.6e-5    *****

-----------------------------------------------
CPU time used                    :  00:01:15.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:33.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.60e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 7.46e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.04e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.77e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:34.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 7.14e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:33.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.10
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.20
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:48.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.83
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:42.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.58
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.05
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.00
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.00
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17302.48
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.33
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.61
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.97
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.42
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.91
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.05
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.46
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.42
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.49
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.60
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:39.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.91
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.61
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.89
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.03
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.62
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.60
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.12
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.55
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.66
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.12
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.52
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.47
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.87
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.95
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.96
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.54
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.78
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4924.48
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.29
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.99
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:34.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   34.60
p-value of test                       :  5.4e-4    *****


-----------------------------------------------
Normal statistic for number of jumps  :    1.23
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:23.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.86
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :    1.13
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:26.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.29e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.78
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.12
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.24
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:07.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.18e-3
p-value of test                       :    0.9967

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:08.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9973.84
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9991.88
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:49.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.36
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4994.51
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:50.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4192.08
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.02
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12191.05
p-value of test                       :  9.1e-3

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11769.94
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:28.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.78
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999915860

Normal statistic for number of bits   :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.26
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999974810

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.89
p-value of test                       :    0.97

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    2.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:39.00
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 51  SampleProd, t = 16             1 -  8.6e-5
 80  LinearComp, r = 0               5.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2424858.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:50.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5382
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:48.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:38.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:37.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:55.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:01.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:02.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:53.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:59.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.9906


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    2.20
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     833
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:46.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     565
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:12.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:42.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.99
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.71
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.25
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.59
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.87
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.96
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.43
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:01.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7124.93
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:44.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.58
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:00.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.33
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.14
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:34.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5164.15
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:02.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45695
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869695
  j =  1                              :        399908615
  j =  2                              :            45685
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46225
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870225
  j =  1                              :        399907553
  j =  2                              :            46219
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:31.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:18.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:45.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:01.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:33.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 9.79e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.50e-4
p-value of test                       :  7.4e-3

Kolmogorov-Smirnov- statistic = D-    : 8.16e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:21.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:34.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:33.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.02
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.30
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.32
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.80
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.32
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.36
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.36
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.60
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.32
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.31
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:37.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17309.13
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.17
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.71
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.72
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.21
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.51
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:39.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.94
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.65
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.22
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.74
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.21
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.33
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.54
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.50
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.39
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.96
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.27
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.61
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.25
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.26
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.02
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  448.35
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.43
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.82
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.44
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.37
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.11
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.79
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4840.73
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.44
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.95
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.05
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :    0.93
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:22.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.71
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :   -1.05
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:25.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.55e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.63
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.08
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.28
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:06.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.93
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:06.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9798.69
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9914.91
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:50.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    3.74
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4656.34
p-value of test                       :    0.9917

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.68
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:49.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3973.97
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4198.34
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12073.14
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11643.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:29.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.98
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000012925

Normal statistic for number of bits   :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.45
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999995273

Normal statistic for number of bits   :  -0.037
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    2.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   0.057
p-value of test                       :    0.48

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.56
p-value of test                       :    0.06

Sample variance                       :    1.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.14

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:02.70

 All tests were passed




Server wird beendet - Lösche Semaphor 3506202.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:50.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5441
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:53.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:38.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:39.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:55.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:55.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:02.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:02.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:53.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:58.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.95
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    2.18
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:46.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.72
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     331
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:10.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.98
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:40.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.67
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.82
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:55.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.37
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.37
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.96
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.76
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1361.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:01.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6977.15
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:43.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.43
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:03.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.03
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.29
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4981.28
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:32.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:26.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45942
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869942
  j =  1                              :        399908121
  j =  2                              :            45932
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46230
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870230
  j =  1                              :        399907543
  j =  2                              :            46224
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:14.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:30.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:18.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:44.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:55.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:33.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 4.40e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 9.10e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      : -1.99e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.95
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.15
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.80
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:48.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.13
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   16.55
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.14
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:38.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.26
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.09
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.57
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.27
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.55
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17578.08
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.97
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.34
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.90
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.39
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.94
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.79
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.47
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.56
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.45
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.17
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.82
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.94
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.00
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.04
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.18
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.26
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.89
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.98
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.92
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.19
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.65
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.77
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4935.84
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.42
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.30
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.37
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.60
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.00
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.60
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.66
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.42
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :   -0.37
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:24.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   29.14
p-value of test                       :  3.8e-3


-----------------------------------------------
Normal statistic for number of jumps  :    1.56
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:23.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.02e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:47.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 9.73e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.86
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.63
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.91
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:04.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:06.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9991.78
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10188.51
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:45.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5022.42
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4709.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:49.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4150.16
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4228.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11596.29
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11805.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:29.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.55
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000153883

Normal statistic for number of bits   :    1.22
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.64
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999908909

Normal statistic for number of bits   :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   0.042
p-value of test                       :    0.48

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.71
p-value of test                       :    0.04

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.55
p-value of test                       :    0.94

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:50.56

 All tests were passed




Server wird beendet - Lösche Semaphor 4489242.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5447
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:54.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:39.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:02.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7180
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:03.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:53.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:57.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.31
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:46.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    2.52
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.09
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:12.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:39.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.68
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.03
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.35
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.98
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.82
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.26
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.17
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:43.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1414.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:02.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7095.55
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:42.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.69
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.22
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:02.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.93
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:46.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.81
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:32.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4972.39
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:59.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45597
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869597
  j =  1                              :        399908809
  j =  2                              :            45591
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45869
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869869
  j =  1                              :        399908268
  j =  2                              :            45857
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:29.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 6.06e-3
p-value of test                       :    0.9928

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:18.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:44.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:58.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.61e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -4.95e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:32.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:32.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.20
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:48.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  100.66
p-value of test                       :  4.9e-3

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.23
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.04
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.15
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.02
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.89
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:40.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.15
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17497.05
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.76
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.67
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.72
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.85
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.92
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.87
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.79
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.91
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.21
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.06
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  192.13
p-value of test                       :  6.3e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.44
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.37
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.67
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.95
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.13
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  544.00
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.06
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   47.33
p-value of test                       :    0.9933


-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.85
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.50
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5140.04
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.38
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.02
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.98
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.50
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5100.65
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.00
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.41
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.98
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :    1.36
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:23.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.99
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :    1.74
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:23.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    2.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 5.18e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 4.36e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.95
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.11
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.59
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:04.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.04e-3
p-value of test                       :    0.9914

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.23
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:07.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.5e-3

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9779.79
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10134.80
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:56.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.39
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:48.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4995.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:49.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4035.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4213.19
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11604.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12014.18
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.83
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000003616

Normal statistic for number of bits   :   0.029
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.85
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000133939

Normal statistic for number of bits   :    1.06
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.23
p-value of test                       :    0.9901

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:33.14

 All tests were passed




Server wird beendet - Lösche Semaphor 5472282.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5507
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:04:00.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:43.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:43.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:59.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4437
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:00.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:10.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7171
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:11.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:07.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:04:08.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.87
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.96
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     947
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.60
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     567
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    2.82
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.33
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.97
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     265
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:15.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    3.29
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     128
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:46.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.25
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.48
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.39
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.43
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.91
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.26
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.77
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.53
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.80
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1369.03
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:06.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7034.08
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:56.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.71
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:19.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.72
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:46.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.19
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4924.83
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:02.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45534
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869534
  j =  1                              :        399908932
  j =  2                              :            45534
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45683
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869683
  j =  1                              :        399908639
  j =  2                              :            45673
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:32.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:20.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:51.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 6.70e-3
p-value of test                       :    0.9924

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:07.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :  4.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    3.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:56.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:37.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 3.46e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:24.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:43.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:44.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.12
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.72
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.22
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.15
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.83
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.99
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:51.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.57
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.56
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  155.49
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17407.20
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.40
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.47
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.61
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.78
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.73
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:37.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.89
p-value of test                       :    0.9915


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.66
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.52
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.00
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.43
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.09
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.91
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  437.10
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.14
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.10
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.58
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.78
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  442.26
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.96
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.46
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.38
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.76
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4865.69
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.06
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.82
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.77
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.71
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4891.37
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.42
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.37
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:34.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.05
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:23.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.61
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  : 2.98e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:22.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    1.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 8.61e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.35e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 7.45e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9906

-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   23.04
p-value of test                       :  3.3e-3

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.37
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.29
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:07.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:08.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9908.75
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10102.44
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:04:29.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5028.87
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.28
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:59.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4161.75
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.94
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11963.85
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:35.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11888.48
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:37.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.15
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000027847

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.28
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000023707

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.64
p-value of test                       :    0.05

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.92
p-value of test                       :    0.97

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:47.88

 All tests were passed




Server wird beendet - Lösche Semaphor 6520858.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:51.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5397
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:55.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4432
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:41.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4475
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:57.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:58.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:07.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:06.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:58.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:03.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    4.11
p-value of test                       :  7.7e-3

-----------------------------------------------
CPU time used                    :  00:02:13.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:41.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.17
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.20
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.31
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.83
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.39
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.25
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.77
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  261.97
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1471.29
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:04.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7177.78
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:50.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.53
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.88
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:09.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.88
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   93.34
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:36.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4976.94
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:00.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46104
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870104
  j =  1                              :        399907798
  j =  2                              :            46092
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45763
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869763
  j =  1                              :        399908476
  j =  2                              :            45759
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:30.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:18.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:46.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:03.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 9.27e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 6.60e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.40e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:38.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:39.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.27
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.70
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.22
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   64.19
p-value of test                       :  3.7e-3

-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.58
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.28
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.44
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:46.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.94
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.82
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17285.52
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.80
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.19
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.05
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.13
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   34.27
p-value of test                       :  7.7e-3


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.18
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.99
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.68
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.82
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.04
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.85
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.82
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.15
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.30
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.32
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.20
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.56
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  546.77
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  100.16
p-value of test                       :    0.9908


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.92
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.58
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.46
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.74
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.04
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.96
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.62
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.31
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4878.35
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.42
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.91
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.38
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :    1.87
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:24.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.66
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:23.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.79e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.80e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.37
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.50
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.15
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:06.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.56
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:07.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9926.85
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10141.94
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:04:18.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.81
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:53.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.04
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.73
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3935.94
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11855.73
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:31.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11938.69
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:31.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.80
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999957437

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.51
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  7999995183

Normal statistic for number of bits   :  -0.038
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    4.29
p-value of test                       :  6.6e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.62
p-value of test                       :    0.9957

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:49.63

 All tests were passed




Server wird beendet - Lösche Semaphor 7864346.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1520
p-value of test                       :  1.8e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334640
  j =  1                              :        599996960
  j =  2                              :             1520
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5574
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:54.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:41.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:56.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4232
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:57.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:04.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:04.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:54.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:59.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:46.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     566
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.96
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:12.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.81
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:40.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.31
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.98
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.09
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.20
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.70
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.25
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.70
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:43.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1371.67
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:03.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7069.99
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:44.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.25
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.20
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:03.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.95
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.90
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:34.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5011.82
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:55.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45897
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869897
  j =  1                              :        399908211
  j =  2                              :            45887
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45657
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869657
  j =  1                              :        399908688
  j =  2                              :            45653
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:28.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:18.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :  3.3e-3

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:35.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.94e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 7.96e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9943

-----------------------------------------------
CPU time used                    :  00:00:22.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 8.41e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:35.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:36.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.25
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.38
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.20
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.54
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.85
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.05
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:44.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.78
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.18
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17361.99
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.47
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.29
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.17
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.94
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.43
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.48
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.43
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.87
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.28
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  191.61
p-value of test                       :  6.7e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.32
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.65
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  174.12
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.51
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.56
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.42
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.61
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.22
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.46
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.73
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.55
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.36
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.21
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.46
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.11
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.90
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.83
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.26
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.30
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.94
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:24.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.66
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :    1.64
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:25.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.84
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.97
p-value of test                       :    0.98

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 3.44e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.01e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.06
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.45
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.88
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:07.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.47
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:07.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9992.10
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9920.52
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.13
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:43.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.82
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:48.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4826.68
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4017.50
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.27
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11501.36
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11920.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:29.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.65
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000076447

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.44
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999961133

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:27.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           1.8e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8978458.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997269
  j =  2                              :             1364
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5431
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:56.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:41.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:56.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:57.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:04.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7460
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:04.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:54.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:00.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.54
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.87
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.12
p-value of test                       :    0.9997    *****

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     273
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:13.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.69
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:43.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.19
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.11
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.77
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.49
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.60
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.81
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.64
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.42
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.89
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:43.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1485.35
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:01.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7166.07
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:43.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.60
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.86
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.45
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:03.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.37
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:46.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  151.76
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:31.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4934.11
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:52.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45921
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869921
  j =  1                              :        399908160
  j =  2                              :            45917
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45778
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869778
  j =  1                              :        399908449
  j =  2                              :            45768
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:27.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:19.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    3.43
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:46.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:59.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:35.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.15e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.72e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 7.84e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:22.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.029
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:36.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:36.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.09
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.51
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.25
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.12
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.75
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.30
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.73
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.77
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.90
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.83
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.60
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17481.99
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.08
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.08
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.84
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.57
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.72
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.05
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.73
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.31
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.19
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.76
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.49
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.76
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.73
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.40
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.98
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.87
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.18
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.05
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.68
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.62
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.30
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.20
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.41
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.27
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.40
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.56
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.43
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5168.10
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.82
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.51
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.54
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :   -1.25
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:24.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.51
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:24.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 7.17e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.75e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.37
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.29
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:06.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.46
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:04.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9949.92
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10102.47
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.70
p-value of test                       :    0.9965

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:51.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.34
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:48.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.71
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:49.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4069.69
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11818.67
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11932.24
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:29.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.91
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999895604

Normal statistic for number of bits   :   -0.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.77
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000096694

Normal statistic for number of bits   :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.31e-3
p-value of test                       :    0.9955

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.84
p-value of test                       :    0.97

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:48.71
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs mNP2, t = 5          0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9863194.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1469
p-value of test                       :  2.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334589
  j =  1                              :        599997062
  j =  2                              :             1469
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1472
p-value of test                       :  2.0e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334592
  j =  1                              :        599997056
  j =  2                              :             1472
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5461
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:04:00.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:43.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:43.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:57.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:57.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:05.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:06.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:55.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7162
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:04:00.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     860
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    2.55
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     643
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    2.10
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    2.43
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:13.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:44.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.10
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.23
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.78
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.14
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.56
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.18
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.38
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  474.18
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:44.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1471.51
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:00.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7192.45
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.95
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.23
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:02.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.01
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:32.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5006.15
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:58.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45969
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869969
  j =  1                              :        399908072
  j =  2                              :            45949
  j =  3                              :               10
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46036
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870036
  j =  1                              :        399907930
  j =  2                              :            46032
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:28.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:19.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:47.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:00.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:55.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.99e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 2.52e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 8.31e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:34.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:37.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.26
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:51.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.57
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.57
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.95
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   45.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:42.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.98
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.50
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.64
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17425.35
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.81
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.23
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.14
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.55
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.90
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.05
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.72
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.49
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.09
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.15
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  106.03
p-value of test                       :    0.9947


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.69
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.87
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.98
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.76
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.63
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.20
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  446.09
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  191.40
p-value of test                       :  1.2e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.42
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.54
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.09
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4904.19
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.66
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.38
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.88
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.95
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4806.98
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.85
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.50
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.79
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:27.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.38
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :   -1.50
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:26.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.27e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 5.20e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 4.00e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.13
p-value of test                       :    0.9973

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.67
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :  1.4e-3

Anderson-Darling statistic = A2       :    5.28
p-value of test                       :  2.2e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  260.46
p-value of test                       :  2.6e-3

-----------------------------------------------
CPU time used                    :  00:02:07.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-3
p-value of test                       :    0.9984

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  247.89
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:05.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10060.50
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9856.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.06
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:43.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5041.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4993.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:49.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.04
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4220.96
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11604.23
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11696.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:30.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.54
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000124570

Normal statistic for number of bits   :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.00
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000002113

Normal statistic for number of bits   :   0.017
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.71
p-value of test                       :    0.96

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :  -0.097
p-value of test                       :    0.54

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:42.54

 All tests were passed




Server wird beendet - Lösche Semaphor 10911770.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  6.1e-3


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5458
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:59.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:42.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:44.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:59.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:06.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:06.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:55.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:01.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:14.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    3.40
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:47.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.67
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.20
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.12
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.93
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.81
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.64
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.87
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:44.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1372.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:01.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7163.77
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:42.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.25
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:03.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.52
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.43
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:31.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5005.87
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:57.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45745
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869745
  j =  1                              :        399908514
  j =  2                              :            45737
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45642
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869642
  j =  1                              :        399908721
  j =  2                              :            45632
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:27.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:18.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:46.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.9903


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:01.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:54.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:32.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 4.21e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.56e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:34.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.049
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:33.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.31
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.10
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.88
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.13
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.81
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.00
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:44.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.42
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.21
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.45
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.78
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17402.19
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.23
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.93
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.64
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.06
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.14
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.32
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.36
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.71
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.29
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.38
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.70
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.87
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  180.08
p-value of test                       :  6.8e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.65
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.78
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.16
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  554.95
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.82
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.96
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.09
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.21
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4887.40
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.57
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.63
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  450.15
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.62
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4938.72
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.17
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.01
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.11
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:24.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.90
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:24.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.96
p-value of test                       :    0.98

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.16
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.33
p-value of test                       :    0.99

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.48e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.78e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 5.28e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.99
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.23
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.39
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:07.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.09
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:04.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10030.15
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10071.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:55.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:47.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4845.49
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.22
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:49.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4175.34
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4179.80
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11682.04
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11927.05
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:30.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.92
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000029914

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.72
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000046786

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.77e-4
p-value of test                       :    0.9996    *****

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -2.21
p-value of test                       :    0.99

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.55
p-value of test                       :    0.94

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:49.10

 All tests were passed




Server wird beendet - Lösche Semaphor 11960346.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:50.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5533
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:59.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:44.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:46.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:01.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:02.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:12.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:12.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:09.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:04:13.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    2.42
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:48.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.98
p-value of test                       :  9.3e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:14.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:40.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.01
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.01
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.76
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.83
p-value of test                       :    0.9915

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.56
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.17
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.26
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.96
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:54.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.05
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:06.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7111.69
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:56.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.42
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:17.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.03
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.20
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:40.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4896.92
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:59.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45760
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869760
  j =  1                              :        399908485
  j =  2                              :            45750
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45665
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869665
  j =  1                              :        399908670
  j =  2                              :            45665
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:33.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:21.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:05.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:56.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:38.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.27e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 9.90e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:24.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.030
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:24.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:24.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:43.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.13
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.56
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.41
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.62
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:50.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.13
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.69
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.11
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:50.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.53
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.05
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:28.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.20
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.38
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17480.51
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.72
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.60
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.68
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.46
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.05
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.56
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.34
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.85
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.34
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.20
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.88
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.27
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  441.28
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.60
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.28
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.81
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.35
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.72
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.40
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.10
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.31
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.73
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4945.16
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.49
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.07
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.02
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.62
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5109.87
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.90
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.08
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.88
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:23.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.00
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :   -0.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:22.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.53
p-value of test                       :    0.06

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.71
p-value of test                       :    0.96

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:11.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.52e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.04e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.55
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.67
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.75
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:06.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.70
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:07.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10000.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.056
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:04:25.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5000.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:56.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4839.87
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:00.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4147.45
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3947.67
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:28.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11787.57
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:36.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11703.43
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:37.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.46
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000050632

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.07
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000153421

Normal statistic for number of bits   :    1.21
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.20
p-value of test                       :    0.9939

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:57.00

 All tests were passed




Server wird beendet - Lösche Semaphor 12976154.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  2.0e-3


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5233
p-value of test                       :    0.9948


-----------------------------------------------
CPU time used                    :  00:03:58.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4456
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:43.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:44.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4215
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:00.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:02.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:10.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:09.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:04:03.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:05.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:48.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:14.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.92
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     128
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:46.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.21
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.67
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.97
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.96
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.49
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.98
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.94
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:49.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1450.35
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:04.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6977.13
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:52.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.61
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.80
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:13.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.06
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.43
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:36.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5011.84
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:08.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45685
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869685
  j =  1                              :        399908633
  j =  2                              :            45679
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45708
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869708
  j =  1                              :        399908589
  j =  2                              :            45698
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:31.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:19.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:48.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:06.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.97
p-value of test                       :  9.1e-3

-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:36.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 8.80e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.018
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:47.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:48.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.99
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.26
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.73
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.22
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:47.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.63
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.24
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.89
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.98
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17572.71
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.22
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.28
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.90
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.44
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.28
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.66
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.88
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.46
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   43.42
p-value of test                       :  8.9e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.21
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.15
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.23
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.70
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.92
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.99
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.55
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.56
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.76
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.06
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.86
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.15
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.98
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4895.73
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.68
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.76
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.30
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.40
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.72
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.65
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.57
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.04
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:26.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.82
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :    1.56
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:23.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.65
p-value of test                       :    0.95

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 1.92e-3
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.67
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.41
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.83
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:05.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.69
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:07.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9936.14
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9912.34
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.016
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:04:19.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4805.32
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:54.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4997.13
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:57.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4207.75
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11985.77
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:31.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11984.51
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:33.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.85
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999860585

Normal statistic for number of bits   :   -1.10
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.56
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999913427

Normal statistic for number of bits   :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:02.29

 All tests were passed




Server wird beendet - Lösche Semaphor 14155802.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:40.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:50.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5349
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:55.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:42.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4456
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4439
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:57.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:05.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:05.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:54.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7465
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:00.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.00
p-value of test                       :  8.8e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    4.03
p-value of test                       :  8.4e-3

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.66
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.45
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:12.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:42.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.11
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.90
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.26
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.00
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.75
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.61
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.57
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.59
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:44.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.76
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:02.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7071.16
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:41.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.89
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.43e-3
p-value of test                       :    0.9954

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   84.54
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:02.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.76
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.50
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:33.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5220.23
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:10.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45842
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869842
  j =  1                              :        399908319
  j =  2                              :            45836
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45715
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869715
  j =  1                              :        399908574
  j =  2                              :            45707
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:26.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:19.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:46.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:59.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:55.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:34.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.06e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.93e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:35.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:34.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.59
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.51
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.41
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.08
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:39.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.71
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.71
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.19
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  8.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17148.20
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:54.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.10
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   60.76
p-value of test                       :  4.4e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.21
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.98
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.10
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.54
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.69
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.06
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.57
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.34
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.22
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.67
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.70
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.58
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.46
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.29
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.77
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.10
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.33
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.54
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.58
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.43
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5108.75
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.97
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.64
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.30
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.37
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.44
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.70
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.17
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.82
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:21.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.09
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :   -1.84
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:22.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.64e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.40e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 8.00e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.63
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   23.30
p-value of test                       :  3.0e-3

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.97
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:07.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.15
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:06.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10189.78
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10054.21
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.81
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:40.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.00
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.42
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:50.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4180.18
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4238.58
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11660.16
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11841.63
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.59
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000048985

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.86
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999987281

Normal statistic for number of bits   :   -0.10
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.85
p-value of test                       :    0.97

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:39.70

 All tests were passed




Server wird beendet - Lösche Semaphor 15269914.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1266
p-value of test                       :    0.9963

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334386
  j =  1                              :        599997468
  j =  2                              :             1266
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5372
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:57.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7481
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:40.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:58.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7453
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:06.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:06.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:56.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:00.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:47.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:16.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.25
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.16
p-value of test                       :    0.9981

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.25
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:46.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.61
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.17
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.34
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.46
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.39
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.98
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.86
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.61
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.83
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:44.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1363.90
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:01.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7193.31
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:41.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.03
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:02.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   19.06
p-value of test                       :  1.9e-3


-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.86
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:32.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5124.20
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:58.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46565
p-value of test                       :  7.1e-4    *****


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870565
  j =  1                              :        399906874
  j =  2                              :            46557
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46055
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870055
  j =  1                              :        399907894
  j =  2                              :            46047
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:27.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:19.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:45.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:59.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:55.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:35.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.58e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:21.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:34.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:34.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.60
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.53
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.22
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.52
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.25
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.94
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:43.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9925

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.60
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.68
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.14
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17249.27
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.27
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.87
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.92
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.80
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.33
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.62
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.00
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.12
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.64
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.07
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.02
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.37
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.03
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.53
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   47.06
p-value of test                       :    0.9939


-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.84
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.27
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.93
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.99
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.59
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.47
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.66
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4767.82
p-value of test                       :    0.9907


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.24
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  160.52
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.36
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.97
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5096.38
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.61
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.95
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.35
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :    1.17
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:22.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.23
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:23.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.52
p-value of test                       :    0.94

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 8.99e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.44e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.72
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.39
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.81
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:05.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.67
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:05.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9686.67
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10111.67
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:43.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.98
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4957.86
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:50.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3979.19
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4049.71
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12024.76
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11679.51
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.80
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999877775

Normal statistic for number of bits   :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.41
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000122017

Normal statistic for number of bits   :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:08.93
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 44  CollisionPermut, r = 0          7.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16285722.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5444
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:59.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4236
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:43.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:44.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:59.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:59.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:09.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:08.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:04.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:04:02.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     942
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.42
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:13.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    2.90
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    2.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:44.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.72
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.55
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.46
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.88
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.83
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.80
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.43
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.33
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1352.94
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:05.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7092.45
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:50.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.06
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:09.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.12
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   87.87
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:37.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5112.58
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:59.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45544
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869544
  j =  1                              :        399908916
  j =  2                              :            45536
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46192
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870192
  j =  1                              :        399907619
  j =  2                              :            46186
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:30.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:18.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:47.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 2.91e-3
p-value of test                       :    0.9969

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:04.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:36.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.23e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 6.74e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:22.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:39.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.26
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:40.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.65
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:50.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.30
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.84
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.09
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.31
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.70
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.70
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.89
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.35
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.8e-3

Kolmogorov-Smirnov- statistic = D-    : 4.02e-3
p-value of test                       :    0.9958

Anderson-Darling statistic = A2       :    3.75
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   89.87
p-value of test                       :    0.9971

-----------------------------------------------
CPU time used                    :  00:00:39.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17658.29
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.00
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.53
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.23
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.64
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.52
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.67
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.59
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.11
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.08
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.14
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.60
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.34
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.55
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.92
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.37
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.60
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.92
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.81
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.78
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.25
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.34
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.28
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5086.37
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.47
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.38
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:34.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.47
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.92
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4777.49
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.71
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  159.26
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:34.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.17
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   0.012
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:22.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.34
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :    1.21
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:24.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    1.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.43e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.20e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.14
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.84
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.38
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:06.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.33
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:08.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9860.14
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10036.96
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.51
p-value of test                       :    0.9939

-----------------------------------------------
CPU time used                    :  00:04:16.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4851.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:53.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4858.21
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:54.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4061.12
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4172.09
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11914.95
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:31.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11654.16
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:31.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.69
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999981614

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.43
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000063739

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.71
p-value of test                       :    0.04

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.79
p-value of test                       :    0.04

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         : 8.66e-3
p-value of test                       :    0.50

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:12.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:10.95

 All tests were passed




Server wird beendet - Lösche Semaphor 17301530.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5364
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:56.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:41.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:58.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:59.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:07.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:07.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:53.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:59.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.82
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.55
p-value of test                       :  4.8e-3

Test on the Nm values of W_{n,i}(mNP1):    2.32
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     845
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:13.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.90
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.74
p-value of test                       :  4.2e-3

Test on the Nm values of W_{n,i}(mNP1):    2.17
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:44.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.91
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.99
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.72
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:10.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.53
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.09
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.94
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:43.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1478.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:01.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6841.37
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:43.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.07
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.27
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:03.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.39
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:46.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.45
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:34.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5074.65
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:58.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45946
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869946
  j =  1                              :        399908109
  j =  2                              :            45944
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46206
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870206
  j =  1                              :        399907590
  j =  2                              :            46202
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:28.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:20.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:47.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:02.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:35.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.83e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.33e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 8.36e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 3.69e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:35.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.58
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.54
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.45
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.03
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.27
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.19
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.62
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:45.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.41
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.78
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9997    *****

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17461.30
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.45
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.64
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.66
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.45
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.67
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.62
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.47
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.41
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.26
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.90
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.53
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.43
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.66
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.10
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  105.33
p-value of test                       :  9.8e-3


-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.99
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.22
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.82
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.14
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.34
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.12
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.75
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4993.96
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.35
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  239.51
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.83
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.19
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5134.00
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.66
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.05
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:34.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.34
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :    1.80
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:22.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.52
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :   -2.02
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:23.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.15e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 5.15e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.80e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.55
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.11
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:06.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.01
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:07.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10285.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10048.45
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:47.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.91
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:49.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4988.28
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:50.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.51
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.67
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11557.14
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11655.73
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:29.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.58
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  7999982973

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.92
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000092920

Normal statistic for number of bits   :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :  -0.087
p-value of test                       :    0.53

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:05.96

 All tests were passed




Server wird beendet - Lösche Semaphor 18350106.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5348
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:55.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:42.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:57.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:59.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:07.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:06.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7141
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:55.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:02.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:47.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.70
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    2.92
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:12.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:45.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.52
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.66
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.44
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.43
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:10.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.08
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.49
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.78
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  263.83
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  478.59
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:43.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1462.33
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:01.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6995.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.00
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.43
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:04.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.58
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:46.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.58
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5004.18
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:12.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:59.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45951
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869951
  j =  1                              :        399908105
  j =  2                              :            45937
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46159
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870159
  j =  1                              :        399907688
  j =  2                              :            46147
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:28.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  1.1e-3

Anderson-Darling statistic = A2       :    3.91
p-value of test                       :  9.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:18.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:45.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:58.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:35.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.71e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 7.38e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:33.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:33.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.86
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.24
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.86
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.66
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.83
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.32
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:40.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.01
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.68
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.26
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.52
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9967

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17424.10
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.81
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.99
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.37
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.35
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.68
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.38
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.63
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.12
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.44
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.75
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.58
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.36
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.71
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.73
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.70
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.51
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.84
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.36
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.25
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.63
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.05
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.81
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.06
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.15
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.14
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.73
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4883.63
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.26
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.80
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.66
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :   -0.92
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:24.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.61
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:24.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 8.14e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.62
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.02
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:06.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.97
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:06.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9969.94
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:43.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4948.33
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:48.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.72
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:50.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.25
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.58
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11708.91
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11810.36
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:29.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.19
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999999605

Normal statistic for number of bits   : -3.12e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.44
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000095302

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:53.76

 All tests were passed




Server wird beendet - Lösche Semaphor 19365914.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:50.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5486
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:56.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:41.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:41.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:57.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:59.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7094
p-value of test                       :    0.9957


-----------------------------------------------
CPU time used                    :  00:03:06.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7493
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:06.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:56.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7454
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:01.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:46.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    3.57
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:13.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.84
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.36
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.14
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:10.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.72
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.58
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.82
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  466.14
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:43.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1529.54
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:01.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6980.79
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.37
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.65
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:03.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.38
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.23
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:33.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5065.47
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:55.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45638
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869638
  j =  1                              :        399908725
  j =  2                              :            45636
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46100
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870100
  j =  1                              :        399907801
  j =  2                              :            46098
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:28.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:18.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:44.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:57.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:35.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 8.40e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:21.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:32.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:32.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.57
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.56
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.78
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.27
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.93
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.01
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:39.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.69
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.91
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.99
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.83
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17259.64
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.12
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.91
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.53
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.07
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.30
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.17
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.13
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.55
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.61
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.72
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.07
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.45
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  570.01
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.73
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.58
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.69
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.58
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.12
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.92
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.15
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.51
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.46
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4825.57
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.02
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.08
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.46
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.81
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.68
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.32
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  243.62
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.00
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :   0.057
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:21.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.86
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   -1.17
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:23.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.82
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.55
p-value of test                       :    0.9947

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.04e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.27e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.34
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.92
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.07
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:08.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.51
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:06.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9962.11
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10106.92
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:37.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4887.24
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:42.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5092.94
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:50.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.51
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.38
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:18.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11874.88
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11675.35
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.50
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000035755

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.26
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000077242

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :  -0.080
p-value of test                       :    0.53

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.07
p-value of test                       :  8.4e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.73
p-value of test                       :    0.9968

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.92

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:46.20

 All tests were passed




Server wird beendet - Lösche Semaphor 20381722.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:18.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:19.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:18.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5385
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:45.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:38.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:48.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:58.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:09.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:27.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:27.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:11.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:47.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:47.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    5.31
p-value of test                       :  2.1e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    3.19
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:07.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    2.48
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:48.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.03
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.32
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.70
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.50
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.70
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.92
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.76
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:38.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.25
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:35.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1510.85
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:28.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7014.42
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.93
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.20
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:17.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.16
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.18
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:43.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5170.89
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:21.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46106
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870106
  j =  1                              :        399907793
  j =  2                              :            46096
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46481
p-value of test                       :  2.5e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870481
  j =  1                              :        399907041
  j =  2                              :            46475
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:31.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:26.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:53.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:12.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:54.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:37.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 7.70e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9980

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.46
p-value of test                       :    0.9931

-----------------------------------------------
CPU time used                    :  00:00:24.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:46.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:45.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.56
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.09
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   63.78
p-value of test                       :  4.0e-3

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.36
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.67
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.64
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:51.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.45
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.80
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.02
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.47
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.58
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17470.87
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:54.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.41
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.89
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.77
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.43
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.02
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.01
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.47
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.22
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.84
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.47
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:39.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.59
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.52
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.89
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.84
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.14
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.19
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.36
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.83
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.98
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  111.25
p-value of test                       :  3.3e-3


-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.46
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.51
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5034.14
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.71
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.92
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.75
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.76
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5147.70
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.95
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.09
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.48
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:30.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.27
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :   -1.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:29.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.88e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 7.30e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.78
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.32
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.96
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:14.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.19
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:16.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9895.53
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10041.22
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:04:25.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4795.61
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:55.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4851.18
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:59.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4025.21
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4209.74
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11908.97
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:35.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11759.88
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:34.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.04
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999831428

Normal statistic for number of bits   :   -1.33
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.15
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000157480

Normal statistic for number of bits   :    1.24
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:11.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :  -0.014
p-value of test                       :    0.51

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:10.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:27:27.27

 All tests were passed




Server wird beendet - Lösche Semaphor 1015835.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5280
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:50.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:39.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:41.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:55.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:59.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7487
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:08.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7469
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:09.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:56.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:05.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:17.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:45.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.28
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.09
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.04
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.23
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   83.00
p-value of test                       :  6.8e-3

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.91
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.63
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  202.02
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:32.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:47.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.49
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:19.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6884.92
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:49.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.81
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.69
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:06.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.18
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:35.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5254.27
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:59.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45665
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869665
  j =  1                              :        399908670
  j =  2                              :            45665
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46021
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870021
  j =  1                              :        399907962
  j =  2                              :            46013
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:25.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:16.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:45.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:00.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:55.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:33.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 7.08e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.55e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.90e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.33
p-value of test                       :    0.9901

-----------------------------------------------
CPU time used                    :  00:01:32.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.092
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:32.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.21
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:49.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.22
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.85
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.07
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.73
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.08
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.73
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.39
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17291.95
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:58.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.74
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.23
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.26
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.82
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.85
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.88
p-value of test                       :    0.9916


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.47
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.54
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.93
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.79
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.95
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.05
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.27
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.61
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.37
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:46.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.93
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.18
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.01
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.22
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.85
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.24
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4948.34
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.52
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.67
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.98
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.21
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4925.40
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.21
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.43
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.34
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :    0.99
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:26.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.40
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:27.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.95
p-value of test                       :    0.97

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.21e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 5.51e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.61e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 8.54e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.26
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.48
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:10.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:10.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10101.04
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9880.03
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:44.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5032.66
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.6e-3

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5071.71
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:51.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.05
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4207.54
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11732.11
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:29.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11653.80
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.58
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000005209

Normal statistic for number of bits   :   0.041
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.39
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000017647

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :  -0.076
p-value of test                       :    0.53

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    2.39
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:22.28

 All tests were passed




Server wird beendet - Lösche Semaphor 2195483.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:46.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5331
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:50.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:39.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:38.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:03.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:04.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:54.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7107
p-value of test                       :    0.9933


-----------------------------------------------
CPU time used                    :  00:04:01.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.27
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    4.94
p-value of test                       :  3.1e-3

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:15.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:17.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    2.00
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:49.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.08
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.88
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.68
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.08
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.06
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.18
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.59
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.91
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:44.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.42
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:58.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6983.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:45.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.12
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:04.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.39
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  150.19
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:35.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5425.07
p-value of test                       :  8.6e-5    *****


-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:59.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45984
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869984
  j =  1                              :        399908032
  j =  2                              :            45984
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45768
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869768
  j =  1                              :        399908467
  j =  2                              :            45762
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:25.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:16.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:44.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:01.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:33.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:22.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.33
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:22.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:33.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:33.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.47
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:50.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.61
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.97
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.73
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.10
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.55
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:42.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.99
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.18
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17253.40
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.82
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.57
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.96
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.67
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.73
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:39.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.78
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.95
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.02
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.48
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.37
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.98
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.27
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.55
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.94
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.03
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.32
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.03
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.24
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.34
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.27
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.74
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.88
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.55
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.35
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.59
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.63
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.30
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.76
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.88
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.87
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.06
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :  -0.051
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:27.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.74
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :    0.82
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:28.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   0.071
p-value of test                       :    0.47

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.5e-3

Anderson-Darling statistic = A2       :    5.85
p-value of test                       :  1.2e-3

Tests on the sum of all N observations
Standardized normal statistic         :    3.22
p-value of test                       :  6.4e-4    *****

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 3.18e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 3.32e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.80
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.76
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.21
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:07.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:07.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10079.89
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9983.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : -3.14e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:43.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.37
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.14
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:51.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.82
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.47
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11835.15
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11924.20
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.56
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999959102

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.75
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999992816

Normal statistic for number of bits   :  -0.057
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.45e-3
p-value of test                       :    0.9920

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.71
p-value of test                       :    0.04

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9935

Tests on the sum of all N observations
Standardized normal statistic         :  -0.054
p-value of test                       :    0.52

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:57.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 42  Permutation, t = 7              8.6e-5
 83  LempelZiv, r = 15               6.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 3080219.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5507
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:49.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:39.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:37.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:55.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4234
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:03.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:03.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:55.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:00.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    2.77
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     855
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.17
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     552
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.63
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.26
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:15.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.83
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:44.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.20
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.62
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.47
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.07
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.11
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.10
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.40
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.12
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.25
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:44.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1543.60
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:02.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7171.95
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:45.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.57
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:02.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.34
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.69
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:35.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5077.71
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:58.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46051
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870051
  j =  1                              :        399907902
  j =  2                              :            46043
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45962
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869962
  j =  1                              :        399908079
  j =  2                              :            45956
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  8.7e-3

Kolmogorov-Smirnov- statistic = D-    : 5.42e-3
p-value of test                       :    0.9933

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:27.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:18.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:46.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 5.37e-3
p-value of test                       :    0.9941

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:00.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:55.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:34.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.028
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:34.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:33.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.80
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.52
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.21
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.35
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.75
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   47.52
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:42.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.39
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.25
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.11
p-value of test                       :    0.9901

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.93
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.27
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17103.02
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.18
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.27
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.07
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.93
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.11
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.59
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.53
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.75
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.75
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.03
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.70
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.00
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.36
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.18
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.98
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.19
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.19
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.68
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.17
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.13
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.39
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.32
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.94
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.75
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.48
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.61
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.59
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5137.38
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.57
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.10
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:36.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.35
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :    1.63
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:29.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.96
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:28.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.35

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 8.28e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.65e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.15
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.02
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:07.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.41
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:07.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10054.91
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9857.32
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.10
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:44.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4954.76
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4972.58
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:51.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.35
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4141.64
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11486.93
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12168.04
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:29.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.63
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000023068

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.10
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999981275

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.85e-3
p-value of test                       :    0.9938

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  8.1e-3

Anderson-Darling statistic = A2       :    4.37
p-value of test                       :  6.0e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.90
p-value of test                       :  1.9e-3

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:22.26

 All tests were passed




Server wird beendet - Lösche Semaphor 3964955.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:55.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1265
p-value of test                       :    0.9966

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334385
  j =  1                              :        599997470
  j =  2                              :             1265
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1460
p-value of test                       :  5.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334580
  j =  1                              :        599997080
  j =  2                              :             1460
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5485
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:50.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:39.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:39.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:55.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4463
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:03.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7160
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:03.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:54.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:59.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    2.19
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:14.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.99
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    2.85
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:43.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.34
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.40
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.85
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.57
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.55
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.92
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.45
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:44.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1289.77
p-value of test                       :    0.9977

-----------------------------------------------
CPU time used                    :  00:02:02.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7065.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:43.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:01.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.99
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.43
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:35.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4961.62
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:02.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45914
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869914
  j =  1                              :        399908174
  j =  2                              :            45910
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46205
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870205
  j =  1                              :        399907591
  j =  2                              :            46203
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:28.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:18.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:45.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9940


-----------------------------------------------
CPU time used                    :  00:02:01.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:55.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:34.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 5.63e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9935

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.069
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:35.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.83
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:48.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.22
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.16
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.72
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.76
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.49
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.82
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:59.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.32
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.91
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.28
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17337.78
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.74
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.48
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.87
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.63
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.37
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.72
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.17
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.31
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.30
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.53
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.47
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.28
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.72
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.33
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.58
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.27
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.30
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.51
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.71
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.99
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.33
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.74
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4991.66
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.84
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.26
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.51
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.31
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.04
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.37
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.48
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.24
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:25.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.01
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:26.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.32e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:46.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.79e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 8.69e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.33
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.29
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.01
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:07.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.65
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:08.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9900.30
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9760.68
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:45.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:49.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.06
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3939.53
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11587.37
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11608.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:29.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.24
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999933689

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.21
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999964625

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.17
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.67e-3
p-value of test                       :    0.9906

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.52
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.65
p-value of test                       :  4.0e-3

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.94
p-value of test                       :  9.7e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.56
p-value of test                       :    0.9948

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9977

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:05.52

 All tests were passed




Server wird beendet - Lösche Semaphor 4980763.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5486
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:52.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:40.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:04.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:04.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:59.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:04:03.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:48.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:15.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:41.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.79
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.49
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.04
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.76
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:12.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.55
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.49
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.74
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.36
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  384.44
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:48.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1444.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:03.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7191.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:51.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.97
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.94
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:12.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.65
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:36.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5068.12
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:00.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45856
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869856
  j =  1                              :        399908293
  j =  2                              :            45846
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45926
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869926
  j =  1                              :        399908152
  j =  2                              :            45918
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:30.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:18.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:45.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 5.87e-3
p-value of test                       :    0.9934

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:02.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:55.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 4.08e-3
p-value of test                       :    0.9956

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 3.20e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.017
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:38.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.31
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.87
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.83
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.67
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.73
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:47.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.05
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.34
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.31
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17273.58
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.01
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.85
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.87
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.19
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.24
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:38.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.55
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.81
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.96
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.86
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.50
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.91
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.83
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  431.22
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.39
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.83
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.34
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.33
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.57
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.77
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.84
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.04
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  321.95
p-value of test                       :    0.9906


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.54
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.01
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.36
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.93
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.79
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4941.97
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.99
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  239.25
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.34
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :   -1.20
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:25.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.08
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :    1.96
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:24.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.66e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:46.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.50e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.52
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.01
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.61
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:07.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.65
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:07.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9827.74
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9739.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:04:22.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4703.56
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:53.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5022.96
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:55.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.10
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.33
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11739.84
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:32.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11917.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:31.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.01
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999975107

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.71
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999865112

Normal statistic for number of bits   :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   0.068
p-value of test                       :    0.47

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:12.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.10

Sample variance                       :    2.30
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:33.20

 All tests were passed




Server wird beendet - Lösche Semaphor 5931035.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:51.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5456
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:53.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:39.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4166
p-value of test                       :    0.9953


-----------------------------------------------
CPU time used                    :  00:01:57.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:58.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:07.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:07.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:04:00.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:04:05.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.90
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     964
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    3.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    3.03
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     254
p-value of test                       :    0.9964

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:16.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.40
p-value of test                       :  6.1e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.9906

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    2.20
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:45.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.02
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.02
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.56
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.56
p-value of test                       :    0.9937

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.52
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.76
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.77
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.69
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:50.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1347.89
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:59.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7016.67
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:51.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.60
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:08.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.77
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.07
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5076.92
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:06.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45900
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869900
  j =  1                              :        399908202
  j =  2                              :            45896
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46004
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870004
  j =  1                              :        399907996
  j =  2                              :            45996
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:30.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:18.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.90
p-value of test                       :  1.0e-2


-----------------------------------------------
CPU time used                    :  00:01:46.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:02.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:36.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 9.35e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.66
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.96
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:48.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:47.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.29
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.29
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.90
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.45
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.55
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.53
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.27
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:46.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.34
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.61
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.38
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  8.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17051.41
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.20
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.82
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.84
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.68
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.83
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.57
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.26
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.57
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.89
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.09
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.39
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.41
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.41
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.83
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.76
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.65
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.15
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.61
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.13
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.21
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.99
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.43
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4802.30
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.14
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.10
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.65
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.96
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.69
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.28
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.42
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.76
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :   -1.13
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:24.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.15
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:23.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   0.076
p-value of test                       :    0.47

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.74e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 8.14e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:46.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.51e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 6.08e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.52
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.56
p-value of test                       :    0.9916

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.76
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:06.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.78
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:06.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9964.74
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:04:17.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5015.42
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:53.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4947.02
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:55.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.17
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4248.39
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11608.06
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:31.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11776.02
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.48
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  7999943997

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.13
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000013891

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:11.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:11.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:36.72

 All tests were passed




Server wird beendet - Lösche Semaphor 7012379.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:40.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5315
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:54.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:39.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:57.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:05.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:04.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:56.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:00.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.22
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.97
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.70
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     539
p-value of test                       :    0.9939

Stat. AD (mNP2)                       :    1.77
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    2.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:13.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    2.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:41.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.08
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.50
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.64
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.68
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.01
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.77
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.69
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.09
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  274.52
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.18
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:44.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1528.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:01.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6918.96
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:45.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.14
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.35
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:01.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.92
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.23
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:33.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5081.62
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:59.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45789
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869789
  j =  1                              :        399908425
  j =  2                              :            45783
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46098
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870098
  j =  1                              :        399907809
  j =  2                              :            46088
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:28.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:21.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:45.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:00.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:56.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:36.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 6.43e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 3.54e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:38.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.98
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.67
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.70
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.28
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.95
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.58
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:45.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.47
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.03
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.63
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.22
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.94
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:37.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17271.15
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.22
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.93
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.82
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.16
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.56
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.24
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.05
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.75
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.96
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.23
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.54
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.42
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.40
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.60
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.47
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.89
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.05
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.33
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.86
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   42.92
p-value of test                       :    0.9986


-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.74
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.73
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4935.46
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.57
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.66
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.36
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.01
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5132.68
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.20
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.47
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.77
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :   -1.35
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:24.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.38
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:25.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.91
p-value of test                       :    0.03

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.80
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.95
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.56
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:06.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.75
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:06.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10105.45
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10244.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:50.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4824.78
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:48.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4804.31
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:50.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.88
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.21
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11723.72
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11805.73
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:29.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.92
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000028750

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.47
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999890984

Normal statistic for number of bits   :   -0.86
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :  -0.034
p-value of test                       :    0.51

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:52.92

 All tests were passed




Server wird beendet - Lösche Semaphor 8093723.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:43.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:52.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5367
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:53.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:40.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4242
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:57.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:04.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:05.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:55.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:04:01.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.87
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    2.61
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.16
p-value of test                       :    0.9975

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:14.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.76
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:46.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.71
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.96
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.90
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.16
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.78
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.07
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:43.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1533.82
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:02.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7136.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:42.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.55
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:01.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.54
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.51
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5235.38
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:58.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45864
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869864
  j =  1                              :        399908279
  j =  2                              :            45850
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46099
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870099
  j =  1                              :        399907804
  j =  2                              :            46095
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:27.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:17.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:44.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:59.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :  4.8e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    5.60
p-value of test                       :  1.5e-3

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    5.37
p-value of test                       :  2.0e-3

-----------------------------------------------
CPU time used                    :  00:01:35.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.59e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:35.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.03
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.03
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.35
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.08
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.85
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.26
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.45
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:45.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.70
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.80
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.44
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17309.75
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.65
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.92
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.71
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.71
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.07
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.14
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.35
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.83
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   43.65
p-value of test                       :  8.4e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.63
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.20
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.88
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.13
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.67
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.55
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.67
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.69
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.63
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.26
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.50
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.92
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.22
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4933.43
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.98
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.82
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:36.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.23
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.18
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5084.84
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.93
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  246.97
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.69
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:25.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.91
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:26.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.24
p-value of test                       :    0.01

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 6.90e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.73e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.24
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.68
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:07.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.37
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:05.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9963.51
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10055.35
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:47.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5100.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:47.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4831.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:50.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4042.59
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.66
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11693.40
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11501.84
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:28.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.06
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000178234

Normal statistic for number of bits   :    1.41
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.72
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000054382

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:54.47

 All tests were passed




Server wird beendet - Lösche Semaphor 9142299.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5448
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:53.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:39.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:39.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:57.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:04.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:05.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:54.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:59.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     867
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:46.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.80
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:12.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.19
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:40.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.99
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.91
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.58
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.10
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.85
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.75
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.74
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.72
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.75
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:43.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1343.21
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:01.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7060.72
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:42.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.32
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:03.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.72
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:46.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.98
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:34.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5048.55
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:59.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45738
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869738
  j =  1                              :        399908525
  j =  2                              :            45736
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45975
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869975
  j =  1                              :        399908057
  j =  2                              :            45961
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:28.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:18.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:45.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:59.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:36.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.099
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.22
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:34.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:36.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.20
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:48.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.97
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.56
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.46
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.96
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.82
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.81
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:44.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.29
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.17
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.19
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  2.0e-3

Anderson-Darling statistic = A2       :    5.41
p-value of test                       :  2.0e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17984.80
p-value of test                       :  1.6e-3



-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.59
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.79
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.05
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.93
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.97
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.64
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.13
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.59
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.06
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.49
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.11
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.74
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.80
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.54
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.67
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.31
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.27
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.28
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.86
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.62
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.65
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.70
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.78
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.00
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.96
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.05
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.43
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5039.82
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.27
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.63
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.94
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:24.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.65
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :   -2.05
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:22.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.21e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 6.76e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.15e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 8.35e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.53
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.55
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.13
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:07.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.88
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:07.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10051.58
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10146.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.031
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:44.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 6.83e-3
p-value of test                       :    0.9927

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4710.01
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:48.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4889.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.48
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4130.07
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11788.40
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11954.53
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.78
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000097027

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.29
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000060163

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.76

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:19.64

 All tests were passed




Server wird beendet - Lösche Semaphor 9994267.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1462
p-value of test                       :  4.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334582
  j =  1                              :        599997076
  j =  2                              :             1462
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5462
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:55.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4461
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:42.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4479
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:57.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4225
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:58.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:06.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:55.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:59.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:12.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    3.73
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:42.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.57
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.06
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.01
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.66
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.41
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.56
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.46
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:42.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1487.33
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:00.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6751.47
p-value of test                       :    0.9940

-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.51
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.70
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:01.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.14
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:30.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5110.32
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:05.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46168
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870168
  j =  1                              :        399907668
  j =  2                              :            46160
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45815
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869815
  j =  1                              :        399908375
  j =  2                              :            45805
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :  1.9e-3

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:27.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:17.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:45.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:59.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:35.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 9.57e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.46
p-value of test                       :    0.9931

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:35.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:35.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  103.38
p-value of test                       :  2.9e-3

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.70
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.31
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.59
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.46
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.72
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:45.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.21
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.07
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.56
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.28
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17537.22
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.61
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.41
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.28
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.07
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.40
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.94
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.57
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.52
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.57
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.97
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.82
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.46
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.43
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.75
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.60
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.52
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.14
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.94
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.35
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.70
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.11
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.21
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4922.58
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.33
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.45
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.83
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.36
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4880.13
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.62
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.74
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.72
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :   -2.00
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:23.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.83
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   -0.54
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:21.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.31e-4
p-value of test                       :    0.9992    *****

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    2.16
p-value of test                       :    0.02

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 3.87e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 8.02e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.81
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.25
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.93
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:05.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.12
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:07.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9911.50
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9858.52
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:41.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4707.66
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4737.86
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:51.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4116.52
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.71
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11829.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11802.82
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:30.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.58
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000005566

Normal statistic for number of bits   :   0.044
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.27
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999932549

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:51.60

 All tests were passed




Server wird beendet - Lösche Semaphor 11010075.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5333
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:57.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:42.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:57.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:58.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:06.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:05.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:55.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7483
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:59.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9944


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.94
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    2.54
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:47.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    4.51
p-value of test                       :  4.9e-3

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.17
p-value of test                       :    0.9960


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:12.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:41.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.30
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.79
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.95
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  470.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:43.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.51
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:01.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7055.12
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.19
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.07
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:01.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.41
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.69
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:34.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4954.07
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:04.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46256
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870256
  j =  1                              :        399907491
  j =  2                              :            46250
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45878
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869878
  j =  1                              :        399908245
  j =  2                              :            45876
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:28.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:18.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  4.7e-3

Anderson-Darling statistic = A2       :    4.50
p-value of test                       :  5.1e-3


-----------------------------------------------
CPU time used                    :  00:02:01.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:36.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.81e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 9.22e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:38.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:37.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.29
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.14
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.31
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.10
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:49.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.44
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:40.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.25
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17445.22
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.81
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.84
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.98
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.98
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.48
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.15
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.64
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.88
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.65
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.26
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.53
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.06
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.08
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.01
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.42
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  109.51
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.82
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.18
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.45
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.52
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.76
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.07
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4856.17
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.87
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.08
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.08
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.01
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5064.84
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.05
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.38
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.50
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :    1.03
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:23.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.66
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:21.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.60

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :  -0.098
p-value of test                       :    0.54

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 6.36e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 8.40e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.92
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.42
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.87
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:07.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:09.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10147.59
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9929.81
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.041
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:40.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4836.69
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:48.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4920.68
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:51.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3958.67
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4206.92
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11896.54
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12037.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:30.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.46
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000087445

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.85
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999968057

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.86e-3
p-value of test                       :    0.9971

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.31
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.60
p-value of test                       :  4.7e-3

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:04.84

 All tests were passed




Server wird beendet - Lösche Semaphor 11993115.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5305
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:58.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:41.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4176
p-value of test                       :    0.9928


-----------------------------------------------
CPU time used                    :  00:01:57.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4251
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:58.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:06.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7181
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:07.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:56.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:04:00.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:14.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:41.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.86
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.33
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.68
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.84
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.19
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.80
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.69
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.73
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.96
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:43.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1353.03
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:02.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7065.02
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:42.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:04.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.52
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.06
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5130.55
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:15.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45775
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869775
  j =  1                              :        399908451
  j =  2                              :            45773
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46092
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870092
  j =  1                              :        399907818
  j =  2                              :            46088
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:27.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:19.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:46.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:01.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:35.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.67e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 6.96e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.00
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:37.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:38.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.57
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.66
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.21
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:42.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.00
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.33
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.85
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.93
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9916

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.38
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:39.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17321.42
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.64
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.34
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.12
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.50
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.17
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.59
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.50
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.66
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.72
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.64
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.00
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.35
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.07
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  201.62
p-value of test                       :  2.2e-4    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.30
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.48
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.08
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.18
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.92
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.11
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.16
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.68
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4888.70
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.58
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.52
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.76
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.63
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4938.33
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.56
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.29
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.04
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :   0.097
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:23.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.83
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:22.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 2.15e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 3.24e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.18
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.55
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:06.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:07.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9886.15
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9958.14
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:41.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4787.10
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:48.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4723.24
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:50.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4206.54
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4311.84
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11741.72
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11586.16
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:30.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.69
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999988961

Normal statistic for number of bits   :  -0.087
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.87
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999954722

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.037
p-value of test                       :    0.51

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   0.093
p-value of test                       :    0.46

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.056
p-value of test                       :    0.48

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:46.40
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 R (L=1000, r=0)     2.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13074459.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5457
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:58.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4205
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:43.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:59.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:06.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:06.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7170
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:55.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:04:00.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    3.64
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.88
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     269
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:15.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.60
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.94
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:42.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.21
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.80
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.68
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:11.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.26
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.68
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.12
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.71
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:43.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1521.85
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:01.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7020.12
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.74
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:03.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.44
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.96
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:33.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5112.53
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:59.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45973
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869973
  j =  1                              :        399908055
  j =  2                              :            45971
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45927
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869927
  j =  1                              :        399908149
  j =  2                              :            45921
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:30.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:26.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:57.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:12.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:54.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.5e-3

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:35.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 5.28e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 9.49e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:34.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:35.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.37
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.87
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.56
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.91
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.26
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:44.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.92
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.15
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.40
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:39.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17300.47
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.38
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.04
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.86
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.62
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.27
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.37
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.92
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.18
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.71
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.08
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.73
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.71
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.19
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.51
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.89
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.05
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.76
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.76
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.40
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.03
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.47
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.17
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.44
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.59
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.69
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.98
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.93
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.96
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.97
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.72
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:23.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.97
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :  -0.086
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:23.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :  -0.033
p-value of test                       :    0.51

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.13e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.70e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.26
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.24
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.18
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:07.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.13
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:08.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10228.11
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9837.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:43.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4833.90
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5017.84
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:50.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.56
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4021.64
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11703.54
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11829.09
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.69
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999978617

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.57
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000014761

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.93
p-value of test                       :    0.97

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.67
p-value of test                       :    0.05

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:05.96

 All tests were passed




Server wird beendet - Lösche Semaphor 14090267.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5336
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:58.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:43.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:46.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:01.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4250
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:04.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:12.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:13.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:08.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:04:11.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.49
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:50.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.42
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:13.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.63
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:42.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   22.12
p-value of test                       :  2.4e-3

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.29
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.98
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.71
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:29.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.86
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:55.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1402.11
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:06.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6987.12
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:56.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.91
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.72
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:17.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.11
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:40.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5043.37
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:00.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46004
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870004
  j =  1                              :        399907996
  j =  2                              :            45996
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45861
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869861
  j =  1                              :        399908280
  j =  2                              :            45857
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:32.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :  2.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.42
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:21.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :  2.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.46
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.9919


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:49.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:08.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:56.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:38.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-5
p-value of test                       :    0.9951

Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:41.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.068
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.15
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:50.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.31
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.80
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.36
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.03
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.69
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.08
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:51.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.48
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.70
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.51
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.79
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.39
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17260.97
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.64
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   59.09
p-value of test                       :  6.6e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.06
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.66
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.45
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.54
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.87
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.60
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.45
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.57
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.99
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.26
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.78
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.86
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.42
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.51
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.93
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.39
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.41
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.80
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.55
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5023.14
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.41
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.53
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.28
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.53
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.90
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.06
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.71
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.88
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :    1.47
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:26.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.30
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:24.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    2.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 4.31e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.97e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 8.24e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.21
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.14
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.77
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:08.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.07
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:09.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  4.2e-3

Anderson-Darling statistic = A2       :    3.52
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10338.37
p-value of test                       :  8.9e-3

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.04
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:10.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:04:24.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5075.31
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:56.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5089.93
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:59.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.67
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4290.59
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12099.33
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:36.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11842.92
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:37.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.90
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000129970

Normal statistic for number of bits   :    1.03
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.93
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000172435

Normal statistic for number of bits   :    1.36
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.36
p-value of test                       :  9.2e-3

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:21.93

 All tests were passed




Server wird beendet - Lösche Semaphor 15138843.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:41.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5324
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:58.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:42.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:58.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:00.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:10.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:09.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:04:01.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:03.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     853
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:47.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.40
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:14.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.95
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     129
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:43.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.54
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.27
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.89
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.71
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.50
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.32
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.77
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.12
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.29
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.76
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:49.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1386.63
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:04.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6979.04
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:52.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   86.95
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:03:11.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.87
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.82
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4792.37
p-value of test                       :    0.9936


-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:17.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45972
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869972
  j =  1                              :        399908056
  j =  2                              :            45972
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45979
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869979
  j =  1                              :        399908046
  j =  2                              :            45971
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:30.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:18.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:46.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:06.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:36.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 6.12e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:45.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.88
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.12
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.50
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.42
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.44
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.89
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.52
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.99
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.33
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.98
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.07
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17515.11
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.89
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.38
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.00
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.23
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.35
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.99
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.52
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.91
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.97
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.13
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.67
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.86
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.93
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.07
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.30
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.30
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.01
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.94
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.72
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.43
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.02
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.55
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.04
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.27
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.06
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.49
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.10
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.79
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.92
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  253.05
p-value of test                       :  6.5e-3


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.52
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:24.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.53
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :  -0.033
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:25.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    2.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 4.35e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.78e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 6.42e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.37
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.59
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  245.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:06.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 4.86e-4
p-value of test                       :    0.9995    *****

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.01
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:07.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.94
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9970.43
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:04:15.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4940.35
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:53.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.92
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:54.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4027.62
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3966.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11774.40
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:32.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12283.61
p-value of test                       :  1.6e-3

-----------------------------------------------
CPU time used                    :  00:01:32.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.13
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999838958

Normal statistic for number of bits   :   -1.27
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.26
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000000778

Normal statistic for number of bits   : 6.15e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.78

Sample variance                       :    2.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:13.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.21
p-value of test                       :    0.9928

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:34.97

 All tests were passed




Server wird beendet - Lösche Semaphor 16318491.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:50.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1463
p-value of test                       :  4.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334583
  j =  1                              :        599997074
  j =  2                              :             1463
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5419
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:57.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:43.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4463
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:01.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:01.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:12.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:10.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:04.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:09.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    2.13
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     961
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    2.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:49.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.81
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9904

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:14.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:46.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.92
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.13
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.91
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.71
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.55
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.06
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.20
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:53.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1582.02
p-value of test                       :  4.3e-3

-----------------------------------------------
CPU time used                    :  00:02:05.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6816.38
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.25
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:16.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.50
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:37.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4956.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:03.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45994
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869994
  j =  1                              :        399908015
  j =  2                              :            45988
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45972
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869972
  j =  1                              :        399908059
  j =  2                              :            45966
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:32.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:20.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:51.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 9.23e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:06.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:37.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.11e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:24.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:51.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:51.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:50.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.23
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.44
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.09
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.67
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.07
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.52
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.63
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.49
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.84
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17239.61
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.42
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.75
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.03
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.18
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.08
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.43
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.99
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.29
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.39
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.52
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.22
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.34
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  562.03
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.51
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.17
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.69
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.14
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.36
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.95
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.79
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.85
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.40
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5204.15
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.44
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.82
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.38
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.54
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4837.70
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.39
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.00
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.71
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :   -1.14
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:26.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.65
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :   -1.05
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:25.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
p-value of test                       :    0.9998    *****

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -2.16
p-value of test                       :    0.98

Sample variance                       :    1.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.25e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 6.77e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 5.88e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.81
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.24
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  242.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:03.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.20
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:06.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10012.28
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9833.97
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.027
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:04:23.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4978.66
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:55.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5061.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4162.79
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4230.03
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11870.23
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:34.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11826.97
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:36.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.94
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000052567

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.88
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000151234

Normal statistic for number of bits   :    1.20
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:15.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:02.67

 All tests were passed




Server wird beendet - Lösche Semaphor 17399835.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:51.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5476
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:57.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7186
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:39.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:57.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:05.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:05.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:56.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:04:02.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:48.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.93
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:14.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:43.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.64
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.91
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.21
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.95
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.07
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.67
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.82
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  261.82
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.82
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:45.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1399.30
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:02.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7061.08
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:41.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.47
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.54
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:00.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.55
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:46.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.27
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:33.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5286.31
p-value of test                       :  7.5e-3


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:02.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45812
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869812
  j =  1                              :        399908377
  j =  2                              :            45810
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45551
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869551
  j =  1                              :        399908905
  j =  2                              :            45537
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:28.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:18.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9955

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:45.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:01.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:35.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 6.76e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.35e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:36.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:38.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.76
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:49.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.13
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.71
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.70
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.62
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.50
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.93
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:40.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.79
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.93
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 2.41e-6
p-value of test                       : 1 -  2.4e-6    *****

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.10
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9903

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17434.32
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:54.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   58.02
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.75
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.64
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.52
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.02
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:39.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.18
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.72
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.75
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.27
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   35.10
p-value of test                       :  6.0e-3


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.94
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.61
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.72
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.28
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.81
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  107.48
p-value of test                       :    0.9929


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.20
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.61
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.94
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.72
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.87
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.11
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.17
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.26
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.05
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.35
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.25
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5139.81
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.73
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.92
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.20
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:23.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.98
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:25.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.98e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 6.00e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.10
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.84
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.16
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:07.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:05.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9743.56
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9977.46
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:55.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:44.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4801.16
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:47.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    3.52
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4683.65
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:50.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4193.32
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.78
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11932.59
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11925.09
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.08
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999997814

Normal statistic for number of bits   :  -0.017
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.81
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000051838

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   0.084
p-value of test                       :    0.47

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:30.65

 All tests were passed




Server wird beendet - Lösche Semaphor 18546715.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:51.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5451
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:58.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:43.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:57.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:00.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:09.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:07.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:01.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:06.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.39
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    2.93
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.64
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    2.42
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:15.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9949


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:41.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.85
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.19
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.09
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:12.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.77
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.38
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.63
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.77
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  396.20
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:48.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1472.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:05.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7051.68
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:50.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.23
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.33
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:09.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.64
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.69
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5074.70
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:00.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45811
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869811
  j =  1                              :        399908382
  j =  2                              :            45803
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46091
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870091
  j =  1                              :        399907820
  j =  2                              :            46087
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:29.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:18.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:46.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:02.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:56.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.56e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 9.34e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.011
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:45.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.96
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.44
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.54
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.00
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.14
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.67
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.65
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.32
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17219.60
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.82
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.65
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.72
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.48
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   34.45
p-value of test                       :  7.3e-3


-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.56
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.91
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.90
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.77
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.96
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.64
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.07
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.82
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.54
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.05
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.20
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.28
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.66
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.46
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.48
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.81
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.86
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5053.61
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.84
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.45
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  324.29
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.62
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4817.49
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.29
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.52
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.66
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:23.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.46
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:25.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 5.10e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 9.77e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.56
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.11
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.16
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:07.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.33
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:06.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9774.83
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10045.06
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.088
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.031
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:04:13.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4897.49
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:53.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.40
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:53.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3998.74
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.14
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11789.53
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11681.31
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:31.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.99
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999906041

Normal statistic for number of bits   :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.51
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999924824

Normal statistic for number of bits   :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:51.06

 All tests were passed




Server wird beendet - Lösche Semaphor 19595291.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:40.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5294
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:56.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4216
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:56.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:57.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:05.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:05.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:55.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:01.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    1.99
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    2.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:16.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.84
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:46.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.70
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.54
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.06
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.90
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.46
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.69
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  270.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.91
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:43.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1406.82
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:02.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7368.10
p-value of test                       :  3.7e-3

-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.47e-3
p-value of test                       :    0.9944

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.18
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.74
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:01.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.44
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.41
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:32.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4970.33
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:02.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45548
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869548
  j =  1                              :        399908906
  j =  2                              :            45544
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45604
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869604
  j =  1                              :        399908797
  j =  2                              :            45594
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:28.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:18.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:45.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:00.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:56.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:36.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-5
p-value of test                       :    0.9947

Kolmogorov-Smirnov- statistic = D-    : 2.62e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.052
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:21.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:21.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:37.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.29
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.27
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.13
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.24
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:42.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.21
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.94
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.17
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.18
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:28.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.15
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:39.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17445.59
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.64
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.98
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.47
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.76
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.77
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.61
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.74
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.10
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.43
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.33
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.05
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.17
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.88
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.35
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.82
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.51
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.69
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.67
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  107.08
p-value of test                       :  7.2e-3


-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.11
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.08
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.80
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.43
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.51
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.37
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.09
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5026.46
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.28
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.62
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.52
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :    0.51
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:19.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.89
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :    1.05
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:18.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.66e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.74e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 5.18e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :   0.078
p-value of test                       : 1 -  6.1e-7    *****

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.39
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.70
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.20
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:59.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.43
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:59.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10129.53
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:55.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:30.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.3e-3

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5081.12
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:40.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.36
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:33.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.12
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4303.75
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11791.00
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11739.82
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:12.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.44
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  7999947555

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:58.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.21
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000039772

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   02:59:43.09
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 85  Fourier3, r = 27               1 -  6.1e-7
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 20742171.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:18.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:20.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997269
  j =  2                              :             1364
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:17.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5371
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:43.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:37.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:36.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:04.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:05.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:04:01.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:04:06.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.9907


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.75
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.69
p-value of test                       :  4.3e-3

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:08.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    3.08
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:46.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.31
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.64
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.72
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.93
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.91
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.72
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.04
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.69
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.54
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1468.50
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:05.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7020.87
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:55.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.55
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 6.98e-3
p-value of test                       :    0.9926

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.69
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:18.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.58
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  144.62
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:42.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5068.87
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:30.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:21.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46191
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870191
  j =  1                              :        399907622
  j =  2                              :            46183
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45842
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869842
  j =  1                              :        399908317
  j =  2                              :            45840
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:29.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:16.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.24e-3
p-value of test                       :    0.9917

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:44.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:02.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:37.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 8.23e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:24.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:46.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.37
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:51.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.90
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.21
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.67
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.78
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.78
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.19
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:52.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.9e-3

Anderson-Darling statistic = A2       :    3.67
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.96
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:12.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.58
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17180.40
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.68
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.86
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.55
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.79
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.08
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.06
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.27
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.49
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.75
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.02
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:39.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.58
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.40
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.53
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.45
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.45
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.43
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.91
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.93
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  167.94
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.75
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.66
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.25
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.83
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.22
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.37
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.01
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.68
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.75
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.53
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:36.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.76
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  :    2.02
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:30.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.59
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:30.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   0.092
p-value of test                       :    0.46

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:46.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 4.10e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.81
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.10
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.36
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:09.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-3
p-value of test                       :    0.9982

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  239.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:08.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10236.97
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10181.09
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.65
p-value of test                       :  4.0e-3

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:04:22.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.44
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:01.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4220.26
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11686.83
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:35.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11702.72
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:35.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.34
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000160915

Normal statistic for number of bits   :    1.27
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.01
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000090244

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:10.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.87e-3
p-value of test                       :    0.9971

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.89
p-value of test                       :    0.97

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:22:33.71

 All tests were passed




Server wird beendet - Lösche Semaphor 1048604.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5315
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:53.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:40.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7510
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:40.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:59.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:00.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:10.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:11.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:09.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:11.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.79
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:49.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    3.39
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:17.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     122
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    3.52
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:49.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.66
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.28
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.47
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.44
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:50.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.79
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:48.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.00
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:50.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.10
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:31.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  493.91
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:54.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:02.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6933.13
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:03.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.78
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:09.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.01
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:48.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.86
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5022.10
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:55.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45810
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869810
  j =  1                              :        399908385
  j =  2                              :            45800
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45595
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869595
  j =  1                              :        399908813
  j =  2                              :            45589
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:30.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:22.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :  1.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    4.09
p-value of test                       :  8.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:54.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:09.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:56.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 8.89e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:38.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.91e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.96e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.073
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:49.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:51.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.55
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.95
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.79
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.75
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.13
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.66
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:51.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.92
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.30
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.33
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.097
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:01:30.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.87
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17375.75
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.99
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.04
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.16
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.32
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.88
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.05
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.20
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.79
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.93
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.46
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.60
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.95
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.28
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.51
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.37
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.56
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  109.84
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.85
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.51
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.24
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.31
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.31
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4954.21
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.94
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  159.51
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.96
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.39
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5088.42
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.06
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.60
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.14
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :   -0.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:25.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.03
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :    1.98
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:25.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.40e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 7.73e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.60
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.87
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:32.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.31
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:22.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.01
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:26.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9893.83
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10241.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:04:32.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4790.49
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:50.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.34
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:53.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4180.95
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.21
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11443.20
p-value of test                       :    0.9939

-----------------------------------------------
CPU time used                    :  00:01:31.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11860.86
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:32.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.13
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000036370

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.84
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999945902

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.23

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.88

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:16:01.85

 All tests were passed




Server wird beendet - Lösche Semaphor 2129948.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:49.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5394
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:52.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4224
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:40.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:42.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:58.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:00.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:09.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:08.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:57.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:00.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.32
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     862
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    3.68
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     549
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    3.73
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.55
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    2.21
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:13.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.19
p-value of test                       :    0.9936

-----------------------------------------------
CPU time used                    :  00:02:44.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.27
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.02
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.96
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.11
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.55
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.98
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.11
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.66
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  389.65
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1433.20
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7065.23
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:44.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.23
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.62
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:03.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.17
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:46.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.18
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:35.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5101.61
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:53.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45907
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869907
  j =  1                              :        399908191
  j =  2                              :            45897
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45827
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869827
  j =  1                              :        399908352
  j =  2                              :            45815
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  9.7e-3

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:25.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:19.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:58.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:38.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 9.17e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.62e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 2.80e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:39.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:39.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.34
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.85
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:55.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.40
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:50.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.14
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.95
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:55.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.63
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:45.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.70
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.20
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.76
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 4.20e-3
p-value of test                       :    0.9956

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   97.56
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17613.44
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.32
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.48
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.09
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.02
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.36
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.44
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.22
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.55
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.57
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.70
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.23
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.03
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.34
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.24
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.95
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.41
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.21
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.93
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.87
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.53
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.99
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.78
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.41
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.39
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.47
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.30
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5151.91
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.41
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.09
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.29
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :   -0.60
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:24.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.73
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:25.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    2.25
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 8.91e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 6.40e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.14
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.62
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:07.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.74
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:07.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9939.17
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9823.01
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:41.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.62
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:45.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4967.91
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.48
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4116.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11622.74
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11872.12
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.53
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000027094

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.06
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000093661

Normal statistic for number of bits   :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.10
p-value of test                       :    0.02

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:30.45

 All tests were passed




Server wird beendet - Lösche Semaphor 3244060.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:39.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.33

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5400
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:52.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:40.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:58.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:06.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:05.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:56.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:04:03.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.94
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:46.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:12.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    2.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:41.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.16
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.18
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.76
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.12
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.23
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.01
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.32
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.83
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  513.21
p-value of test                       :  5.2e-3

-----------------------------------------------
CPU time used                    :  00:01:49.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.35
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:02.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6967.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.27
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.31
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:03.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.47
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.44
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:34.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5131.86
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:53.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46017
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870017
  j =  1                              :        399907970
  j =  2                              :            46009
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45831
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869831
  j =  1                              :        399908342
  j =  2                              :            45823
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:26.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :  4.4e-3

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:17.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:45.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  6.8e-3

Anderson-Darling statistic = A2       :    3.86
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:59.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:38.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 9.23e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9908

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 2.81e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:36.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:39.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.66
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:48.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.23
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.52
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.14
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.28
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.88
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.33
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.75
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17462.28
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.59
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.97
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.58
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.09
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.23
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.01
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.68
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.12
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.34
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.30
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.26
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.20
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.65
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.67
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.50
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.25
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.19
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.38
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.25
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.80
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.87
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.60
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.24
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.33
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.40
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.85
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.83
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.54
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.03
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.73
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.13
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -0.60
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:25.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.97
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:26.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.25e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 4.53e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.29e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 9.52e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.05
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.36
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.25
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:07.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.48
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:07.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10152.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10066.19
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:41.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.28
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4960.17
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:49.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4218.57
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3991.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11868.84
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11945.17
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.70
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000114844

Normal statistic for number of bits   :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.23
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000166693

Normal statistic for number of bits   :    1.32
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   0.030
p-value of test                       :    0.49

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   0.100
p-value of test                       :    0.46

Sample variance                       :    2.52
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:05.90

 All tests were passed




Server wird beendet - Lösche Semaphor 4259868.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.99

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5438
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:51.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:40.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:57.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:06.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:06.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:55.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:04:01.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.30
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    2.57
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     846
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    3.29
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:46.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.68
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:13.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.71
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    5.81
p-value of test                       :  1.2e-3

-----------------------------------------------
CPU time used                    :  00:02:42.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.61
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.03
p-value of test                       :    0.9944

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.11
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.14
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.17
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.08
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.70
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.50
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.93
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:44.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1444.03
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:01.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6901.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:42.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.85
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.64
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:03.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.82
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.30
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:34.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5066.29
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:57.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45863
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869863
  j =  1                              :        399908277
  j =  2                              :            45857
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45939
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869939
  j =  1                              :        399908124
  j =  2                              :            45935
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:26.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:18.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:01.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:34.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.12e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.00
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:22.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:38.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:36.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.07
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.48
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.92
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.67
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.36
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.43
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:45.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.97
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.53
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.22
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.71
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17426.80
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.08
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.89
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.61
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.86
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.88
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.64
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   55.91
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.65
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.05
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.46
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.64
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.47
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.69
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.69
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.46
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.67
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.64
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.96
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.26
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.22
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.06
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.71
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5149.15
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.96
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.85
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.75
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.54
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4836.88
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.39
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.67
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.29
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :  -0.082
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:24.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.93
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:25.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.49e-3
p-value of test                       :    0.9942

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.60
p-value of test                       :    0.05

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.41e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 5.41e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.46
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.14
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.5e-3

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.27
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:06.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.54
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:06.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10159.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.33
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:48.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4995.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4838.36
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:49.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3936.91
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3997.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11892.76
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11952.56
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:29.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.37
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000043930

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.08
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000130183

Normal statistic for number of bits   :    1.03
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.66
p-value of test                       :    0.95

Sample variance                       :    2.52
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:26.19

 All tests were passed




Server wird beendet - Lösche Semaphor 5242908.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9979


-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5478
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:51.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:40.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7178
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:41.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:57.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4447
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:58.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:08.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7149
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:07.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:02.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:05.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.9913

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    4.06
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    2.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    3.27
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:12.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:41.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.15
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:55.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.61
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.42
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.99
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.11
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.41
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.63
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  270.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.27
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:53.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1349.08
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:02.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7028.33
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:49.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.05
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:08.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.34
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.47
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:36.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5171.52
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:54.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45497
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869497
  j =  1                              :        399909009
  j =  2                              :            45491
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45879
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869879
  j =  1                              :        399908246
  j =  2                              :            45871
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:29.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 4.37e-3
p-value of test                       :    0.9950

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:17.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:46.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:05.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:55.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:35.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.92e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.083
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:22.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:46.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:48.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.04
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.40
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.59
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.53
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.91
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.48
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:45.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.16
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.01
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.59
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.75
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:39.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17489.28
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.91
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.33
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.98
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.89
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.32
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.97
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.48
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.94
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.01
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.74
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.86
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.23
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.48
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.92
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.98
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.34
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.73
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.48
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.48
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.96
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.92
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.94
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5048.81
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.71
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.97
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.60
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.59
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.40
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.69
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.91
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :   -2.69
p-value of test                       :    0.9964



-----------------------------------------------
CPU time used                    :  00:02:28.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.35
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :   -1.71
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:29.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.88e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.84e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.32
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.45
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:07.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.87
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:08.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.45
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9664.08
p-value of test                       :    0.9918

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9999.75
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:04:13.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4783.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:51.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4809.50
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:52.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.53
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.71
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11963.78
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:29.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12121.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.24
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999952934

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.40
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999968549

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.72
p-value of test                       :    0.04

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:40.72

 All tests were passed




Server wird beendet - Lösche Semaphor 6225948.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:50.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5542
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:53.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:41.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:57.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7179
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:06.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:06.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:55.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:01.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    2.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.38
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    2.13
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:15.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.07
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:45.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.80
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.04
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.51
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.77
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.50
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.08
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.33
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.40
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1492.90
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6935.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:01.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.12
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.75
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:32.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4940.17
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:58.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45816
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869816
  j =  1                              :        399908370
  j =  2                              :            45812
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46044
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870044
  j =  1                              :        399907915
  j =  2                              :            46038
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 6.79e-3
p-value of test                       :    0.9912

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:28.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:17.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:59.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:56.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9988

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:35.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 6.40e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.43e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 6.18e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:38.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:38.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.83
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.37
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.48
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.87
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.03
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.25
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:44.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.51
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.67
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.68
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.93
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.09
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.06
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17587.51
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.15
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.40
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.47
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.64
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.09
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.32
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.14
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.82
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.91
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.97
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.75
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.90
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.61
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.47
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.94
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.16
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.27
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.71
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.97
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.10
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.37
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.04
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5217.44
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  322.93
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.34
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.58
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  439.88
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5019.55
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.07
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.42
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:36.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.87
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   0.034
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:24.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.54
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :    0.95
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:25.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.14e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.93e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.78
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.41
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9940

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.11
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:07.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.12
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:09.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10087.44
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10095.91
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:44.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 2.08e-3
p-value of test                       :    0.9979

Anderson-Darling statistic = A2       :    4.41
p-value of test                       :  5.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4611.95
p-value of test                       :    0.9979

-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:50.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3989.45
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11796.64
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11702.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.73
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999961859

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.89
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000032809

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:22.54

 All tests were passed




Server wird beendet - Lösche Semaphor 7241756.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997173
  j =  2                              :             1412
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1481
p-value of test                       :  9.4e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334601
  j =  1                              :        599997038
  j =  2                              :             1481
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1479
p-value of test                       :  1.1e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334599
  j =  1                              :        599997042
  j =  2                              :             1479
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5540
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:53.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:41.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:57.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:05.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:06.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:55.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:00.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    2.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    2.63
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     518
p-value of test                       :    0.9997    *****

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.60
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:14.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:42.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.46
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.52
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.74
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.76
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.55
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.06
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.17
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.93
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:42.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.91
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:00.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6911.02
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.03
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.14
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:02.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.08
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.21
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:32.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4902.13
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:55.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45628
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869628
  j =  1                              :        399908749
  j =  2                              :            45618
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45733
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869733
  j =  1                              :        399908538
  j =  2                              :            45725
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:28.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:19.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:46.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 7.24e-3
p-value of test                       :    0.9917

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:35.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 7.86e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.78e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.55e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.29
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:37.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:38.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.46
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.36
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.17
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.93
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.06
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.23
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:51.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.74
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.04
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.72
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.49
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.05
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17181.20
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.63
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.17
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.50
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.09
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.20
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.28
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.46
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.52
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.85
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:42.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.69
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.38
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.27
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.48
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.17
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.39
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.15
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.88
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.49
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.78
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.35
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.45
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.90
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.29
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.37
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  329.23
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.19
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.31
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.33
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  160.27
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.83
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:24.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.09
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:24.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 6.56e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 5.12e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.73
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.96
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.08
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:07.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.23
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:08.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9840.63
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9994.39
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:39.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.61e-3
p-value of test                       :    0.9941

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5063.07
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:48.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5058.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:49.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4053.08
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3971.43
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12087.29
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11437.96
p-value of test                       :    0.9945

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.62
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999879761

Normal statistic for number of bits   :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.66
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999966881

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.81
p-value of test                       :    0.04

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :  -0.026
p-value of test                       :    0.51

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:12.77
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  8  CollisionOver, t = 7            9.4e-4
 23  ClosePairs NJumps, t = 5        0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8192028.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1463
p-value of test                       :  4.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334583
  j =  1                              :        599997074
  j =  2                              :             1463
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5425
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:53.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4430
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:40.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:56.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:58.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7509
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:08.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:07.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:00.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:04:04.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.58
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.33
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:46.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.01
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.17
p-value of test                       :    0.9960

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.19
p-value of test                       :    0.9933

-----------------------------------------------
CPU time used                    :  00:02:14.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.92
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:42.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.05
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.93
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.99
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.01
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.21
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.25
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.14
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.31
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:49.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1359.83
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:02.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6935.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:50.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.14
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:09.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.18
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  153.16
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5001.98
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:54.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45630
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869630
  j =  1                              :        399908743
  j =  2                              :            45624
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46001
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870001
  j =  1                              :        399908003
  j =  2                              :            45991
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:29.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:19.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 3.26e-3
p-value of test                       :    0.9965

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:46.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:04.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:36.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 7.90e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.73e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.078
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.098
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.95
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:47.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.48
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.94
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.35
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.63
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.91
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.30
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.70
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:46.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.80
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.64
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.58
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.42
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17514.73
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.05
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.56
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.70
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.48
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.43
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.40
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.62
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.32
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.52
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.40
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.87
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.98
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.88
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.54
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  105.29
p-value of test                       :  9.8e-3


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.75
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.93
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.46
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  176.17
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.66
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.44
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.50
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.48
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.17
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.57
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.98
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.85
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4831.50
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.17
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.59
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.18
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :   -0.96
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:22.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.08
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.49e-3
p-value of test                       :    0.9964

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.87
p-value of test                       :    0.03

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.72e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9950

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 7.92e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.83
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.90
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.23
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:07.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.68
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:06.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9905.13
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10079.48
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.013
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.042
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:04:15.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4978.28
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:53.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4769.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:54.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.78
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.37
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11965.19
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11859.64
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.09
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999933302

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.30
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999931190

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:11.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:10.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:21.62

 All tests were passed




Server wird beendet - Lösche Semaphor 9175068.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:49.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5438
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:54.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:42.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4432
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:58.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:07.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:07.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7488
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:59.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:05.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:48.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.85
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    2.06
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:15.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:44.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.96
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.60
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.87
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.42
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.19
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.08
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.77
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.77
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.59
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  395.58
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1412.39
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:04.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6754.29
p-value of test                       :    0.9935

-----------------------------------------------
CPU time used                    :  00:01:49.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.02
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   90.25
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:03:08.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.47
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   85.53
p-value of test                       :    0.9911


-----------------------------------------------
CPU time used                    :  00:01:36.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4994.32
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:55.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45950
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869950
  j =  1                              :        399908103
  j =  2                              :            45944
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45763
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869763
  j =  1                              :        399908475
  j =  2                              :            45761
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:30.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 2.67e-4
p-value of test                       :    0.9997    *****

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:18.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:45.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:07.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.35e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.39e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 7.86e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:26.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:43.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:44.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.67
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:49.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.35
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.19
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:49.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.66
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.88
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:46.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.12
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.87
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.38
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17634.92
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.30
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.96
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.84
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.59
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.32
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.47
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.31
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.05
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.57
p-value of test                       :    0.9917


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.68
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.39
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.65
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.21
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.38
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.16
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.96
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.83
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.09
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.54
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.37
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.12
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.57
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5014.65
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.25
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.44
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.19
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.96
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.52
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.90
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.14
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.49
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :    1.45
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:25.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.48
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :   -0.37
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:26.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.78
p-value of test                       :    0.96

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.78e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 8.94e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.91
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.63
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.07
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:06.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  243.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:05.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10241.51
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9826.71
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:04:13.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:52.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5037.02
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:53.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4204.64
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4210.08
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11622.04
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:30.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11736.80
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:30.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   32.83
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  8000000424

Normal statistic for number of bits   : 3.35e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.54
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999997316

Normal statistic for number of bits   :  -0.021
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    2.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:11.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:59.88

 All tests were passed




Server wird beendet - Lösche Semaphor 10223644.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:40.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5503
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:55.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4228
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:41.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:41.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:56.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:57.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:04.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7502
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:05.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:55.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:59.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9935


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:44.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    2.04
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:11.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    2.04
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:08.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:38.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.75
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.97
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.46
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.22
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.07
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.86
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.26
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.03
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.13
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:59.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6972.89
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:41.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.78
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.06
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:01.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.75
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.56
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:33.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5002.15
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:55.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46038
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870038
  j =  1                              :        399907932
  j =  2                              :            46022
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46041
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870041
  j =  1                              :        399907919
  j =  2                              :            46039
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:28.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:18.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:46.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:58.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:56.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:34.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.92e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 4.52e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.093
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:42.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.84
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.00
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.86
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.16
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.96
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.89
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.97
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:44.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.96
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.22
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.51
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17532.48
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.28
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.23
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.06
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.96
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.53
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.13
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.93
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.53
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.03
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.05
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.96
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.20
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.11
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.19
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.38
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.63
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.61
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.39
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.21
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.64
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.02
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.59
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.87
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.88
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.28
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.58
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.00
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5138.41
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.56
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.79
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.19
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -1.86
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:23.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.37
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:24.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.20
p-value of test                       :    0.99

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.80e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 8.76e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.84e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.73
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.63
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.21
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:06.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.35
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:06.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9956.72
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9873.54
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:45.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5052.16
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:49.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4889.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:51.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.73
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.08
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11719.77
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11727.92
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:30.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.41
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999973559

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.85
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000004588

Normal statistic for number of bits   :   0.036
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   0.058
p-value of test                       :    0.48

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.93
p-value of test                       :    0.03

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:14.77

 All tests were passed




Server wird beendet - Lösche Semaphor 11337756.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5398
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:55.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:41.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7127
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:04.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:05.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:55.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:04:01.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:48.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.89
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.72
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:15.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.51
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.71
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:46.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.33
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.58
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   29.51
p-value of test                       :    0.9973

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.45
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.98
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.65
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.98
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.49
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:44.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1384.24
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:01.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6886.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:40.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.63
p-value of test                       :  1.0e-2

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.13
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:16.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.15
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:03.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.44
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.43
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:30.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5056.12
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:59.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45258
p-value of test                       :    0.9982


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869258
  j =  1                              :        399909489
  j =  2                              :            45248
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46120
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870120
  j =  1                              :        399907761
  j =  2                              :            46118
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:29.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:19.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:47.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:00.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:58.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  6.0e-3

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 9.38e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:36.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:38.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.78
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.91
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.68
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.38
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.83
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.71
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.85
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:44.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 5.73e-3
p-value of test                       :    0.9940

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.90
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.00
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:28.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.65
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.65
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17290.65
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.24
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.84
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.62
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   49.37
p-value of test                       :  1.7e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.20
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.20
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.49
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.97
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.59
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.20
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.81
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.22
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  445.31
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.10
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.90
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.16
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.60
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.01
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.85
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.38
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.86
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.08
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.09
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.89
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.39
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.46
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.47
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4759.64
p-value of test                       :    0.9926


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.94
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.16
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.12
p-value of test                       :    0.9946


-----------------------------------------------
Normal statistic for number of jumps  : -5.96e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:23.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.61
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :    1.77
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:23.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.99e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.91e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.77
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.16
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.77
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:06.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.09
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:06.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9848.34
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9949.10
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:40.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5069.35
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:46.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4973.08
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:50.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.42
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.40
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11530.63
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12059.62
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:29.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.53
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000117655

Normal statistic for number of bits   :    0.93
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.39
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999980501

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.57

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:18.89

 All tests were passed




Server wird beendet - Lösche Semaphor 12255260.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5439
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:56.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:41.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:57.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:58.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:05.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7167
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:06.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:55.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:04:00.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.83
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:47.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.33
p-value of test                       :  6.2e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.66
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:14.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.52
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:44.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.70
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.59
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.57
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.21
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.83
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.16
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.44
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.45
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  482.38
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:43.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.28
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:01.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6951.71
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:40.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.32
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.96
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:02.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.89
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.50
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:32.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4944.37
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:54.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45610
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869610
  j =  1                              :        399908783
  j =  2                              :            45604
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45755
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869755
  j =  1                              :        399908493
  j =  2                              :            45749
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:28.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:18.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :  5.3e-4    *****

Anderson-Darling statistic = A2       :    4.77
p-value of test                       :  3.8e-3


-----------------------------------------------
CPU time used                    :  00:01:46.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9933


-----------------------------------------------
CPU time used                    :  00:01:59.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:57.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:37.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.77e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 8.53e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:34.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:35.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.65
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.62
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.92
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.23
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.01
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.11
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.23
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:44.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.50
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.96
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  158.30
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17111.88
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.46
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.57
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.10
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.23
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.29
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   60.89
p-value of test                       :  5.9e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.29
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.93
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.57
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.70
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.96
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.75
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.92
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.50
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.72
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.84
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.54
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.42
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  180.92
p-value of test                       :  6.0e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.09
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.37
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.42
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5079.49
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.52
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.02
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.82
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.12
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.54
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.48
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.51
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.91
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:22.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.26
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :    1.85
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:24.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 5.06e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.41e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 7.95e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.43
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.06
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.62
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:05.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.85
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:07.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.67
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9664.96
p-value of test                       :    0.9916

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9823.32
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.039
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:45.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4961.40
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:46.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    4.13
p-value of test                       :  7.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4638.98
p-value of test                       :    0.9950

-----------------------------------------------
CPU time used                    :  00:01:50.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4263.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4029.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11668.57
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11824.19
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:29.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.00
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  7999975245

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.18
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999975740

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.85

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:39.67

 All tests were passed




Server wird beendet - Lösche Semaphor 13271068.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:48.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1471
p-value of test                       :  2.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334591
  j =  1                              :        599997058
  j =  2                              :             1471
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:27.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1470
p-value of test                       :  2.4e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334590
  j =  1                              :        599997060
  j =  2                              :             1470
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5318
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:56.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:58.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:05.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:05.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7479
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:56.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:01.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:46.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:13.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:42.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.80
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.78
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.01
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.16
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:10.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.31
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.71
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  197.33
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  390.39
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:43.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.88
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:02.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7213.18
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.55
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.49
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:03.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.09
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:47.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.87
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5038.94
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:54.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45940
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869940
  j =  1                              :        399908124
  j =  2                              :            45932
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46105
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870105
  j =  1                              :        399907794
  j =  2                              :            46097
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:28.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:19.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:46.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:59.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 9.49e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.62e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 8.64e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:21.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:42.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.47
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.73
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.50
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.80
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.10
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.58
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:43.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.36
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.39
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17296.07
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.45
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.20
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.01
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.62
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.16
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.72
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.21
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.33
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.44
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.61
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.30
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  444.98
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.76
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.14
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.70
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.91
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.70
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.61
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.15
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.82
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.73
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.10
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  450.77
p-value of test                       :  5.9e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.54
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  313.76
p-value of test                       :    0.9964


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.32
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4841.05
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.93
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.52
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.45
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :    3.27
p-value of test                       :  5.3e-4    *****



-----------------------------------------------
CPU time used                    :  00:02:24.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.41
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :  -0.082
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:24.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.66
p-value of test                       :    0.95

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.33
p-value of test                       :    0.01

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 5.07e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 6.05e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.81
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.82
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:05.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.46
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:06.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9840.45
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 5.93e-3
p-value of test                       :    0.9937

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9667.71
p-value of test                       :    0.9911

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:48.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4813.54
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:48.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4907.28
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:51.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.66
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4234.19
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11800.88
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11828.29
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:29.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.10
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000042961

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.35
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999980456

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :  -0.046
p-value of test                       :    0.52

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.14

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.15
p-value of test                       :    0.9981

-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:28.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0               5.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14319644.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:40.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5339
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:56.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:40.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:41.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:57.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:05.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:04.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7489
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:55.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:00.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     867
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:46.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    2.54
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:14.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    6.07
p-value of test                       :  9.2e-4    *****

-----------------------------------------------
CPU time used                    :  00:02:43.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.97
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.90
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.99
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.43
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.51
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.73
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:43.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:03.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7042.58
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.79
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.36
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:03.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.44
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.40
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:35.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4874.27
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:12.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:00.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45523
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869523
  j =  1                              :        399908957
  j =  2                              :            45517
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45562
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869562
  j =  1                              :        399908878
  j =  2                              :            45558
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:27.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9951

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:18.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:59.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.00e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:35.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 8.69e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.33e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 8.69e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.45
p-value of test                       :  7.2e-3

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:35.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:36.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.89
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.13
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.29
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.13
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.82
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:42.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.74
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.97
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.13
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.59
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:39.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17623.52
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.35
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.33
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.66
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.04
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.15
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.97
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.40
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.30
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.53
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.74
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.17
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.37
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.18
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.85
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.38
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.10
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  187.00
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  556.48
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.62
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.01
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.53
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.14
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.87
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.53
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.36
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.98
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.48
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.56
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.07
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.14
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.99
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:24.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.66
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :   -1.51
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:24.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.59e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.69e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 4.70e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.73
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.08
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.35
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:05.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.44
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:06.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9731.64
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10039.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:45.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4780.19
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:48.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5031.80
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:50.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3986.33
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.77
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11957.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11740.67
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.41
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999997361

Normal statistic for number of bits   :  -0.021
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.02
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000133027

Normal statistic for number of bits   :    1.05
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :  -0.044
p-value of test                       :    0.52

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:21.59
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs mNP2S, t = 16        9.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 15302684.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:54.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:41.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:57.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4199
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:58.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:06.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:05.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7560
p-value of test                       :  2.5e-3


-----------------------------------------------
CPU time used                    :  00:03:55.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7186
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:01.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    2.43
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     330
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:13.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:45.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.96
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.50
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.54
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.16
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.49
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.44
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.65
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.37
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.30
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:43.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1495.41
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7065.32
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:40.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.91e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.11
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:02.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.59
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.78
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:33.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5235.46
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:02.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45842
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869842
  j =  1                              :        399908318
  j =  2                              :            45838
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46032
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870032
  j =  1                              :        399907936
  j =  2                              :            46032
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:27.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:19.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:47.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  9.8e-3

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:00.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:36.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 6.28e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.27e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:32.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:48.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.46
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.67
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.90
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.10
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.95
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:44.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.41
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.58
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.71
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.95
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17567.30
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:52.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.24
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.22
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.04
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.53
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.74
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   61.41
p-value of test                       :  5.2e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.82
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.08
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.64
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.37
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.33
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.14
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.15
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.91
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.60
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.44
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  191.38
p-value of test                       :  6.9e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.53
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.62
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.21
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.84
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.26
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5072.07
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  315.17
p-value of test                       :    0.9918


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.74
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.05
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.26
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5076.70
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.70
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.86
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.42
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :    1.15
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:24.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.32
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   -1.32
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:23.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.55
p-value of test                       :    0.94

Sample variance                       :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.08e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 8.24e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 9.78e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.52
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.97
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.93
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:06.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.23
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:08.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9950.06
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.61
p-value of test                       :  1.9e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    5.65
p-value of test                       :  1.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9581.95
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:39.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.55
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4810.88
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:49.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4285.19
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4198.55
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.86
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11676.10
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:30.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.49
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999944984

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.58
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999780809

Normal statistic for number of bits   :   -1.73
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 6.86e-4
p-value of test                       :    0.9993    *****

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.61
p-value of test                       :    0.9955

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:24.15

 All tests were passed




Server wird beendet - Lösche Semaphor 16351260.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5388
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:57.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:41.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:57.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:05.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:06.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:56.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:59.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.17
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    2.21
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    3.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.79
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:15.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.26
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.69
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:43.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.68
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.02
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.32
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.54
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.00
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.62
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.84
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.53
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.03
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:44.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1427.16
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:01.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7159.12
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:41.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.90
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.2e-3

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.11
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:03.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.96
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.77
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:32.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4965.38
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:03.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45911
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869911
  j =  1                              :        399908180
  j =  2                              :            45907
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45910
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869910
  j =  1                              :        399908184
  j =  2                              :            45902
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.17e-3
p-value of test                       :    0.9988

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:27.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:18.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:46.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:00.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.98e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:34.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:34.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.62
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:48.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   96.29
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.94
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.97
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.70
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.61
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.90
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:41.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.95
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.39
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.59
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.86
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17209.53
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.90
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.12
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   45.28
p-value of test                       :  7.8e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.64
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.49
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.28
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.59
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.20
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.60
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.97
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.72
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.78
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.85
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.25
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.45
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.76
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.10
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.76
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.06
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.70
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.91
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.84
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.79
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.26
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.30
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.78
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4982.17
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.88
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.84
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:34.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.34
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :    1.46
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.73
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :   -0.54
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:22.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :7.02e-17
p-value of test                       :    0.50

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 9.08e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.36e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.72
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.29
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.99
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:05.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.77
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:07.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10027.31
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10141.38
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:42.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.57
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:47.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :  1.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.57
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4665.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:49.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.58
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4220.45
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11970.86
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11814.05
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.28
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000108832

Normal statistic for number of bits   :    0.86
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.01
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000182041

Normal statistic for number of bits   :    1.44
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.07
p-value of test                       :    0.98

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:28.70

 All tests were passed




Server wird beendet - Lösche Semaphor 17367068.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:40.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5467
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:56.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:43.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:43.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:00.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:01.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:13.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:07.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7145
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:04:08.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.49
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     953
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    2.76
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     635
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    4.39
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:02:14.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9917

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:40.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.62
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.82
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.34
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.55
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.39
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.68
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   86.86
p-value of test                       :  3.0e-3

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.52
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:28.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.39
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1433.64
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:04.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6987.37
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.35
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:18.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.50
p-value of test                       :    0.9920


-----------------------------------------------
CPU time used                    :  00:00:46.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.18
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:42.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5047.47
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:04.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45543
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869543
  j =  1                              :        399908918
  j =  2                              :            45535
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46044
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870044
  j =  1                              :        399907915
  j =  2                              :            46038
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:33.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:20.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:50.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:07.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:56.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:38.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.33e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:24.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:24.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:49.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.92
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.52
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.35
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   59.54
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.11
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.06
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:50.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.85
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.69
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17569.46
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.78
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.70
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.55
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.52
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.57
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.74
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.94
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.76
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.72
p-value of test                       :    0.9909


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.84
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.06
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.02
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.47
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.94
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  117.71
p-value of test                       :  9.3e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.62
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.72
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.41
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.04
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.76
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.63
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.98
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.16
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.77
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.58
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.55
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.52
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.09
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.47
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.32
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.80
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:25.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.42
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:25.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.62
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 8.51e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 2.40e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.60
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:28.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.85
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.01
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:06.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.18
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:06.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9852.31
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9838.87
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:04:26.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4895.26
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:57.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.09
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:00.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4286.42
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4061.83
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11534.80
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:36.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11860.89
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:36.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.47
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  7999958946

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.27
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000105691

Normal statistic for number of bits   :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.26
p-value of test                       :    0.99

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 3.17e-3
p-value of test                       :    0.9967

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -2.17
p-value of test                       :    0.99

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    2.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:09.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 C (L=1000, r=0)     9.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 18284572.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:58.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:42.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:41.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:58.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:58.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:05.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:06.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:59.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:04:01.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.24
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.11
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:14.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9956


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:43.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.23
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:55.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.97
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.72
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:11.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.20
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.31
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.10
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  263.91
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.72
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:43.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1522.71
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:03.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7048.25
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.67
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.50
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:01.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.07
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.57
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4809.98
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:31.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:24.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45731
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869731
  j =  1                              :        399908543
  j =  2                              :            45721
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46363
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870363
  j =  1                              :        399907277
  j =  2                              :            46357
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:28.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:18.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:45.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:01.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:32.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:37.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.94
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.16
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.47
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.70
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.00
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:43.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.76
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.42
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.77
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.97
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17363.22
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.78
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.86
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.71
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.42
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.75
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.63
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.24
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.52
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.87
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.21
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.10
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.83
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.12
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.58
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.34
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.42
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.61
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.70
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.66
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.82
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  325.02
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4891.98
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.19
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.29
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.55
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.26
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4904.82
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.22
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.02
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.99
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :   -1.92
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:23.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.77
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :    1.43
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:26.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.18
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 9.90e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.42e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 6.52e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.42
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.46
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.92
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:07.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.89
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:07.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9807.63
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10219.12
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    3.29
p-value of test                       :  5.0e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.19
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.40
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:03:48.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4995.56
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:49.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.38
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4217.26
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4169.95
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11694.26
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:28.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11688.79
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:29.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.32
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999901643

Normal statistic for number of bits   :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.04
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000024739

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :  -0.077
p-value of test                       :    0.53

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:28.75
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 92  HammingCorr, L = 30             5.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 19496988.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:40.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:50.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5425
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:58.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:41.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7171
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:42.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:57.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:05.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:05.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:55.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:04:01.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.57
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     639
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.57
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    3.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:13.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.84
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    2.08
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     123
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:46.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.85
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.24
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.03
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:15.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.72
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.31
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.42
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.74
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  486.30
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:44.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:03.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6822.61
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:41.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.74
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:00.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.31
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.65
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:33.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5194.31
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:01.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46012
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870012
  j =  1                              :        399907981
  j =  2                              :            46002
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45679
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869679
  j =  1                              :        399908645
  j =  2                              :            45673
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:28.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:18.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:45.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:00.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:34.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.79e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.81e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    3.66
p-value of test                       :  1.3e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.084
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:36.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:37.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.35
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:49.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.94
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.06
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.68
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.32
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.79
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.62
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.59
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.35
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.88
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.60
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16986.88
p-value of test                       :    0.9916



-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.95
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.45
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.28
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.57
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.40
p-value of test                       :    0.9901


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.96
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.80
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.33
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.60
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.38
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.18
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.71
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  569.27
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.42
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.16
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.61
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.33
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.12
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.89
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.00
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.06
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.35
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.72
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.73
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.25
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.50
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  318.15
p-value of test                       :    0.9938


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4959.22
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.00
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.87
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.96
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :   0.034
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:25.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.15
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :   0.021
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:22.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.72
p-value of test                       :    0.96

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.58e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.72
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.90
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.82
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:04.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.39
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:04.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10007.26
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10232.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:55.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:35.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4970.61
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4924.89
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:37.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3973.11
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4072.43
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12077.33
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11352.60
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.49
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000101383

Normal statistic for number of bits   :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.60
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000164857

Normal statistic for number of bits   :    1.30
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:42.22
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 55  SampleCorr, k = 1               1.3e-4
 100  HammingIndep, L=1200, r=25      0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 20512796.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:18.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:20.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:42.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:36.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7164
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:35.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:55.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:55.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:02.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:01.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:53.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:59.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9952

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:51.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.64
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    3.33
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     341
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:11.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.72
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:34.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.72
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.20
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.52
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.90
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.98
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.54
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.04
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.20
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:46.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1343.65
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:02.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7086.44
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:44.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.96
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.94
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:01.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.58
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.07
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:35.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4918.01
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:01.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46284
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870284
  j =  1                              :        399907438
  j =  2                              :            46272
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46157
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870157
  j =  1                              :        399907690
  j =  2                              :            46149
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:28.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:19.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:44.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.42
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:00.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:53.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:34.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.11e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.84e-5
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.062
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:34.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:35.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.61
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.18
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.45
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.12
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.69
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.59
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:40.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.53
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.63
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:31.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.22
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:31.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.08
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17512.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:55.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.23
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.61
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.49
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.11
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.73
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.48
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.41
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.65
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.05
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:40.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.57
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.10
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.95
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.12
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.42
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.14
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.15
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.57
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  192.47
p-value of test                       :  1.0e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.00
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.27
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.03
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.41
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.52
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.23
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.15
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.27
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5089.53
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.65
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.32
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.87
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :    1.18
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:25.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.45
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :    1.16
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:17.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 6.77e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.44e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 9.08e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.74
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.71
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.07
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:11.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.32
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:11.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10059.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10063.80
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : -7.95e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:57.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4697.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4973.68
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4363.72
p-value of test                       :  3.7e-3

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4000.39
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11797.36
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:28.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11912.23
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:29.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.57
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  8000049972

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.33
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000122722

Normal statistic for number of bits   :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.50
p-value of test                       :    0.93

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.35

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:29.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:17:43.57

 All tests were passed




Server wird beendet - Lösche Semaphor 1081373.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:39.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5220
p-value of test                       :    0.9969


-----------------------------------------------
CPU time used                    :  00:03:43.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:37.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:36.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:54.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:01.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:01.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:54.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:59.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    6.41
p-value of test                       :  6.5e-4    *****


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:46.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:12.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.30
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:42.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.34
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.14
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.94
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.30
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.92
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.68
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.54
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.54
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.83
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:45.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1343.64
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:01.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7028.23
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:44.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.28
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:01.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.62
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.70
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:33.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5125.22
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:04.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45791
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869791
  j =  1                              :        399908423
  j =  2                              :            45781
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45599
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869599
  j =  1                              :        399908806
  j =  2                              :            45591
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:11.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:32.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:18.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:45.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:59.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:54.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:34.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.57e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 9.73e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9919

-----------------------------------------------
CPU time used                    :  00:00:22.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.46e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:32.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:33.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.77
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:48.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.77
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.75
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:49.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.00
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.41
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.76
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:39.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.75
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.89
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:29.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.08
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17577.51
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.33
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.55
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.50
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.50
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.79
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.64
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.69
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.07
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.06
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.54
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.15
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.02
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.38
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.43
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.95
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.00
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.81
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.36
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.85
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.73
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.11
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.66
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4960.96
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.13
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.67
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.89
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.44
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4982.09
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  329.87
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.59
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.89
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:25.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.84
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:26.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.72
p-value of test                       :    0.96

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.86e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 6.98e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.38e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.21
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.96
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.80
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:09.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:11.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9901

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9937.47
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10080.67
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:54.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5008.33
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.26
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:49.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4218.17
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.59
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12129.83
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12014.00
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.26
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999901139

Normal statistic for number of bits   :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.28
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000114265

Normal statistic for number of bits   :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.55
p-value of test                       :    0.06

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.35

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:29.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:37.60
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs NP, t = 3            6.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1474589.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5404
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:42.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:37.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:36.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4225
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:54.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4211
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:02.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:03.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:54.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:00.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.72
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     865
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:49.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.53
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:16.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:41.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.02
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.95
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.25
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.92
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.30
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:11.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   85.89
p-value of test                       :  3.7e-3

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.16
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.51
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.35
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1372.55
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:00.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6862.03
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:43.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.99
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:15.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.17
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:00.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.46
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.98
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:34.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4972.82
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:00.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45962
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869962
  j =  1                              :        399908081
  j =  2                              :            45952
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45874
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869874
  j =  1                              :        399908259
  j =  2                              :            45860
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:31.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:18.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:44.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:58.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:55.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:15.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:34.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.96e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 9.57e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      : 8.65e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:31.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.086
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:32.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.81
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.11
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.01
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.43
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.79
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.89
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:39.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.35
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.52
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.86
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.89
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:38.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17324.00
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.05
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.56
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.23
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.34
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.28
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.12
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.41
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.59
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.46
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.88
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.40
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.17
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.57
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.88
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.30
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.40
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.02
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.27
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.57
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.09
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.59
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.65
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.60
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.50
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  237.41
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.72
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.17
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.78
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.80
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.86
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.78
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -1.96
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:22.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.28
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :    1.21
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:25.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.91e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.70
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.52
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.49
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:08.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:08.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10077.22
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9923.96
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:55.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:47.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5013.08
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:49.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.10
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:50.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4207.49
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4286.61
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11851.27
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11852.98
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.56
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000016483

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.56
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000001474

Normal statistic for number of bits   :   0.012
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.56
p-value of test                       :    0.06

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:39.57

 All tests were passed




Server wird beendet - Lösche Semaphor 2392093.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:50.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5527
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:48.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:38.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:36.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:55.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:55.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:02.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7172
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:02.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7490
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:54.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:00.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    3.01
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     943
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9925

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:49.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.75
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.23
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:16.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.96
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     130
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    2.12
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.20
p-value of test                       :    0.9904

-----------------------------------------------
CPU time used                    :  00:02:44.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.67
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.88
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.47
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.41
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.90
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.12
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:16.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1475.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:03.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7007.00
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:43.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.71
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.36
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:02.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.13
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.99
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:33.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4943.24
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:01.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45943
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869943
  j =  1                              :        399908120
  j =  2                              :            45931
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46065
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870065
  j =  1                              :        399907874
  j =  2                              :            46057
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:31.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:19.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:46.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:01.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:15.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:33.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 4.00e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:22.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    3.06
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.06
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.24
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.17
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.72
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.52
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.07
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:38.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.23
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.86
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.21
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.23
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.42
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.09
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 6.51e-3
p-value of test                       :    0.9931

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17715.87
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.74
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.81
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.66
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.21
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.12
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.16
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.33
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.44
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.22
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.79
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.21
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.48
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.65
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.72
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.61
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.43
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.26
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.42
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.31
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.99
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.76
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4856.19
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.57
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.41
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.03
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.00
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4802.23
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.70
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.13
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.33
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :   -0.96
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:22.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.75
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:23.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    0.20
p-value of test                       :    0.9939

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 4.97e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.60e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.37
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.84
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.41
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:05.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.93
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:06.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.58
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10296.34
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10092.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:50.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4920.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:49.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.57
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:50.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.50
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3966.86
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12082.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:28.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11743.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:28.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.40
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000067372

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.61
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000034702

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    2.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.83
p-value of test                       :    0.97

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:02.92

 All tests were passed




Server wird beendet - Lösche Semaphor 3440669.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9953


-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5433
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:52.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:38.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:02.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:03.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:55.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:04:00.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     862
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:13.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:40.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.90
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.08
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.01
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.10
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.60
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.62
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.33
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.28
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  262.84
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.47
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:42.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1444.31
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:01.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7015.11
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:42.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.79
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.68
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:02.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.39
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:46.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.68
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:33.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4983.04
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:01.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45858
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869858
  j =  1                              :        399908285
  j =  2                              :            45856
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45481
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869481
  j =  1                              :        399909039
  j =  2                              :            45479
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:30.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:17.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:44.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:58.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:33.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.82e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:35.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:34.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.78
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.86
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.35
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:48.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.21
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.83
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.25
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:36.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.89
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.97
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.08
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17514.92
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.50
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.07
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.42
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.94
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.20
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.30
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.32
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.01
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.05
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.78
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.48
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.89
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.29
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.89
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.03
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.38
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.14
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.03
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.30
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.45
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:43.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.71
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.98
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4923.56
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.74
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.65
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.10
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.09
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5039.05
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.72
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.55
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.64
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:26.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.70
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :   -0.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:25.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.85
p-value of test                       :    0.97

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.49e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.09e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.09
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:28.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.83
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.88
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:05.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.31
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:06.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 5.44e-3
p-value of test                       :    0.9943

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9751.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10018.57
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.080
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : -3.03e-5
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:52.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.14
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:50.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4766.73
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:50.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.15
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4230.72
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11821.64
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11658.04
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:29.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.97
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000136468

Normal statistic for number of bits   :    1.08
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.89
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000227647

Normal statistic for number of bits   :    1.80
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.025
p-value of test                       :    0.51

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.83
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.62
p-value of test                       :  4.4e-3

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:23.07

 All tests were passed




Server wird beendet - Lösche Semaphor 4456477.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5444
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:52.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:40.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:39.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:03.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:04.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:54.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7499
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:58.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     940
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:49.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    2.93
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:12.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:42.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.62
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.43
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.83
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.37
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.80
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.77
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.46
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.71
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.06
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:43.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.72
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:02.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7064.90
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:42.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.55
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.78
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:04.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.08
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.24
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4799.70
p-value of test                       :    0.9922


-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:00.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45603
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869603
  j =  1                              :        399908797
  j =  2                              :            45597
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45819
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869819
  j =  1                              :        399908364
  j =  2                              :            45815
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :  4.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.35
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:29.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:18.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:44.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:58.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:35.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 3.65e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:35.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.96
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:35.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.92
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.39
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:49.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.74
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.46
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.03
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:38.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.82
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.89
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.15
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  162.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17268.52
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.07
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.17
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.44
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.50
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.85
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:37.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.77
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.00
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.36
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.29
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.84
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.17
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.07
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.11
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.39
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.17
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.39
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  429.03
p-value of test                       :    0.9903


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   99.79
p-value of test                       :    0.9915


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.90
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  314.95
p-value of test                       :    0.9958


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.70
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.10
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.54
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.79
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  309.56
p-value of test                       :    0.9979


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.64
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4991.68
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.62
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.25
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.91
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:23.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    2.15
p-value of test                       :    0.9991    *****


-----------------------------------------------
Normal statistic for number of jumps  :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:23.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -2.03
p-value of test                       :    0.98

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.53e-3
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.20e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.01
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.04
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.45
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:06.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.42
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:05.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10105.77
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9966.96
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.044
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      : 9.49e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:57.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.59
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:47.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9996    *****

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.92
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:49.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4182.68
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3942.76
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11956.59
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11921.75
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:30.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   81.84
p-value of test                       :  8.6e-3


-----------------------------------------------
Total number of bits:  7999868766

Normal statistic for number of bits   :   -1.04
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.14
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000031720

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 3.53e-3
p-value of test                       :    0.9964

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.91

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:42.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 81  LinearComp, r = 0               0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 5439517.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5278
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:57.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4430
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:40.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:55.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:56.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:03.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:04.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:54.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7121
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:59.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.65
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     941
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:50.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.96
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    2.56
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:17.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:47.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.68
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.10
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.65
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.65
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.42
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.85
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.83
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.37
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  496.01
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:43.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1359.16
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:01.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7221.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:42.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.75
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.00
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:02.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.77
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:33.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4888.90
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:00.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45830
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869830
  j =  1                              :        399908344
  j =  2                              :            45822
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45710
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869710
  j =  1                              :        399908585
  j =  2                              :            45700
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:28.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:18.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:44.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:58.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:34.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.74e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 5.71e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:21.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.052
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.059
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:37.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.46
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:48.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.33
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:51.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.12
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.78
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.82
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.13
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:38.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  1.9e-3

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    3.75
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   94.19
p-value of test                       :    0.9923

-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17493.97
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.49
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.71
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.49
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.04
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.75
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:37.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.66
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.65
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.85
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.51
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.89
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.38
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.30
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.77
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.97
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.94
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.97
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.49
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.78
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.89
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.91
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.88
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.76
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.76
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.78
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.24
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.09
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5137.32
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.73
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.32
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.66
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :  -0.051
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:22.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.01
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :  -0.082
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:23.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 5.20e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.72e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 8.30e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.17
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.43
p-value of test                       :    0.9938

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.26
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:05.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.32
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:05.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10104.68
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9964.63
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:44.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4821.48
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4913.77
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:49.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.85
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4257.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11944.46
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11664.55
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.36
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000010795

Normal statistic for number of bits   :   0.085
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.98
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999971174

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    2.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:36.31

 All tests were passed




Server wird beendet - Lösche Semaphor 6455325.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5527
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:56.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:44.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:58.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:58.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:06.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:05.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:56.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:04:01.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:52.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    8.56
p-value of test                       :  6.6e-5    *****

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:17.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:48.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.54
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.29
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.04
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.52
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.25
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.75
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.34
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.55
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  453.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:43.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.87
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:02.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7112.94
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:42.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.78
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.43
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:01.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.42
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.46
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:32.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5095.81
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:53.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45821
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869821
  j =  1                              :        399908360
  j =  2                              :            45817
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45975
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869975
  j =  1                              :        399908059
  j =  2                              :            45957
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.77e-3
p-value of test                       :    0.9981

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:27.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:17.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:45.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:58.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.99e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.011
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:21.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:35.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:34.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.84
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.20
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.93
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.89
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.77
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.01
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:38.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.74
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.92
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.39
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.62
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:16.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.00
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17129.57
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.26
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.43
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.54
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.29
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.33
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.89
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.08
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.28
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.04
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.39
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.05
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.01
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.43
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.59
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.47
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  109.86
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.86
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.45
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.03
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.72
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.09
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  320.10
p-value of test                       :    0.9923


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4878.37
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.17
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.24
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.06
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.20
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4945.75
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.99
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.44
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.93
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :    1.45
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:22.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.22
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :  -0.055
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:23.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.78

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.82e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.78e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.46
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.34
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.38
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:06.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.72
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:06.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9890.12
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10039.45
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:42.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.13
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:47.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.6e-3

Anderson-Darling statistic = A2       :    4.04
p-value of test                       :  8.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5140.63
p-value of test                       :  6.2e-3

-----------------------------------------------
CPU time used                    :  00:01:49.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4270.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.43
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11769.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11701.44
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:30.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.72
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999955049

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.07
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000053146

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:07.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs mNP2, t = 5          6.6e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7503901.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5502
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:04:01.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:43.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7192
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:45.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4433
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:58.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:58.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:06.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:05.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:56.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:04:01.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     936
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:51.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    2.27
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    2.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.17
p-value of test                       :    0.9959

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:18.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:46.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.97
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.73
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.43
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.64
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.28
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.54
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.13
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.07
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.37
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:43.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.17
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:02.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6950.74
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:42.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.64e-3
p-value of test                       :    0.9973

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   51.61
p-value of test                       :  8.4e-3

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.75
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:03.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.73
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.99
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:31.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5092.09
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:53.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45577
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869577
  j =  1                              :        399908847
  j =  2                              :            45575
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46066
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870066
  j =  1                              :        399907873
  j =  2                              :            46056
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:27.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:18.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:45.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 2.57e-4
p-value of test                       :    0.9997    *****

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:59.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:35.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.45e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.010
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:37.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.63
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.23
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.81
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.63
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.59
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:41.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.26
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.12
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.96
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.07
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:39.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17447.49
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.20
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.38
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.83
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.97
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.67
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.84
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.09
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.65
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.54
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.38
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.97
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.84
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.46
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.10
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.01
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.47
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  107.41
p-value of test                       :    0.9930


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.31
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.70
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.26
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.51
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.33
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5098.70
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.40
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.04
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  439.55
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.24
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.79
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.83
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.01
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:23.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.28
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :   -1.02
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:22.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.56e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 4.55e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9922

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.36e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.16
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.04
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.47
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:04.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.94
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:04.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10129.17
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9960.89
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:55.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:41.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4800.63
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:48.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4949.07
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.71
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4090.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11956.53
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11917.09
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:29.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.14
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  7999911831

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.95
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999841037

Normal statistic for number of bits   :   -1.26
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9962

Tests on the sum of all N observations
Standardized normal statistic         :  -0.044
p-value of test                       :    0.52

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:17.59

 All tests were passed




Server wird beendet - Lösche Semaphor 8552477.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1259
p-value of test                       :    0.9979

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334379
  j =  1                              :        599997482
  j =  2                              :             1259
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5455
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:00.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:44.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:45.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:01.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:00.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:09.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:08.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:03.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:04:03.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     861
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    2.32
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    4.23
p-value of test                       :  6.8e-3

-----------------------------------------------
CPU time used                    :  00:02:19.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.11
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:48.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.18
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.71
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.52
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.72
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.79
p-value of test                       :    0.9931

-----------------------------------------------
CPU time used                    :  00:01:10.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.84
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.83
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.27
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.56
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.35
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:45.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.22
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:04.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6989.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:45.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.91
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:06.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.73
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.28
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:35.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5073.68
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:08.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45594
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869594
  j =  1                              :        399908816
  j =  2                              :            45586
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45986
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869986
  j =  1                              :        399908030
  j =  2                              :            45982
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:28.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:17.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:45.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:01.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.43e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:22.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:36.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:37.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.33
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.07
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.99
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.53
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.97
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:45.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.62
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.08
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.11
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.48
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.40
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17448.40
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.91
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.80
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.17
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.09
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.97
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.43
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.86
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.24
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.24
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.35
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.69
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.82
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.60
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.71
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.29
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.51
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.78
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.03
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  171.95
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.34
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.13
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.69
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5138.92
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  427.04
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.85
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:34.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.27
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.55
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.37
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.09
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.96
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:34.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.56
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:21.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.14
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :    1.81
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:23.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.01e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 7.20e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.79
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.09
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.78
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:05.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.07
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:06.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9759.07
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10048.19
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.068
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:04:03.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4985.26
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4931.27
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:51.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4136.16
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4141.42
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12003.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12035.17
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:29.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.39
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999864014

Normal statistic for number of bits   :   -1.08
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.68
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000037579

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:11.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:56.27

 All tests were passed




Server wird beendet - Lösche Semaphor 9601053.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5476
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:01.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:45.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:59.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:08.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:09.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:59.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7485
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:02.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:51.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.78
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    2.47
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     635
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:18.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:49.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.73
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.36
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.07
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.64
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.83
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.81
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  202.73
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.31
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1460.18
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7121.05
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:43.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.22
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.11
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:02.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.40
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.56
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:30.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5251.20
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:11.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:03.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45806
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869806
  j =  1                              :        399908390
  j =  2                              :            45802
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45827
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869827
  j =  1                              :        399908346
  j =  2                              :            45827
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:27.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:18.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 5.51e-3
p-value of test                       :    0.9939

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:45.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:00.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:01:55.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:33.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.90e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.18e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.54
p-value of test                       :  5.6e-3

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:36.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:37.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.73
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.76
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.86
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:48.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.21
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.05
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.50
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:39.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.33
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:28.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.98
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17542.10
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.20
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.85
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.22
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.88
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.67
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.04
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.71
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.94
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.54
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.95
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.80
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.47
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.19
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.36
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.94
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.97
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.03
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.09
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.45
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.44
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.44
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.59
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5146.52
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.61
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.26
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.83
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.24
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4875.22
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.39
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.24
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.64
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:23.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.31
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :   -0.27
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:22.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.93
p-value of test                       :    0.97

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.87
p-value of test                       :    0.97

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 2.54e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 3.98e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.95
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.08
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.04
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:05.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.77
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:06.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10175.72
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10111.43
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.52
p-value of test                       :    0.9941

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:45.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5018.43
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4709.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:48.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3942.16
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4214.42
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11967.72
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11538.41
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:29.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.66
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999818438

Normal statistic for number of bits   :   -1.44
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.68
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000007168

Normal statistic for number of bits   :   0.057
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    2.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:06.82

 All tests were passed




Server wird beendet - Lösche Semaphor 10682397.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5385
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:59.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:43.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:44.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:58.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4213
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:59.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:07.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7469
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:08.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:57.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:04:02.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:50.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     650
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:18.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:50.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.32
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.74
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.26
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.66
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.08
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.88
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.72
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  277.66
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.77
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.57
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:04.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7142.29
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:46.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.81
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:03.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.97
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  148.39
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:29.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5050.92
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:59.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46697
p-value of test                       :  7.1e-5    *****


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870697
  j =  1                              :        399906613
  j =  2                              :            46683
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45545
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869545
  j =  1                              :        399908915
  j =  2                              :            45535
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :  6.4e-3

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:27.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:19.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:46.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:01.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:33.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 6.46e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 6.95e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:34.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:35.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.79
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.86
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.83
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.80
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.94
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.02
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:37.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.35
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.61
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.63
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.80
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17244.72
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.80
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.36
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.47
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.97
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.12
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   56.13
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.42
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.35
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.74
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.78
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.06
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.12
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.32
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.32
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.61
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.08
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.96
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.87
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.28
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.73
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.83
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.06
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.88
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  237.01
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.48
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.10
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4945.42
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.38
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.42
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.20
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:24.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.34
p-value of test                       :    0.9926


-----------------------------------------------
Normal statistic for number of jumps  :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:25.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.78e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 9.98e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.02
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.25
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.27
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:07.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.68
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:06.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10086.06
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9964.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:39.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4943.41
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4771.39
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:49.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.47
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4182.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11684.11
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12252.16
p-value of test                       :  3.0e-3

-----------------------------------------------
CPU time used                    :  00:01:29.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.09
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999898970

Normal statistic for number of bits   :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.46
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999973496

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.039
p-value of test                       :    0.52

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   0.019
p-value of test                       :    0.49

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:55.60
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 44  CollisionPermut, r = 0          7.1e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11698205.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1481
p-value of test                       :  9.4e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334601
  j =  1                              :        599997038
  j =  2                              :             1481
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5355
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:04.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:43.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:46.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:01.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4182
p-value of test                       :    0.9907


-----------------------------------------------
CPU time used                    :  00:02:02.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:13.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:13.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:09.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:13.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    2.04
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:53.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.51
p-value of test                       :  5.1e-3

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:19.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:48.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.69
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.94
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.99
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.51
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:10.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.72
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.91
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.15
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.96
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:29.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  498.29
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.09
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:07.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7030.86
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:58.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.34
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.16
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.81
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.14
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:43.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5108.09
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:59.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45816
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869816
  j =  1                              :        399908372
  j =  2                              :            45808
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45749
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869749
  j =  1                              :        399908509
  j =  2                              :            45735
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:31.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:22.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:54.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:09.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:56.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:38.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.26e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.62e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:24.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:51.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:52.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.00
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.21
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.43
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.00
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.86
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.82
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.72
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:52.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.73
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.29
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17408.28
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.33
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.22
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.24
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.48
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.74
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.14
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   60.58
p-value of test                       :  4.6e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.64
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.46
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.89
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.89
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  103.80
p-value of test                       :    0.9967


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.59
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.80
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.15
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:43.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.18
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.25
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  550.84
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.35
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.27
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.19
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.91
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.14
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.00
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.51
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.15
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.96
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4778.88
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.59
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.81
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.49
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:23.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.35
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :   -0.69
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:23.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.16
p-value of test                       :    0.98

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 2.94e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.04e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.23
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.14
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.23
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:04.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.94
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:10.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10153.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10108.82
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:04:38.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4726.03
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:51.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5051.25
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:54.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4026.94
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4320.58
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12081.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:32.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11975.79
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:35.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.34
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999953639

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.76
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999980711

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:11:06.07
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           9.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12714013.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5378
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:58.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:43.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:58.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:59.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:07.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7098
p-value of test                       :    0.9951


-----------------------------------------------
CPU time used                    :  00:03:07.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:58.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:00.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:15.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.89
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:45.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.65
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.05
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.99
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.46
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.60
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.61
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.32
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.99
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.23
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  476.60
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:43.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1501.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:03.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7085.49
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.02
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:03.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.59
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.79
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:34.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4900.87
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:58.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46034
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870034
  j =  1                              :        399907935
  j =  2                              :            46028
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46124
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870124
  j =  1                              :        399907755
  j =  2                              :            46118
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:28.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:18.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:44.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:32.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.13e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.55e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.96e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:35.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.27
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.98
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.45
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   17.72
p-value of test                       :    0.9969

-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.65
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.04
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:45.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.34
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.46
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.64
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  102.84
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17386.57
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.64
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.15
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.80
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.03
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.69
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.88
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.33
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.92
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.11
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.17
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.33
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.78
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.03
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.82
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.02
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.90
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.87
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.11
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.42
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.67
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.41
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.65
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5095.58
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.76
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.92
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.74
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.71
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5149.62
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.23
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  238.79
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.79
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:24.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.98
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :   0.066
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:24.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.80e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.06
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.78
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.34
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:04.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.40
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:06.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10154.94
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9939.64
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:46.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.44
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4811.62
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:48.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4280.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.67
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11850.79
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11874.71
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.35
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999981287

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.90
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999823763

Normal statistic for number of bits   :   -1.39
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:17.95

 All tests were passed




Server wird beendet - Lösche Semaphor 13991965.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5378
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:59.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:43.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:45.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4228
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:59.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:00.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:11.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:12.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:03.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:05.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.12
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.83
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.77
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.65
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.21
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    2.80
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:15.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:44.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.95
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:55.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.43
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.18
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.77
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.77
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.72
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.09
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.77
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.38
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:05.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7049.36
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.79
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:07.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.47
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.29
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:36.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4933.27
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:59.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45977
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869977
  j =  1                              :        399908052
  j =  2                              :            45965
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45640
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869640
  j =  1                              :        399908723
  j =  2                              :            45634
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:29.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:18.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  6.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:46.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:02.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:36.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.60e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 6.96e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.089
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.034
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:40.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.047
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:41.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.05
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.16
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.42
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.25
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.22
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:55.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.12
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:45.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.91
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.51
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   63.52
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   14.41
p-value of test                       :  2.4e-3

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.66
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17302.19
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.98
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.82
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.18
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    8.13
p-value of test                       :    0.9989


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.92
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.66
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.77
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.92
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.86
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.03
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.51
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.75
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.85
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.20
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.28
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.41
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.12
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.37
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.30
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.43
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.95
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.84
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.86
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.18
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.14
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.14
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.85
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5162.48
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.80
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.65
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.69
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.57
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:20.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.21
p-value of test                       :    0.99

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.18e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 9.97e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.46e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.21
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.98
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.23
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:06.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.81
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:08.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9958.33
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.085
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.078
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:04:16.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4910.40
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:53.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4988.74
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:53.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4290.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.40
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11738.78
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:30.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11759.28
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:31.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.00
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999923771

Normal statistic for number of bits   :   -0.60
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.57
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000032266

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :  -0.076
p-value of test                       :    0.53

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.61
p-value of test                       :    0.05

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:19.28

 All tests were passed




Server wird beendet - Lösche Semaphor 15007773.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:50.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1474
p-value of test                       :  1.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334594
  j =  1                              :        599997052
  j =  2                              :             1474
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1229
p-value of test                       :    0.9999    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334349
  j =  1                              :        599997542
  j =  2                              :             1229
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5417
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:57.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:43.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:45.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4454
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:01.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4247
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:03.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:09.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:09.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:04:01.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7186
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:06.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:49.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.90
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     551
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.88
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.45
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     270
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:15.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:41.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.82
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.08
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.45
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.72
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.73
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.47
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.83
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.24
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.93
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:49.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1565.15
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:02:04.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7263.79
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:49.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.32
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.35
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:09.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.34
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  159.82
p-value of test                       :  7.5e-3


-----------------------------------------------
CPU time used                    :  00:01:37.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4905.79
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:59.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45676
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869676
  j =  1                              :        399908655
  j =  2                              :            45662
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46044
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870044
  j =  1                              :        399907916
  j =  2                              :            46036
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:30.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:19.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:47.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:04.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.55e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9929

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:38.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:39.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.91
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.41
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.93
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.25
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.17
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.35
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.53
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17636.45
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.28
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.00
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   42.13
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.56
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.14
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.65
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.26
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.84
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.31
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.43
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.04
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.42
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.07
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  180.80
p-value of test                       :  6.1e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.15
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.58
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.21
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.01
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.86
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.14
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.43
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.72
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5071.33
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.25
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.83
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.54
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.32
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4837.98
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.12
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.28
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.47
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:24.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.83
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :    1.43
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:23.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.21e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 9.83e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.98e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.79
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.53
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.41
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:05.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.37
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:07.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10140.32
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9994.26
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:04:18.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5104.80
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:54.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4696.87
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:54.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.73
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.59
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12011.18
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:31.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11928.85
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:31.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   86.05
p-value of test                       :  3.6e-3


-----------------------------------------------
Total number of bits:  7999875477

Normal statistic for number of bits   :   -0.98
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.63
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999925880

Normal statistic for number of bits   :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   0.050
p-value of test                       :    0.48

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:14.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:04.31
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           0.9999 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 16154653.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1241
p-value of test                       :    0.9996    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334361
  j =  1                              :        599997518
  j =  2                              :             1241
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5510
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:04:00.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:42.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:42.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4454
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:57.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:58.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:06.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:05.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:55.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7519
p-value of test                       :  9.9e-3


-----------------------------------------------
CPU time used                    :  00:04:01.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:45.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.49
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:12.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     177
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:40.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.04
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.48
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.33
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.24
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.96
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.50
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:43.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.79
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:02.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6999.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:42.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.67
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.22
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:03.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.15
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.32
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:31.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5040.59
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:54.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45955
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869955
  j =  1                              :        399908095
  j =  2                              :            45945
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45733
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869733
  j =  1                              :        399908536
  j =  2                              :            45729
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:27.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:19.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:48.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:03.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:34.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.08e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 5.79e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.070
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:32.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:34.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.46
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.49
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.86
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.18
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.37
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.50
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:51.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.64
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:38.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.99
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.07
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17296.32
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.77
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.29
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.49
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.67
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.34
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.18
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.99
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.71
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.70
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.78
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.48
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.60
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.80
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.95
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.94
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.11
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.61
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.48
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.16
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.53
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.54
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.34
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.15
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.82
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.19
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.43
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5044.33
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.22
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.40
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.85
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:25.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.85
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:24.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.81
p-value of test                       :    0.96

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   0.071
p-value of test                       :    0.47

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.43e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.56
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.16
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.91
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:05.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:05.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9949.31
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9823.05
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:42.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4850.49
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:49.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4726.52
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.02
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4261.04
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11680.61
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11836.89
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.90
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999925223

Normal statistic for number of bits   :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.36
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000047176

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.11

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    2.72
p-value of test                       :  3.6e-3

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:51.86
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  5  CollisionOver, t = 3            0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17170461.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1268
p-value of test                       :    0.9956

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334388
  j =  1                              :        599997464
  j =  2                              :             1268
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1463
p-value of test                       :  4.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334583
  j =  1                              :        599997074
  j =  2                              :             1463
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1463
p-value of test                       :  4.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334583
  j =  1                              :        599997074
  j =  2                              :             1463
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5383
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:00.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:43.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:44.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:59.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:58.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:05.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:04.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:55.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:04:01.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.17
p-value of test                       :    0.9964

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:15.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.07
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:14.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.49
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:40.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.46
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.10
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.32
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.70
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.45
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.64
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.85
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.37
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.92
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  496.74
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:43.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1472.58
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:01.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6959.27
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:42.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.54
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.36
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:02.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.11
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.54
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:34.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5081.01
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:58.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46018
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870018
  j =  1                              :        399907969
  j =  2                              :            46008
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45905
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869905
  j =  1                              :        399908197
  j =  2                              :            45891
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9949


-----------------------------------------------
CPU time used                    :  00:02:26.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:18.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-3
p-value of test                       :    0.9980

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:45.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:59.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:56.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:34.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.67e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 6.40e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 4.49e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:34.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:32.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.47
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.55
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.41
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.50
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.84
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.72
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.04
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.21
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.99
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.91
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17376.84
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.01
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.44
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.52
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.59
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.74
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.37
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.34
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.13
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.37
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.83
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  197.24
p-value of test                       :  3.0e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.42
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.92
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.29
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.42
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.68
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.20
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.16
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.43
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.29
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.57
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.50
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4928.53
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.72
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.78
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.38
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.63
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5137.07
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.97
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.65
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.04
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:24.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.39
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :    1.92
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:26.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.96
p-value of test                       :    0.03

Sample variance                       :    2.30
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.16e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.90e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 9.74e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.59
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.71
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.65
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:07.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.65
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:07.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10104.99
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9964.28
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:42.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.72
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:49.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5014.59
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:49.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.16
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.99
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11851.82
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11648.34
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.87
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000089428

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.91
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999963587

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    1.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:56.07

 All tests were passed




Server wird beendet - Lösche Semaphor 18186269.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5386
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:59.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4503
p-value of test                       :  6.2e-3


-----------------------------------------------
CPU time used                    :  00:01:43.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:44.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:59.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:58.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:04.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:05.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:56.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7536
p-value of test                       :  5.7e-3


-----------------------------------------------
CPU time used                    :  00:04:01.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.82
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.96
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:14.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:42.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.51
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.88
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.67
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.14
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.86
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.64
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.32
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.56
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.31
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.14
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:43.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:01.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6906.39
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.88
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.74
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:03.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.52
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.45
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:31.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5061.66
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:57.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45888
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869888
  j =  1                              :        399908228
  j =  2                              :            45880
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45699
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869699
  j =  1                              :        399908608
  j =  2                              :            45687
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:27.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:19.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 4.85e-4
p-value of test                       :    0.9995    *****

Anderson-Darling statistic = A2       :    4.04
p-value of test                       :  8.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9987


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:46.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:59.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:35.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.63e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:21.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:34.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:35.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.73
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.42
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.24
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.63
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.73
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.78
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.00
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:38.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.08
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.43
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17453.63
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.72
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.40
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.09
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.20
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.24
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.42
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.18
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.84
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.68
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.15
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.74
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.73
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.94
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.22
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.61
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.86
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.19
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  562.46
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.88
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.86
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.99
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.66
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4920.28
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.10
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.71
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.65
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.67
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.27
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.16
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.57
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.04
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.43
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:23.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.48
p-value of test                       :    0.07

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 6.32e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.36
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.78
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:05.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.39
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:05.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9908.00
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10179.49
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:44.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5126.11
p-value of test                       :  9.2e-3

-----------------------------------------------
CPU time used                    :  00:01:48.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4824.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.80
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4271.59
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11803.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11681.64
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.13
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  7999985694

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.80
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000171028

Normal statistic for number of bits   :    1.35
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -2.02
p-value of test                       :    0.98

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:47.22

 All tests were passed




Server wird beendet - Lösche Semaphor 19234845.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1484
p-value of test                       :  7.2e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334604
  j =  1                              :        599997032
  j =  2                              :             1484
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5493
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:58.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:43.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:58.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4234
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:58.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:06.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:06.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:56.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7488
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:04:00.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:14.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:42.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.69
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.84
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.40
p-value of test                       :    0.9943

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.77
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.83
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.12
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.70
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.95
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.43
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:44.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.62
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:02.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7067.68
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:42.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.06
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.28
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:01.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.91
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.18
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:30.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5022.11
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:57.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45826
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869826
  j =  1                              :        399908354
  j =  2                              :            45814
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46085
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870085
  j =  1                              :        399907836
  j =  2                              :            46073
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:27.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:17.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:45.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:59.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:56.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:35.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 6.44e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 6.93e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:33.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:35.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.22
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:49.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.92
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.13
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:48.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.49
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.25
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.71
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:38.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.14
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.86
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17616.92
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.95
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.49
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.41
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.04
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.35
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.10
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.86
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.23
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   44.74
p-value of test                       :  6.3e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.06
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.58
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.21
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.42
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.08
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.76
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.98
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.51
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.34
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.29
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.30
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.47
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.78
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.50
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.05
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.89
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.37
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.43
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5058.07
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  315.05
p-value of test                       :    0.9919


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.25
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.50
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:24.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.17
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :    1.61
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:23.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.60
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.45
p-value of test                       :    0.9928

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.75e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 8.41e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.41e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 4.72e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.54
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.90
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.21
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:05.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.30
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    3.67
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9714.89
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9884.87
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.041
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:44.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.33
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:48.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  2.0e-3

Anderson-Darling statistic = A2       :    4.05
p-value of test                       :  8.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5155.46
p-value of test                       :  4.1e-3

-----------------------------------------------
CPU time used                    :  00:01:50.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.34
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4266.02
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11929.18
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12061.87
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:29.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.11
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999897326

Normal statistic for number of bits   :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.31
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999753863

Normal statistic for number of bits   :   -1.95
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.63
p-value of test                       :    0.95

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:16.15
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           7.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 20217885.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:19.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:18.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:16.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5512
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:42.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:34.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:55.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:55.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:01.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:01.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:53.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:59.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.68
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    3.59
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:52.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.91
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    3.15
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     342
p-value of test                       :  9.3e-3

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    3.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:08.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:34.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.17
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.35
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.63
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.61
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:09.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.42
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.89
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.82
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.30
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.83
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:46.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1469.59
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:03.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6936.10
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:45.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.95
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.99
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:01.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.15
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.77
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:34.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5088.81
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:15.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:14.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46004
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870004
  j =  1                              :        399907999
  j =  2                              :            45990
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45438
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869438
  j =  1                              :        399909126
  j =  2                              :            45434
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:14.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:29.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:18.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:45.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:59.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:52.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:34.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.07e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:22.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:36.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:38.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.56
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.20
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.80
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.87
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:49.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.80
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.17
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.08
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:40.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.98
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.068
p-value of test                       :    0.9954

-----------------------------------------------
CPU time used                    :  00:01:31.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:32.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.99
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17381.73
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.04
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.90
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.89
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.97
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.63
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.34
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.18
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.91
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.22
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.08
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.53
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.48
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.35
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.93
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:46.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.10
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.71
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.84
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.66
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.52
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.11
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.53
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4978.88
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.30
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.85
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.76
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.07
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.61
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.04
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.27
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.66
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:26.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.10
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:18.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.28

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.93e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :  6.3e-3

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.85e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 9.15e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.21
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.24
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.46
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:10.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.01
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:10.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10086.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9937.35
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:47.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4723.40
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:48.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4788.79
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:50.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4065.96
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11697.61
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12013.51
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:29.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.99
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999892316

Normal statistic for number of bits   :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.31
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  7999967295

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    1.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:29.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.0e-3

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    1.89
p-value of test                       :    0.03

Sample variance                       :    0.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:17:47.34

 All tests were passed




Server wird beendet - Lösche Semaphor 1114142.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5416
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:42.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:37.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:35.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:54.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:54.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:01.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:01.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:52.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:59.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:47.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    3.07
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.16
p-value of test                       :    0.9973

Stat. AD after spacings (mNP2-S)      :    2.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:13.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.85
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:38.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.63
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.52
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.09
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   40.28
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.31
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:09.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.59
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.26
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.90
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.14
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.90
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:50.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1433.53
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:03.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7165.85
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.04
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.97e-3
p-value of test                       :    0.9937

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   91.12
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:03:01.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.65
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.94
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:34.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5126.35
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:21.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45706
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869706
  j =  1                              :        399908591
  j =  2                              :            45700
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45646
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869646
  j =  1                              :        399908710
  j =  2                              :            45642
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:31.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 5.05e-3
p-value of test                       :    0.9942

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:18.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:45.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:00.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :  3.0e-3

Anderson-Darling statistic = A2       :    4.63
p-value of test                       :  4.4e-3

-----------------------------------------------
CPU time used                    :  00:01:54.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 9.37e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:35.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:35.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.78
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:48.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.80
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.36
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.54
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.90
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.22
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:43.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.45
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 6.79e-3
p-value of test                       :    0.9928

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.15
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.89
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:30.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.02
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:30.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:10.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.28
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17246.93
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:55.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.49
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.45
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.04
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.53
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.19
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.64
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.69
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.82
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.24
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.73
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.93
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.12
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.38
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.67
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.63
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.21
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.38
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.27
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  102.45
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.21
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.13
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5026.98
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.52
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.11
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.81
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.93
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.30
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.92
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.94
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.15
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:26.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.88
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :   0.057
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:21.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    2.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.57e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 4.38e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.84e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.16
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.63
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.54
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:10.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.73
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:10.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10027.70
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9874.93
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.17
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:04:04.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.60
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:48.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4720.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:49.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.32
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4199.64
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12026.84
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11916.90
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:29.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.52
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000010183

Normal statistic for number of bits   :   0.081
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.57
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000101590

Normal statistic for number of bits   :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   0.072
p-value of test                       :    0.47

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:28.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.72
p-value of test                       :    0.96

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:46.70

 All tests were passed




Server wird beendet - Lösche Semaphor 1409054.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5414
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:46.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:38.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:36.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:54.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:01.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:02.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:53.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:58.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     849
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:47.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    2.06
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:13.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.01
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    4.42
p-value of test                       :  5.5e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     124
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:44.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.55
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.45
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.94
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:11.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.03
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.96
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  200.85
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  489.23
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1471.56
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:02.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7083.38
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:44.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.91
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.23
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:59.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.93
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.05
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:35.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4918.39
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:21.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45582
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869582
  j =  1                              :        399908841
  j =  2                              :            45572
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45755
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869755
  j =  1                              :        399908495
  j =  2                              :            45745
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:30.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:18.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:45.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:00.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:55.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:32.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 4.23e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.57e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 5.76e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:36.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.54
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:49.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.81
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.19
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.53
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.24
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.88
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.88
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:45.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.92
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.61
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.66
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.68
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:30.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.88
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:37.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17367.25
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.44
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.22
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.53
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.72
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.65
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   17.18
p-value of test                       :    0.9967


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.76
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.58
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    7.80
p-value of test                       :    0.9993    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.58
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.35
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.12
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.75
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.63
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.80
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.59
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.96
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.65
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.69
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.78
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.83
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.57
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.43
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.68
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.52
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.92
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4901.72
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.10
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.33
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.30
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:25.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.61
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:24.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 7.08e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.85e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.40
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.18
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.80
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:08.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.71
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:09.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9833.98
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10105.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.049
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -3.05
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:04:01.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.8e-3

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5015.20
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:49.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:50.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4372.84
p-value of test                       :  2.8e-3

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.71
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11666.07
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11897.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:31.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.04
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999926852

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.49
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000030976

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:35.77
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 75  RandomWalk1 R (L=50, r=25)      0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 2588702.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5382
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:48.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:38.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7177
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:37.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:54.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:54.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:01.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:01.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:53.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:58.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:45.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:12.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.05
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:40.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.63
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.23
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.78
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.99
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.66
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:11.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.93
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.74
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.12
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  199.13
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.56
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:43.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1429.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:03.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7126.28
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:44.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.19
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:01.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.12
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:35.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4818.72
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:16.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46158
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870158
  j =  1                              :        399907686
  j =  2                              :            46154
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45661
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869661
  j =  1                              :        399908681
  j =  2                              :            45655
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:28.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:19.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:46.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:00.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:55.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:33.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.39e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.75e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:36.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:35.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:48.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.95
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.53
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.26
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.98
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.49
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:42.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.55
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.22
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.22
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.63
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.81
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17556.78
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.36
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.82
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.27
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.32
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.05
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.46
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.45
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.81
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.41
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.83
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.37
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.56
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.02
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.32
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.07
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.76
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.41
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.65
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.90
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.50
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.68
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.83
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.73
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.29
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.41
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.75
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.87
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5122.76
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.07
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.44
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.45
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :   -1.17
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:23.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.68
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :   -0.86
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:22.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :  -0.082
p-value of test                       :    0.53

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.80e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 6.26e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.65e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.04
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.57
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.64
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:08.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:08.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9935.15
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9935.84
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:52.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4727.77
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4962.44
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:50.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.46
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4025.80
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11729.26
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:29.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11540.62
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:30.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.45
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000225712

Normal statistic for number of bits   :    1.78
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.64
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000043018

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.66

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.22
p-value of test                       :    0.99

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:29.01

 All tests were passed




Server wird beendet - Lösche Semaphor 3637278.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:51.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1263
p-value of test                       :    0.9971

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334383
  j =  1                              :        599997474
  j =  2                              :             1263
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5417
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:49.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:39.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:37.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4447
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:55.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:55.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:02.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:04.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:53.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:59.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.53
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     865
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:45.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.47
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    2.85
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:14.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:40.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.97
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.99
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.44
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.40
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.28
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.99
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.07
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.24
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.13
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:45.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1413.65
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:00.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6979.09
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.03
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   40.74
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:01.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.77
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.54
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:34.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4781.92
p-value of test                       :    0.9953


-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:03.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45885
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869885
  j =  1                              :        399908236
  j =  2                              :            45873
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45468
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869468
  j =  1                              :        399909067
  j =  2                              :            45462
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:29.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:18.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:46.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:54.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:34.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.44e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.23e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:34.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:35.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.61
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:48.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.64
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.81
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.02
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:48.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.02
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   59.56
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.74
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:38.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.85
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.40
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.02
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17593.06
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.81
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.45
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.01
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.02
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.79
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.35
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.76
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.56
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.21
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.86
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.24
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.55
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.89
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.42
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.88
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.63
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.31
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.93
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.22
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.76
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.72
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.44
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4745.44
p-value of test                       :    0.9951


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.77
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.42
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.63
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.91
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5052.14
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.23
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.83
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.09
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:26.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.52
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :    1.91
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:25.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.32e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.41
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.75
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.58
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:06.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.56
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:06.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.95
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10198.35
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:46.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4962.18
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4734.24
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:49.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4220.25
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.07
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11830.53
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11904.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.82
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999988772

Normal statistic for number of bits   :  -0.089
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.07
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999981092

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:30.45

 All tests were passed




Server wird beendet - Lösche Semaphor 4653086.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:51.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5438
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:51.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4458
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:39.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:38.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:56.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:58.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:05.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:05.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:56.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7469
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:01.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    2.03
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     859
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.89
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:48.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.16
p-value of test                       :    0.9979

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:15.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.14
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:40.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.91
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.66
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.91
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.06
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.49
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.72
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:49.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1470.77
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:05.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7218.40
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:54.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.59
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.95
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:11.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.65
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:36.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5090.44
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:19.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46120
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870120
  j =  1                              :        399907765
  j =  2                              :            46110
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46208
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870208
  j =  1                              :        399907589
  j =  2                              :            46198
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:31.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:18.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:50.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:05.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:35.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.37e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 5.00e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.64
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 7.31e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:47.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.66
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.69
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.42
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.67
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.55
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.52
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:47.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.29
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.49
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.03
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:28.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.64
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  102.52
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17724.79
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.44
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.96
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.41
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.74
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.56
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.54
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.11
p-value of test                       :    0.9918


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.45
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.69
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.06
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.00
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.26
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.27
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.34
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.21
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.71
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.44
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.38
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.52
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.54
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:43.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.50
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.16
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4960.91
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.76
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.73
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.37
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.69
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.00
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.13
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.47
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.30
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:25.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.12
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:24.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 2.52e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:47.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.36e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.66
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:29.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.44
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.08
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:06.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.16
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:07.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9832.72
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10024.26
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:04:26.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5097.57
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.05
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4029.30
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3922.86
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11937.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:32.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11854.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:33.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.34
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999845975

Normal statistic for number of bits   :   -1.22
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.92
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000004351

Normal statistic for number of bits   :   0.034
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    2.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   0.041
p-value of test                       :    0.48

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:55.46

 All tests were passed




Server wird beendet - Lösche Semaphor 5537822.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5383
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:55.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:42.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:58.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:58.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:07.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:09.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7450
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:05.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:07.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:15.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     128
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.80
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:45.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.11
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.78
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.26
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.55
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:10.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.96
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.42
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.39
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.55
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  381.96
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:53.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1437.77
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:01.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7207.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:52.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.87
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.19
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:18.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.73
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.08
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:51.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5090.30
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:31.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:28.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45692
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869692
  j =  1                              :        399908617
  j =  2                              :            45690
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45996
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869996
  j =  1                              :        399908011
  j =  2                              :            45990
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9906

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:31.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:19.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:49.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:06.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:57.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:38.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.74e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 2.50e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:49.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.72
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.39
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.16
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.45
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.59
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:49.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.72
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.98
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   14.36
p-value of test                       :  7.6e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.00
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17281.26
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.82
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.94
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.10
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.15
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.82
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.91
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.70
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.35
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.83
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.50
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.73
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.26
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.10
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.49
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.69
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.66
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.84
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.74
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.90
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.02
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.85
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.53
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.54
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.19
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.24
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.76
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5144.91
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.00
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.68
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.29
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:24.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.37
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:25.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.29e-3
p-value of test                       :    0.9977

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.3e-3

Anderson-Darling statistic = A2       :    5.13
p-value of test                       :  2.6e-3

Tests on the sum of all N observations
Standardized normal statistic         :    3.17
p-value of test                       :  7.7e-4    *****

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.15e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.13e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 6.75e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9957

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.45
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.36
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.16
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:06.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.28
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:08.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9990.42
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.78e-3
p-value of test                       :    0.9928

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10329.88
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:04:27.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4776.57
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5020.76
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:57.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3886.58
p-value of test                       :    0.9951

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4265.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11817.64
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:35.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12070.18
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:35.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.83
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999825449

Normal statistic for number of bits   :   -1.38
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.93
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999959873

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :  -0.085
p-value of test                       :    0.53

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:11:26.50
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 71  MatrixRank, L=5000              7.6e-4
 82  LempelZiv, r = 0                7.7e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 6914078.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:40.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5407
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:53.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:40.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:56.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:57.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:04.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:05.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:55.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:00.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.66
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     268
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:15.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.83
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:42.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.10
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.84
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.00
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.94
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.90
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.83
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:43.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1500.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:01.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7087.06
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.52
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:00.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.11
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.21
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:32.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5128.98
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:02.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45786
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869786
  j =  1                              :        399908431
  j =  2                              :            45780
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46411
p-value of test                       :  6.7e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870411
  j =  1                              :        399907180
  j =  2                              :            46407
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:28.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:18.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:46.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:00.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:01:35.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.57e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.50e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.56e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:35.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:35.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.44
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.91
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.37
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.40
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.07
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.75
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  151.42
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17227.29
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.98
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.97
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.86
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.70
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.46
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.80
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.49
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.20
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.23
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.68
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.37
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.99
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.60
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.54
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.55
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.56
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.49
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.52
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.12
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.40
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.33
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.23
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.10
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.98
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.71
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.60
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5084.31
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.64
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.82
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.66
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:23.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.11
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  :    1.94
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:25.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 8.03e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.38e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.06
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.49
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.56
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:08.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.68
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:07.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9961.54
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10006.53
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.061
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:55.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:44.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4867.85
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 3.91e-3
p-value of test                       :    0.9960

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4750.94
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:50.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4141.39
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4090.48
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11747.93
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11937.86
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.99
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000032281

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.42
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999891062

Normal statistic for number of bits   :   -0.86
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.75
p-value of test                       :    0.04

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:07.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 52  SampleProd, t = 24              0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8028190.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5433
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:54.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:40.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:57.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:06.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:05.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:55.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:04:02.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     635
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:14.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    2.70
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:42.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.50
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.45
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.51
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.98
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.72
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.05
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.80
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:43.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1410.61
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:02.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7091.73
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:42.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.14
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:01.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.81
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.94
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:33.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5057.59
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:11.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45963
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869963
  j =  1                              :        399908077
  j =  2                              :            45957
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45609
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869609
  j =  1                              :        399908786
  j =  2                              :            45601
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:27.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:18.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:45.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:59.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:55.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:35.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.10e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 4.13e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.015
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:34.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:34.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.79
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.29
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.11
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.04
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.61
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:37.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.71
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.46
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.30
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.94
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17384.67
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.55
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.95
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   10.68
p-value of test                       :    0.9944


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    8.03
p-value of test                       :    0.9991    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.32
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.86
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.55
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.66
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.78
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.45
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.56
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.09
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.17
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.59
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.44
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.67
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.38
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.58
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.59
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.34
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.37
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.99
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4839.64
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.21
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.80
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.02
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.62
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.67
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.18
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.27
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.81
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:22.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.22
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:22.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 9.72e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   20.23
p-value of test                       :  9.5e-3

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.69
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.19
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:07.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.63
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:09.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9832.48
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9902.29
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:42.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.02
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:49.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4770.33
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:50.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.50
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.01
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11980.82
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11964.52
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.49
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000004261

Normal statistic for number of bits   :   0.034
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.09
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999940634

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.66
p-value of test                       :    0.05

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:18.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 R (L=50, r=0)       0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9076766.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  6.8e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5359
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:54.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:40.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:40.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4457
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:57.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7129
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:04.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:05.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:55.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:00.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.9904

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.76
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.22
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    2.49
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     349
p-value of test                       :  3.1e-3

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:11.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:41.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.93
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.22
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.60
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.87
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.70
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.83
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.13
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.62
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.36
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:44.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.66
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:02.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7223.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:42.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.42
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:02.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.93
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.13
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:33.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4925.99
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:53.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45909
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869909
  j =  1                              :        399908182
  j =  2                              :            45909
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45890
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869890
  j =  1                              :        399908220
  j =  2                              :            45890
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  9.5e-3

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:27.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.64
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  5.8e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:18.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:45.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:00.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:36.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.81e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 9.61e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 4.78e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:21.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:33.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:35.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.49
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:49.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.56
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.76
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.43
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.23
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.46
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:39.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.99
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.16
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.77
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:37.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17410.81
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.93
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.80
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.07
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.26
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.92
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.66
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.31
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.73
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.32
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.32
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.05
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.19
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.57
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.61
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.67
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  107.83
p-value of test                       :    0.9923


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.83
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.98
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.45
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.84
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.36
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  325.11
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5026.63
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.88
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.65
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  456.64
p-value of test                       :  6.3e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.77
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5036.93
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.25
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.67
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.80
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :   -1.35
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:22.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.28
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:23.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    2.46
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 5.21e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 9.26e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.62
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.70
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.21
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:04.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.92
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:08.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9935.47
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9971.39
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.09
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:45.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4952.20
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.06
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:49.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.21
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4038.31
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11704.41
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11817.99
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:28.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.29
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999926210

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.38
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000115309

Normal statistic for number of bits   :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   0.051
p-value of test                       :    0.48

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.90

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:31.28
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  2  SerialOver, r = 22              6.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 9928734.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:49.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.83

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5397
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:04:00.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:43.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:42.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:58.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4222
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:00.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:10.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:09.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7055
p-value of test                       :    0.9990


-----------------------------------------------
CPU time used                    :  00:04:00.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:03.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    2.74
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     963
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.68
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.66
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.91
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:15.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    2.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:43.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.95
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.53
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.07
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.33
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.38
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.26
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.62
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.96
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.59
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  352.57
p-value of test                       :    0.9983

-----------------------------------------------
CPU time used                    :  00:01:48.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.84
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:02.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7048.40
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:50.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.99
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.34
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:07.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.00
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.24
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4962.97
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:12.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:56.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45942
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869942
  j =  1                              :        399908118
  j =  2                              :            45938
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46345
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870345
  j =  1                              :        399907314
  j =  2                              :            46337
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:30.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :  2.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    3.27
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:18.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:46.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:02.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:37.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.43e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.61e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:37.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:38.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.90
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.97
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.78
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.01
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.63
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.81
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 7.42e-3
p-value of test                       :    0.9921

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.26
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.66
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:34.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.67
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17376.24
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.55
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.19
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.53
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.70
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.02
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.60
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.74
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.26
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.29
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.63
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.78
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.51
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.72
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.58
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.42
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.27
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.60
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.25
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.11
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.64
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.48
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5062.57
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.25
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.23
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.76
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.89
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5064.03
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  323.55
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.45
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.50
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:23.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.53
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :    0.11
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:22.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 6.43e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.49e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 8.27e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.93
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.44
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.43
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:05.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.49
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:07.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10241.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9824.88
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.055
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:04:15.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4769.88
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:52.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.72
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:54.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4170.89
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.77
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11743.91
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:31.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11741.29
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:31.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.88
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999995948

Normal statistic for number of bits   :  -0.032
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.25
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000133006

Normal statistic for number of bits   :    1.05
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.66

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:11.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:53.45

 All tests were passed




Server wird beendet - Lösche Semaphor 10944542.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:48.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:27.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5490
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:55.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:42.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:57.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:58.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7179
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:06.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:07.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:56.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:04:00.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9943

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    3.78
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:12.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    2.03
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:42.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.82
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.76
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.50
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.05
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.04
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.72
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   86.92
p-value of test                       :  3.0e-3

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.23
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.29
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1505.38
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:04.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6973.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:46.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    4.21
p-value of test                       :  7.2e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   33.32
p-value of test                       :    0.9980

-----------------------------------------------
CPU time used                    :  00:03:02.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.56
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  146.95
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:32.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5060.89
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:58.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46025
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870025
  j =  1                              :        399907954
  j =  2                              :            46017
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45924
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869924
  j =  1                              :        399908160
  j =  2                              :            45908
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:27.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:18.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 6.26e-3
p-value of test                       :    0.9930

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:45.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:35.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.96e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:38.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:35.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.01
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.69
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.74
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.65
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.27
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.54
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.95
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.31e-3
p-value of test                       :    0.9966

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.27
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   68.41
p-value of test                       :  3.4e-3

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.36
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.39
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.91
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.27
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17560.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.73
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.37
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.38
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.20
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.44
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.22
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.58
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.89
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.61
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.73
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.89
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.48
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.43
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.27
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.11
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.65
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.70
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.62
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.57
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.99
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.18
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.04
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4927.74
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  299.77
p-value of test                       :    0.9988


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.96
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.58
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.64
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4945.94
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.70
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.01
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.29
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:22.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.27
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :    0.51
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:22.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :  -0.092
p-value of test                       :    0.54

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.33e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 7.03e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 3.18e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.51
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.29
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.14
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:05.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.67
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:07.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.77
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9934.25
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:40.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4849.16
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:48.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.46
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:50.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4225.25
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3976.18
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11727.21
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:29.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11842.33
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:30.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.17
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  8000108304

Normal statistic for number of bits   :    0.86
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.23
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999930773

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.57
p-value of test                       :  6.6e-4    *****

Kolmogorov-Smirnov- statistic = D-    : 6.42e-3
p-value of test                       :    0.9932

Anderson-Darling statistic = A2       :    7.39
p-value of test                       :  2.4e-4    *****

Tests on the sum of all N observations
Standardized normal statistic         :   -3.71
p-value of test                       :    0.9999    *****

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:00.57
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 103  AutoCor, d=1, r=0               0.9999 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 12091422.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5413
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:58.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:41.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:57.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4480
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:58.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7179
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:06.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:06.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:56.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:04:01.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.73
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    2.54
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:51.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.94
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    6.55
p-value of test                       :  5.5e-4    *****

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     273
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    2.41
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:19.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:47.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.68
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.09
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.04
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.74
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.89
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.30
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.15
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.07
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.74
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:44.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.61
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:02.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6821.06
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:42.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.86
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:03.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.23
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   84.85
p-value of test                       :    0.9924


-----------------------------------------------
CPU time used                    :  00:01:33.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4933.91
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:55.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45846
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869846
  j =  1                              :        399908310
  j =  2                              :            45842
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45929
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869929
  j =  1                              :        399908146
  j =  2                              :            45921
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:27.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:19.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:46.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:01.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:55.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:35.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 7.98e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.28e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      : -6.08e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:21.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:21.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:36.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.049
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:37.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.42
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.07
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:51.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.85
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.74
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.03
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.62
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.55
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.36
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.41
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.25
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.41
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.44
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.44
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17016.31
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.18
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.53
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.71
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.60
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.17
p-value of test                       :    0.9972


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.96
p-value of test                       :    0.9913


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.08
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.16
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.36
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.73
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.70
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.92
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  452.99
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.67
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.20
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  102.72
p-value of test                       :    0.9974


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.29
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.39
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.33
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.54
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.89
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.09
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4811.93
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.83
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.83
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.12
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.64
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5164.66
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.59
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.02
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:36.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.43
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :    1.45
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:24.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.25
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:22.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.68
p-value of test                       :    0.05

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.17e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 9.35e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.16
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.27
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.39
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:05.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.18
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:07.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9813.69
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10123.76
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:42.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5043.43
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9920

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.41
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:49.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.38
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3967.13
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11708.28
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12167.91
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:29.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.65
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000006904

Normal statistic for number of bits   :   0.055
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.58
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000013501

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:24.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs mNP2, t = 5          5.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 13139998.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:50.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5288
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:04:00.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:43.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:44.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:01.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:02.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:13.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:13.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:07.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:12.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.57
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:52.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:17.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:49.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.08
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.52
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.00
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.03
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:29.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1506.00
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:07.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7002.47
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.76
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:19.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.01
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.18
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:40.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5240.87
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:59.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46038
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870038
  j =  1                              :        399907926
  j =  2                              :            46034
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45822
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869822
  j =  1                              :        399908359
  j =  2                              :            45816
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:31.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:19.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 5.40e-3
p-value of test                       :    0.9940

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :  2.9e-3

Anderson-Darling statistic = A2       :    4.67
p-value of test                       :  4.3e-3


-----------------------------------------------
CPU time used                    :  00:02:07.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  6.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.40
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:37.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.44e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.22e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.05e-5
p-value of test                       :    0.9956

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:24.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.04
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:45.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:46.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.32
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.93
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.43
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.98
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.28
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.60
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:51.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.00e-3
p-value of test                       :    0.9902

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.32
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.58
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.40
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.54
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17326.32
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.41
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.15
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.91
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.70
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.71
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.02
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.13
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.28
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.14
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.81
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:37.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.66
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.75
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.92
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.48
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.84
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.29
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.86
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.50
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.19
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  100.74
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:43.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.96
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.34
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5058.00
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.03
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.72
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.22
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.49
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5095.25
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.88
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  155.87
p-value of test                       :    0.9909


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.09
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:26.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.15
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:26.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.4e-3

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.15
p-value of test                       :    0.02

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.79e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 8.64e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.02
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.64
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.92
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:06.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.41
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:06.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9824.42
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10100.02
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:04:27.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.63
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4649.33
p-value of test                       :    0.9932

-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5061.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:59.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4175.30
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4208.63
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11893.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:35.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11957.12
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:36.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.75
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000161173

Normal statistic for number of bits   :    1.27
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.14
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000038410

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         : -6.24e-3
p-value of test                       :    0.50

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:15.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:31.45

 All tests were passed




Server wird beendet - Lösche Semaphor 14057502.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:50.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:56.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4453
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:42.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4472
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:57.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:06.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:06.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7168
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:56.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:04:02.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    2.66
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:50.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:16.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.61
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.57
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     337
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:12.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    3.61
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     177
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.83
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:41.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.81
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.81
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.77
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   84.51
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:01:10.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.71
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.85
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.79
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.48
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.14
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:46.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.39
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:02.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7173.97
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.23
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:02.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.52
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.42
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:32.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4994.45
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:58.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45783
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869783
  j =  1                              :        399908436
  j =  2                              :            45779
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45815
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869815
  j =  1                              :        399908373
  j =  2                              :            45809
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:26.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:18.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:46.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:59.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:59.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:39.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:37.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:33.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.58
p-value of test                       :    0.9914

-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.52
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.50
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.42
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.42
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:39.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.70
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.05
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.11
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.02
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17557.11
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.84
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.71
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.62
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.12
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.39
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.70
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.14
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.13
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.93
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.73
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.14
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.21
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.80
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  172.11
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.15
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.94
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.92
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  423.09
p-value of test                       :    0.9946


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.54
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.79
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.40
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.60
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.80
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.18
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.56
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.28
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.60
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.86
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.63
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.10
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.58
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:22.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.25
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.70e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 9.25e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 9.73e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.87
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.51
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 8.56e-3
p-value of test                       :    0.9908

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.31
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:07.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.27
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:08.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10254.45
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9749.64
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : -2.96e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:39.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.37
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4928.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:49.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.08
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.35
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11974.04
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12047.36
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.56
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000124777

Normal statistic for number of bits   :    0.99
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.68
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000162943

Normal statistic for number of bits   :    1.29
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.43

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:34.04

 All tests were passed




Server wird beendet - Lösche Semaphor 15237150.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5345
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:56.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:41.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4437
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4218
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:57.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7459
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:06.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7500
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:06.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:56.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:04:01.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    3.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:50.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    3.99
p-value of test                       :  8.8e-3

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    3.18
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     266
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:19.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.76
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.99
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:47.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.74
p-value of test                       :    0.9980

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.56
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.57
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.35
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.43
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.67
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.83
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  469.68
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:44.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1413.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:03.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7065.31
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:44.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.81
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:02.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.27
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.06
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:31.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5221.46
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:11.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45909
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869909
  j =  1                              :        399908185
  j =  2                              :            45903
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46093
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870093
  j =  1                              :        399907816
  j =  2                              :            46089
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:28.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:19.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.40
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  4.9e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:46.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:59.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:55.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :  1.2e-3

Anderson-Darling statistic = A2       :    3.59
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 9.04e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.96e-6
p-value of test                       :    0.9975

Kolmogorov-Smirnov- statistic = D-    : 2.52e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:21.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:38.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:35.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.18
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.70
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.71
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:49.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.18
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.65
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.39
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:46.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.08
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.67
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.45
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17414.38
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.98
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.25
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.31
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.64
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.28
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.55
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.40
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.18
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.93
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.63
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  197.90
p-value of test                       :  2.8e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.09
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  593.20
p-value of test                       :  2.5e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.96
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.78
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.10
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.90
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.86
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.70
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.58
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.98
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.71
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4717.37
p-value of test                       :    0.9980


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.71
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.83
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.81
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.73
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4912.09
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.53
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.63
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.91
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :    1.16
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:22.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.06
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:22.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.96
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.38

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.65e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.99
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.70
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:05.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.78
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:05.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10042.79
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10086.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:46.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4916.59
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:48.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.38
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:49.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4133.23
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3962.18
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11532.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11525.10
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:28.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.66
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999856436

Normal statistic for number of bits   :   -1.13
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.86
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  7999997220

Normal statistic for number of bits   :  -0.022
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.40

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    2.02
p-value of test                       :    0.02

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.064
p-value of test                       :    0.53

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:14.55

 All tests were passed




Server wird beendet - Lösche Semaphor 16252958.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:50.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5318
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:58.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:43.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:45.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:01.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:01.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:12.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:11.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:09.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:07.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:51.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.81
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     325
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9946

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:17.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.04
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:50.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.20
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.91
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.79
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.84
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.41
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.01
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  202.20
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:28.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.57
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:54.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.29
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:06.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7023.07
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:56.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.74
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.82
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:16.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.28
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.86
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:39.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4894.10
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:01.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45753
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869753
  j =  1                              :        399908500
  j =  2                              :            45741
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45946
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869946
  j =  1                              :        399908109
  j =  2                              :            45944
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:31.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:20.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:50.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:07.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:56.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:37.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.023
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:45.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:46.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.34
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:51.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   61.36
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.78
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.84
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.84
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:49.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.29
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.76
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.35
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17265.35
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.45
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.87
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.99
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.85
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    4.37
p-value of test                       :    0.9991    *****


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.99
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.74
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.59
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.45
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.68
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.95
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.02
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.76
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.11
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.97
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.76
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.68
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  435.43
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.66
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.45
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.19
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.90
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5029.25
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.31
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.46
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.46
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.52
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4922.08
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.95
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:36.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.11
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :   -0.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:23.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.69
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.85
p-value of test                       :    0.97

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 5.24e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.42
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.90
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.26
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:08.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.25
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:07.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9843.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10232.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      : -1.70e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:04:18.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:55.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4801.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:58.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4035.49
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4049.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11951.79
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:34.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11678.69
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:34.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.09
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999901064

Normal statistic for number of bits   :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.61
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000032776

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.50
p-value of test                       :    0.93

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:39.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 C (L=50, r=0)       0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 17268766.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:48.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1465
p-value of test                       :  3.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334585
  j =  1                              :        599997070
  j =  2                              :             1465
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5450
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:55.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:42.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:58.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:58.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:07.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:04.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:55.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:00.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.29
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    4.27
p-value of test                       :  6.4e-3

-----------------------------------------------
CPU time used                    :  00:01:51.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    3.00
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     261
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:20.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:48.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.77
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.65
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:11.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.08
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.07
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.45
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  474.97
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:44.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.26
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:03.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7075.35
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:43.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.09
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.03
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:02.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.51
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.08
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:34.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4927.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:00.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45878
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869878
  j =  1                              :        399908246
  j =  2                              :            45874
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45502
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869502
  j =  1                              :        399909000
  j =  2                              :            45494
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:27.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:18.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:45.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 6.23e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.09e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:36.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:37.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.23
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.68
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.23
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.66
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.21
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.24
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:45.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   62.04
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.05
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.49
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.29e-3
p-value of test                       :    0.9922

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.03
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17155.83
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.95
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.34
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.08
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.49
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.93
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.98
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.97
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.42
p-value of test                       :    0.9907


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.42
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.32
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:37.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.01
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.34
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.96
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.75
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.65
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.76
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.12
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.24
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.50
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.57
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.89
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.21
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4853.96
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.87
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.91
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.97
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.13
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4993.18
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.17
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.58
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.01
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:25.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.16
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -1.10
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:26.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 8.22e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.22
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.47
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.44
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:07.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.91
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:06.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10205.73
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9915.07
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.045
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:55.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:48.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4813.25
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4956.57
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:50.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4203.15
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.92
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11771.39
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12029.15
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:29.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.68
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999985187

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.74
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999899156

Normal statistic for number of bits   :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:14.34

 All tests were passed




Server wird beendet - Lösche Semaphor 18415646.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5397
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:55.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:42.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:57.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:58.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:06.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7108
p-value of test                       :    0.9931


-----------------------------------------------
CPU time used                    :  00:03:06.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:56.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:01.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    2.51
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:51.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.51
p-value of test                       :  5.1e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    5.30
p-value of test                       :  2.1e-3

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.64
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:17.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:45.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.35
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.62
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.82
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.52
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.33
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.54
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.76
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.18
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:44.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1469.90
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:02.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7212.33
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:43.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.81
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.56
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:03.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.15
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.08
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:31.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5062.90
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:59.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46033
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870033
  j =  1                              :        399907935
  j =  2                              :            46031
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45763
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869763
  j =  1                              :        399908475
  j =  2                              :            45761
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:28.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:18.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:45.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 6.43e-3
p-value of test                       :    0.9927

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:59.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:55.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:34.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 5.00e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.92e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 9.67e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.087
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:32.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:34.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.63
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.70
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.94
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.40
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.00
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:43.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.50
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.84
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.19
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.49
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.36
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17157.26
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.72
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.43
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.67
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.78
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.69
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:37.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.77
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.87
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.30
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.22
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.22
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.98
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.45
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  572.32
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.09
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.64
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  188.80
p-value of test                       :  9.8e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.06
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.22
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.08
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.33
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.37
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.14
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4988.75
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.74
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  161.74
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.41
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.08
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5160.96
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  427.92
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.39
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.25
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:25.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.13
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:26.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   0.065
p-value of test                       :    0.47

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.73e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 8.24e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.23e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.25
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.41
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  240.63
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:07.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10137.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9791.20
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.051
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:47.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4743.81
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:48.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.23
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.77
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.57
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11758.60
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11739.49
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.16
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000117448

Normal statistic for number of bits   :    0.93
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.48
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  8000052636

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   0.066
p-value of test                       :    0.47

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:59.62

 All tests were passed




Server wird beendet - Lösche Semaphor 19431454.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5456
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:54.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:42.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:57.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:06.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:05.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:56.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:04:01.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.20
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.83
p-value of test                       :  3.5e-3

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    4.21
p-value of test                       :  6.9e-3

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.72
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     657
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:16.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     128
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:44.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.76
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.24
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.79
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.02
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.90
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.09
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.86
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  271.46
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.50
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:43.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1478.28
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:02.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7105.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:43.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.00
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.58
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:04.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.61
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.60
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:30.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5084.67
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:55.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45604
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869604
  j =  1                              :        399908795
  j =  2                              :            45598
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45542
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869542
  j =  1                              :        399908919
  j =  2                              :            45536
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:28.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:18.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:44.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 6.25e-3
p-value of test                       :    0.9930

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:00.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:35.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.61e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.049
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:35.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:34.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.05
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.83
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.53
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:49.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.57
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.10
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:44.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.41
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.26
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17273.17
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.62
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.97
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.29
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.23
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.21
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.02
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.00
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.63
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.23
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.60
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.09
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.16
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.06
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.33
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.08
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.69
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.95
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.19
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.83
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   50.63
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.53
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.24
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5147.58
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.96
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.28
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.03
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.67
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4880.71
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.28
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.16
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.57
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :   -1.85
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:25.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.13
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:25.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.15
p-value of test                       :    0.02

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.58e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.34e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 8.16e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.61
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.50
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.24
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:03.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.94
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:07.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9871.10
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10095.60
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:34.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.61
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:46.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4770.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:45.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.49
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3944.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11999.77
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11698.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.03
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  7999902051

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.50
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999965189

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    2.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 3.52e-3
p-value of test                       :    0.9964

Anderson-Darling statistic = A2       :    3.26
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.46
p-value of test                       :    0.9930

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:53.81

 All tests were passed




Server wird beendet - Lösche Semaphor 20414494.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:18.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:18.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1244
p-value of test                       :    0.9995    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334364
  j =  1                              :        599997512
  j =  2                              :             1244
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5477
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:42.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4237
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:36.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:34.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:55.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:55.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:02.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:02.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:54.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:04:00.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.42
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:52.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    2.44
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:16.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:13.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:33.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.67
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.71
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.29
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.03
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.54
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:10.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.69
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.02
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.74
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.37
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.21
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:47.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.19
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:02.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6989.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.86
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.97
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:00.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.25
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.13
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:33.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4908.52
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:08.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45530
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869530
  j =  1                              :        399908942
  j =  2                              :            45526
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45797
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869797
  j =  1                              :        399908412
  j =  2                              :            45785
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:16.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:30.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:17.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 2.78e-3
p-value of test                       :    0.9971

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  6.9e-3

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:44.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:58.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:53.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 6.05e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.69e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 5.66e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:32.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:34.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.07
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.88
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.02
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.08
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.39
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.42
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.41
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:44.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.40
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.12
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.48
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:31.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.77
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17234.80
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.09
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.36
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.49
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.28
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.08
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:39.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.61
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.22
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.16
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   37.66
p-value of test                       :  2.7e-3


-----------------------------------------------
CPU time used                    :  00:00:39.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.98
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.87
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.16
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.23
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.48
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:46.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.32
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.23
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  414.79
p-value of test                       :    0.9978


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.58
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.49
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.16
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4880.17
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.50
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.72
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.61
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.41
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.51
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.07
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  158.61
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.28
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :    0.99
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:33.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.52
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:26.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 8.28e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.59e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 8.25e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.84
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.23
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.02
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:10.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:11.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10058.87
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9899.30
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:44.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.53
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.0e-3

Anderson-Darling statistic = A2       :    3.45
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5115.72
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:48.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4033.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4014.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11824.07
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12039.02
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:28.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.10
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000003319

Normal statistic for number of bits   :   0.026
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.13
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000044215

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:29.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:17:52.43
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 1146911.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5401
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:42.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:36.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:34.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:54.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:54.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:01.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:01.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7491
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:53.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7183
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:59.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:45.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:15.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    3.41
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:42.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.11
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.33
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.77
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.71
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.17
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.97
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.64
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.23
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.32
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.13
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:50.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1414.19
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:04.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7037.35
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.61
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.06
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:07.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.74
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.40
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:35.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5049.03
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:01.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45947
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869947
  j =  1                              :        399908107
  j =  2                              :            45945
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46133
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870133
  j =  1                              :        399907737
  j =  2                              :            46127
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:13.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:33.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:18.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:44.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:59.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.47e-3
p-value of test                       :    0.9960

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:54.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:33.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 4.82e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:33.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:35.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.62
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:49.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.52
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.68
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.92
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.16
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.94
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.70
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.87
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.55
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:29.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.65
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:10.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.57
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17264.39
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.76
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.75
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   10.08
p-value of test                       :    0.9964


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.59
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.47
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.99
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.42
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.18
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.35
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.89
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.25
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.64
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.65
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.30
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.71
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.90
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.84
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.66
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.26
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.94
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.93
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.91
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4927.17
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  441.76
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.11
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  323.22
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.48
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4896.16
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.09
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.93
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.11
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :    1.66
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:26.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.58
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :    1.13
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:26.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.01
p-value of test                       :    0.98

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.42e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.44e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.31
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.41
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.07
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:09.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  159.73
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:11.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9950.00
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 2.07e-3
p-value of test                       :    0.9979

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9734.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:04:01.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4778.92
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:49.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4723.83
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4181.08
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4282.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11669.43
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11924.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.87
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999993395

Normal statistic for number of bits   :  -0.052
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.56
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999820757

Normal statistic for number of bits   :   -1.42
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:29.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:49.46

 All tests were passed




Server wird beendet - Lösche Semaphor 1212447.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:50.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5519
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:42.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:36.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:35.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:54.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4438
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:55.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7152
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:02.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:01.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:53.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:59.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:47.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     558
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    2.08
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:15.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:44.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.37
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.91
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.08
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.38
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.33
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.33
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   83.39
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.70
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  184.91
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.19
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1462.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:59.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7133.18
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:43.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.41
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.69
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:01.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.69
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.08
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:32.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5151.36
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:04.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45981
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869981
  j =  1                              :        399908042
  j =  2                              :            45973
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45864
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869864
  j =  1                              :        399908274
  j =  2                              :            45860
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :  5.1e-3

Anderson-Darling statistic = A2       :    5.90
p-value of test                       :  1.1e-3


-----------------------------------------------
CPU time used                    :  00:02:31.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:19.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:44.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:33.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 3.07e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:22.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:30.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.21
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.90
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.19
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.57
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:48.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.39
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.47
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:38.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.59
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.73
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.17
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.80
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.12
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.32
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 9.00e-3
p-value of test                       :    0.9902

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17687.73
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:55.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.79
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.13
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.64
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.49
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.16
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.58
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.40
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.53
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.23
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.21
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.76
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.17
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.15
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.74
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.89
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.25
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.76
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.53
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.39
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.45
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.41
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5121.74
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.94
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.95
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.14
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.30
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.33
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.86
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.07
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.01
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:24.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.55
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :   0.092
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:22.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.92
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.79e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 9.19e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:46.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 8.09e-4
p-value of test                       :    0.9941

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.55
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.76
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:06.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:08.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9939.18
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10230.22
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:45.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5139.63
p-value of test                       :  6.4e-3

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4760.11
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:50.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4034.17
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4038.66
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11732.58
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11999.92
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:29.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.01
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999936986

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.03
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  8000159847

Normal statistic for number of bits   :    1.26
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    2.30
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:48.80

 All tests were passed




Server wird beendet - Lösche Semaphor 2326559.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:39.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5382
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:48.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4244
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:37.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:36.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:54.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:02.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:02.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:54.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:58.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.13
p-value of test                       :  7.7e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     959
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    4.11
p-value of test                       :  7.7e-3

-----------------------------------------------
CPU time used                    :  00:01:45.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.77
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     561
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.81
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:10.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.77
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:43.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.39
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.83
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.14
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.37
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.58
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.93
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.77
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.20
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.54
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:49.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1384.30
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:06.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7205.84
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:49.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.95
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   41.72
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:09.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.66
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.11
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:37.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5106.65
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:59.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45990
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869990
  j =  1                              :        399908026
  j =  2                              :            45978
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45598
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869598
  j =  1                              :        399908806
  j =  2                              :            45594
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :  3.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.49
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:33.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    4.33
p-value of test                       :  6.1e-3


-----------------------------------------------
CPU time used                    :  00:02:19.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:46.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:01.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.38e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 4.00e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.84e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:22.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:42.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:44.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.87
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.05
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.16
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.50
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.15
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.39
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.88
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.91
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:29.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:29.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.42
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17410.89
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   58.30
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.61
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.39
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.33
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.98
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.63
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.04
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.10
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.14
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.43
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.82
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.18
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.39
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.64
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.88
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.41
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.79
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.67
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.93
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.94
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.66
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.66
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.87
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.41
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.26
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:36.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.86
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  322.03
p-value of test                       :    0.9905


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4734.86
p-value of test                       :    0.9965


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.43
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.30
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.97
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :    1.10
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:25.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.36
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:22.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 5.24e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.93e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.49
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.75
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.90
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:08.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.62
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:09.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9989.77
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9952.89
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:04:20.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4811.58
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:52.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4972.44
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:54.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.96
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.85
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11619.76
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:34.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11824.55
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:31.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.14
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999852686

Normal statistic for number of bits   :   -1.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   33.65
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  7999928856

Normal statistic for number of bits   :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:15.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:59.95

 All tests were passed




Server wird beendet - Lösche Semaphor 3342367.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:41.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:52.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5392
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:50.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:38.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:37.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4415
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:54.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:03.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7537
p-value of test                       :  5.6e-3


-----------------------------------------------
CPU time used                    :  00:03:03.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:53.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:58.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    2.57
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:13.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.75
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.70
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.89
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.97
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.12
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.85
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.25
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.16
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.47
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  382.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:44.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1438.32
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:00.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7174.32
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:43.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.31
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.46
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:02.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.93
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   91.45
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:34.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4965.31
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:13.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45484
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869484
  j =  1                              :        399909038
  j =  2                              :            45472
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46028
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870028
  j =  1                              :        399907946
  j =  2                              :            46024
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:28.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:18.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:45.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    3.70
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:01.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:55.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:15.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:33.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:35.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.14
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.47
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.92
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:40.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.79
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.84
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.96
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.64
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:37.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17370.84
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.88
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.61
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.55
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.63
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.25
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:39.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.12
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.95
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.81
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.77
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.96
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.74
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.29
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.53
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.07
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.98
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.93
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.69
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.19
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.20
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.00
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.34
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.97
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.01
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.66
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.81
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.11
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.03
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.45
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.37
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.50
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:25.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.23
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:23.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.23

Sample variance                       :    0.55
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.68e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 8.78e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.25e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.55
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.36
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.87
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:06.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.49
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:07.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9926.67
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9859.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.077
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:45.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.73
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:48.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.40
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.79
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4314.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11704.81
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11788.11
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:29.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.68
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999903029

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.56
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999880007

Normal statistic for number of bits   :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:53.17

 All tests were passed




Server wird beendet - Lösche Semaphor 4751391.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5294
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:50.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:38.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:38.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:55.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:56.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:03.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:02.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:52.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:58.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    2.10
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:49.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.27
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:15.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:43.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.70
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.46
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.15
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.64
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.93
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.61
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.32
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.43
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.38
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.16
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:43.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1491.68
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:01.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7107.99
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:43.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.20
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:02.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.26
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.42
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:34.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5079.61
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:59.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46081
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870081
  j =  1                              :        399907840
  j =  2                              :            46077
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45828
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869828
  j =  1                              :        399908346
  j =  2                              :            45824
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:28.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:17.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:44.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:58.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.28e-3
p-value of test                       :    0.9916

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:33.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 5.82e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.65e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:36.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.079
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:37.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.91
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.79
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.52
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:49.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.36
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.49
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.95
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   62.48
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.00
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.84
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.00
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17587.44
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.33
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.29
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.21
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.30
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.34
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.28
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.84
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.47
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.61
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.46
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.13
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.11
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  174.13
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.26
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.17
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.96
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.93
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.70
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.40
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.00
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.95
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4919.23
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.40
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.69
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.52
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.35
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.58
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.56
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.88
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:34.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.66
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:22.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.01
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :    1.70
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:25.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.14
p-value of test                       :    0.9984

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.08e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.08e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 5.38e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.28
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.55
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.40
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:08.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.68
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:09.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9907.43
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9930.10
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:49.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4968.29
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:49.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.94
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:51.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3948.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4238.76
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11737.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:29.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11649.94
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.57
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999959291

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.77
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000101473

Normal statistic for number of bits   :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:05.76

 All tests were passed




Server wird beendet - Lösche Semaphor 5701663.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:40.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5371
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:53.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:41.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:57.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:06.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:05.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:56.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:01.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:50.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.57
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    2.14
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     268
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    2.17
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:19.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:48.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   23.77
p-value of test                       :  1.3e-3

-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.26
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.00
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.00
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.01
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.59
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.35
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1470.37
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:04.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6977.95
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:47.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.57
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    3.96
p-value of test                       :  9.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.23
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.19
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:06.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.44
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.34
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4978.57
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:13.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:59.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45674
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869674
  j =  1                              :        399908658
  j =  2                              :            45662
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45689
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869689
  j =  1                              :        399908626
  j =  2                              :            45681
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:29.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:18.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:02.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:55.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:35.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 2.57e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 7.95e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:38.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:39.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.38
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:51.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.88
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.72
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.98
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.60
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.68
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.66
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:45.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.10e-3
p-value of test                       :    0.9924

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   65.85
p-value of test                       :  6.2e-3

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.86
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.14
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17741.36
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.57
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.04
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.91
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.91
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.81
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.39
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.33
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.38
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.88
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.43
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.82
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.11
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  452.47
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.57
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.12
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.10
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.56
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.32
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.75
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.87
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:43.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.20
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.31
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4926.85
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.45
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.00
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.07
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.30
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.33
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.16
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.49
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.98
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:23.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.89
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:23.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.62e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 9.63e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.67e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.75
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.80
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.33
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:06.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.58
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:06.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9978.96
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9826.54
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:04:18.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5075.23
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:52.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4979.31
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:54.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.87
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3995.51
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11858.48
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:32.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12138.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:31.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.18
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999971381

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.30
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000031192

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:12.60

 All tests were passed




Server wird beendet - Lösche Semaphor 6717471.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1267
p-value of test                       :    0.9959

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334387
  j =  1                              :        599997466
  j =  2                              :             1267
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5418
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:54.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:40.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:57.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:05.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:04.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:54.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7179
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:00.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.14
p-value of test                       :    0.9991    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    2.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     334
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:12.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.73
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.89
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:40.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.60
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.35
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.49
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.59
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.53
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.18
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.60
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.91
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.65
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:44.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.41
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:01.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6978.21
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.87
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.05
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:02.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.67
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.89
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:34.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5198.70
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:01.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45614
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869614
  j =  1                              :        399908775
  j =  2                              :            45608
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45852
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869852
  j =  1                              :        399908298
  j =  2                              :            45848
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:28.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:18.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:46.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:01.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:34.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 5.15e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.59
p-value of test                       :    0.9952

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:33.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.64
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   96.79
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:51.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.77
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.03
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.74
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.39
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.91
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:43.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.08
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.11
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.01
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.96
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.45
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17229.22
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.92
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.65
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.98
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.27
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.48
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.72
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.48
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.21
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.07
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.04
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.66
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.20
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.31
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.68
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.45
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.60
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.59
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  423.22
p-value of test                       :    0.9945


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.13
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.27
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.09
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.45
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5073.43
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.90
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.83
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.10
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.07
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.73
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.85
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.39
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.72
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:25.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.20
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :   -0.63
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:24.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.94e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 4.62e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.82e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.92
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.61
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.02
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:05.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.25
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:08.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9924.18
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 8.98e-3
p-value of test                       :    0.9903

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9666.84
p-value of test                       :    0.9913

-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.19
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:03:43.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.84
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:47.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4759.04
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:49.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4016.01
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.00
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11750.12
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11728.33
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:29.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.23
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999968609

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.68
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999879299

Normal statistic for number of bits   :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.5e-3

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.88

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:36.78
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs mNP1, t = 5          0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 7831583.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5390
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:00.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:43.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7199
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:45.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:00.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:01.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:12.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:11.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:09.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:04:13.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.72
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.93
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.69
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     564
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.81
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    2.40
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     273
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:15.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:42.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.79
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.89
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.63
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    5.95
p-value of test                       :    0.9964

-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.51
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.63
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.67
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  170.25
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:00.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1506.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:09.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7031.93
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.48
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:18.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.99
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.77
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:43.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5052.84
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:55.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46195
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870195
  j =  1                              :        399907617
  j =  2                              :            46181
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45525
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869525
  j =  1                              :        399908956
  j =  2                              :            45513
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:32.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:22.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:54.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:11.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:58.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 4.19e-3
p-value of test                       :    0.9955

Anderson-Darling statistic = A2       :    3.43
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:38.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.66e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:24.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:24.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:50.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:55.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.11
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.45
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.56
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.04
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:53.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.64
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.98
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.85
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17450.43
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.33
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.58
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.23
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.03
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.53
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.62
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.29
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.44
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.04
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.10
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.94
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.45
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.93
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.74
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.07
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.46
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.33
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.61
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.06
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.22
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.27
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.45
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5084.29
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.25
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.61
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.52
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.57
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5046.84
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.96
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.05
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:34.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.73
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:22.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.28
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:22.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:11.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.92e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 8.93e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:46.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.09e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.25
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.57
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.82
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:08.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.59
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:09.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9985.47
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10055.58
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:11.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.14
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.090
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:04:34.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4811.44
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:55.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4832.93
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:00.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4225.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11560.55
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:35.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12138.51
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:37.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.12
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999948419

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.71
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999950696

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.43

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:12:00.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 34  Gap, r = 0                      0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 8814623.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:40.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:54.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7110
p-value of test                       :    0.9926


-----------------------------------------------
CPU time used                    :  00:02:41.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:59.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:00.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:08.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:10.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7199
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:02.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:04:03.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:47.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.94
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:14.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:41.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.58
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.36
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.83
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.79
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.28
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.43
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.98
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.04
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.70
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:52.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1510.42
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:04.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6959.40
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:54.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.38
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:13.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.03
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.91
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:37.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4985.53
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:00.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45368
p-value of test                       :    0.9916


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869368
  j =  1                              :        399909271
  j =  2                              :            45354
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45967
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869967
  j =  1                              :        399908073
  j =  2                              :            45953
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:31.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:19.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:52.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:06.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.80e-3
p-value of test                       :    0.9981

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.74e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.60e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 8.94e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:24.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:43.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:43.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.45
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.81
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.82
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.53
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:49.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.13
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.76
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.91
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:46.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.00
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.20
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.35
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.10
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:40.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17501.54
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.87
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.18
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.11
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.33
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.08
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.31
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.55
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.00
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.74
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.19
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.18
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.45
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.65
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.11
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.86
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.78
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.34
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.94
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.34
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.44
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.34
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.57
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4908.68
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.32
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.63
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.61
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.00
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4800.77
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.86
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.22
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.50
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :    1.11
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:26.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.14
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :   -1.36
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:26.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.55
p-value of test                       :    0.94

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 3.96e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.63e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 9.70e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.40
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.56
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.25
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:05.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.29
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:06.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9966.18
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10194.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:04:21.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.52
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:55.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4762.16
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:58.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.39
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.98
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11593.70
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:33.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11884.42
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:33.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.39
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999930893

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.05
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999709571

Normal statistic for number of bits   :   -2.30
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9948

Tests on the sum of all N observations
Standardized normal statistic         :  -0.052
p-value of test                       :    0.52

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:37.34

 All tests were passed




Server wird beendet - Lösche Semaphor 10059807.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:49.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5489
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:58.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:45.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:00.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:01.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:11.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:11.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:06.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:11.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     553
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    3.04
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:15.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    2.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:44.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.06
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.32
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.28
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.88
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.22
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.48
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.68
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.25
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:55.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:05.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6836.51
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.22
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.21
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:18.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.70
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.64
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:40.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4981.49
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  1.7e-3


-----------------------------------------------
CPU time used                    :  00:03:07.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45745
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869745
  j =  1                              :        399908514
  j =  2                              :            45737
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46196
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870196
  j =  1                              :        399907610
  j =  2                              :            46192
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:33.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  7.8e-3

Anderson-Darling statistic = A2       :    4.38
p-value of test                       :  5.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  3.9e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:21.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:50.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:08.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:38.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 5.33e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    3.49
p-value of test                       :  2.4e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:46.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:49.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.68
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:50.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.05
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.48
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:50.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.13
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.98
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.47
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:50.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.92
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.82
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   12.39
p-value of test                       :  6.2e-3

-----------------------------------------------
CPU time used                    :  00:01:29.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17641.44
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.34
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.31
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.75
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.52
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.76
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.93
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.57
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.74
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.54
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.19
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.88
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.93
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.63
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.82
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.99
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.89
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  429.63
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.11
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.89
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.36
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.87
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.05
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.59
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.10
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.95
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.33
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.57
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.17
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.85
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :   -0.40
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:23.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.18
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:23.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.64e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 8.67e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 2.74e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.86
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.74
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.92
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:06.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.09
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:04.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  2.0e-3

Anderson-Darling statistic = A2       :    3.29
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10308.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10008.03
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:10.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:04:27.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.76
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4850.94
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:00.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3950.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4199.77
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:29.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12126.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:36.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.70
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:37.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.54
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000072289

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.49
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  7999972311

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 5.15e-3
p-value of test                       :    0.9946

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -2.12
p-value of test                       :    0.98

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:31.94
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 56  SampleCorr, k = 2               2.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 11108383.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5426
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:58.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:43.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:44.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:59.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:01.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:12.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:04:09.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:15.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:48.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.87
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:13.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:43.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.68
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.70
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.87
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.12
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.05
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:10.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.79
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.83
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:30.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.54
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:57.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1467.41
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:08.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7120.16
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:59.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.04
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.74
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:14.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.03
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:46.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.84
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:41.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4857.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:57.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45970
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869970
  j =  1                              :        399908068
  j =  2                              :            45954
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45936
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869936
  j =  1                              :        399908128
  j =  2                              :            45936
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.56
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:32.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 7.66e-3
p-value of test                       :    0.9904

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:21.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:53.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:08.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:56.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9951

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:38.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:24.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.57
p-value of test                       :    0.9950

-----------------------------------------------
CPU time used                    :  00:00:24.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.095
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:24.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:48.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:54.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.66
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.68
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.62
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.76
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.42
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.54
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:51.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.26
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.98
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.49
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.73
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17460.38
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.57
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.56
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.04
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.59
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.61
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.48
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.27
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.51
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.51
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.91
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.70
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.42
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.40
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.79
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.95
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.29
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.29
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.40
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.02
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.57
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.35
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.56
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.14
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.12
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.76
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.98
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.69
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.13
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.36
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.18
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:24.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.36
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :    1.60
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:24.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :  -0.054
p-value of test                       :    0.52

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.23e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.85
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.86
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.99
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:05.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.22
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:07.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9772.71
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10047.78
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:11.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.092
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:04:28.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4955.78
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:54.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4984.34
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:59.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.28
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4212.10
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:29.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11712.77
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:36.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11630.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:38.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.04
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999820091

Normal statistic for number of bits   :   -1.42
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.70
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999947120

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:24.19

 All tests were passed




Server wird beendet - Lösche Semaphor 12288031.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5483
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:54.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:41.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4250
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:58.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:06.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7186
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:06.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:56.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:01.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.62
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:14.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.65
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:44.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.71
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.41
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.97
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.33
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.95
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.85
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.65
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.79
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  266.75
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  469.23
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:43.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1338.12
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:01.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7049.90
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.86
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:15.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.87
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:00.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.16
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.32
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4988.77
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:01.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45605
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869605
  j =  1                              :        399908795
  j =  2                              :            45595
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45624
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869624
  j =  1                              :        399908755
  j =  2                              :            45618
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:29.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:18.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:45.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.43
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:00.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:55.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:36.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.13e-6
p-value of test                       :    0.9996    *****

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 3.05e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:41.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:38.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.82
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.63
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.66
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.61
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.84
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.78
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.53
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:42.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.29e-3
p-value of test                       :    0.9944

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   61.47
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.49
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:29.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.18
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17515.68
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.86
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.26
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.14
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.31
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.51
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.14
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.52
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.67
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.54
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.76
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.86
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.68
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.42
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.80
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.59
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.81
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.27
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.30
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.93
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.60
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.46
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.90
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.04
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.07
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.35
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.12
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.84
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5172.23
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.24
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.77
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.59
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :    2.65
p-value of test                       :  4.1e-3



-----------------------------------------------
CPU time used                    :  00:02:24.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.53
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :   -1.67
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:22.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.55e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.25e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 7.30e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.99
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.67
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.31
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:07.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.38
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:06.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10082.11
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10181.02
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:40.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4831.48
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.86
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:49.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.81
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4002.22
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11549.10
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11564.30
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.60
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999982502

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.01
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000043393

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    2.38
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:46.38

 All tests were passed




Server wird beendet - Lösche Semaphor 13533215.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9903


-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1520
p-value of test                       :  1.8e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334640
  j =  1                              :        599996960
  j =  2                              :             1520
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5362
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:56.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4487
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:40.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:57.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:06.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:05.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7461
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:55.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:01.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    2.82
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:46.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    2.17
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:14.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:45.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.93
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.16
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.33
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.21
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.09
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.53
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.10
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  378.70
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:43.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.97
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:01.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7033.48
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:43.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.70
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.09
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:03.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.92
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5250.47
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:57.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45879
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869879
  j =  1                              :        399908244
  j =  2                              :            45875
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45702
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869702
  j =  1                              :        399908599
  j =  2                              :            45696
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:28.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:17.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:45.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:36.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 3.15e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.10e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -3.19
p-value of test                       :    0.9993    *****

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.042
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:37.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.94
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.50
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.41
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.22
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.78
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.91
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:43.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.83
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  3.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.93
p-value of test                       :  9.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   19.23
p-value of test                       :    0.9978

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.42
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.99
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17688.69
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.77
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.99
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.48
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.50
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.36
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.68
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   42.67
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.59
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.51
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.39
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.98
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.23
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.73
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.63
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.73
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.54
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.73
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.01
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.67
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.09
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.70
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5102.60
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.17
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.36
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:34.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.90
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.90
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5104.88
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.76
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.40
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:34.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.79
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :   -2.01
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:22.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.40
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:23.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.46e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.05e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.86
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.59
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.15
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:04.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.38
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:05.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9964.45
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9814.91
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:42.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.90
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:46.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5051.06
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:50.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4049.40
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4061.50
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11769.38
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11869.41
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:29.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.90
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999956756

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.06
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999967262

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.68

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.96
p-value of test                       :    0.03

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    2.42
p-value of test                       :  9.6e-3

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:26.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           1.8e-5
 56  SampleCorr, k = 2               0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 14581791.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:10.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1272
p-value of test                       :    0.9939

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334392
  j =  1                              :        599997456
  j =  2                              :             1272
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5355
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:56.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:42.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:44.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:01.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:01.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7496
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:12.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7460
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:09.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:13.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.04
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:49.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.94
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    2.14
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:15.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.63
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:45.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.59
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.55
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.64
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.69
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.08
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.90
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.31
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.37
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  261.20
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  394.11
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1380.27
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:05.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7032.87
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.38
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.00
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:18.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.44
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:46.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.80
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:40.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5029.80
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:01.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45834
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869834
  j =  1                              :        399908338
  j =  2                              :            45822
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45759
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869759
  j =  1                              :        399908485
  j =  2                              :            45753
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:33.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:20.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:53.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:07.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:58.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:38.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.23e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:24.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:52.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:53.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.85
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.25
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.46
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.23
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.34
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:51.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.78
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.88
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.59
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.47
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:42.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17505.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.36
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.82
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.25
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.24
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.75
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.24
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.84
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.28
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.47
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.33
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.62
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.18
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.08
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.19
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.01
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.40
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.72
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.90
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.67
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.41
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.05
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5034.92
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.85
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.09
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:36.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.70
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.06
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5102.79
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.29
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.88
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.22
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:23.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.02
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 6.33e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.58e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.83
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.18
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.32
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:04.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.51
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:06.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10016.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9900.56
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:04:25.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.23
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.07
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:59.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.31
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.42
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11935.10
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:35.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11949.44
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:36.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.05
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999849857

Normal statistic for number of bits   :   -1.19
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.71
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999976301

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    1.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.4e-3

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.17
p-value of test                       :    0.01

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:15.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.76
p-value of test                       :    0.96

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:12:12.98

 All tests were passed




Server wird beendet - Lösche Semaphor 15630367.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:38.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5401
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:56.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7507
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:41.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:56.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:57.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:05.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:06.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:57.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7459
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:00.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:15.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    2.97
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:45.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.82
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.08
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.02
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.45
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:10.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.52
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.85
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  272.97
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.49
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:43.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.96
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:00.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6969.16
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:43.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.46
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.75
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:04.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.13
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.08
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4994.56
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:01.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45638
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869638
  j =  1                              :        399908726
  j =  2                              :            45634
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45726
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869726
  j =  1                              :        399908552
  j =  2                              :            45718
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:29.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:18.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:00.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:56.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.95e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 3.10e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:39.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:39.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.73
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.15
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.07
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.61
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.81
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.42
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.23
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.58
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.46
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17557.44
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.24
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.02
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.96
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.66
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.70
p-value of test                       :    0.9950


-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.64
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.16
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.94
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.11
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.35
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.86
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  196.06
p-value of test                       :  3.6e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.38
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.84
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.63
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.20
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.98
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.30
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.62
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.34
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.47
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.03
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.47
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.52
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.28
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.85
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.00
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4874.71
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  439.13
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.72
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:23.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.70
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :  -0.055
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:22.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9976

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.68e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 9.54e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.19
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.70
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.39
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:05.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.00
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:08.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10229.41
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.24
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:40.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5040.91
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4958.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4147.79
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.03
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11726.02
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11676.34
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.11
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000056374

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.55
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  7999933713

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :  -0.075
p-value of test                       :    0.53

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:46.45

 All tests were passed




Server wird beendet - Lösche Semaphor 16711711.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:48.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5451
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:57.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4432
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7177
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:41.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:56.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4236
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:58.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7193
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:05.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:05.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:55.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:01.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:05.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:15.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    2.18
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:43.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.69
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.41
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.23
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.30
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.52
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.67
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.29
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:42.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1493.39
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:00.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7000.68
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:40.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.99
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.90e-3
p-value of test                       :    0.9949

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   38.83
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:03.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.57
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.15
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:30.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5053.31
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:00.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45641
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869641
  j =  1                              :        399908722
  j =  2                              :            45633
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45970
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869970
  j =  1                              :        399908062
  j =  2                              :            45966
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:28.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:18.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :  6.4e-4    *****

Anderson-Darling statistic = A2       :    5.52
p-value of test                       :  1.7e-3


-----------------------------------------------
CPU time used                    :  00:01:45.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:59.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:55.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:34.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.86e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.71e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:21.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:39.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.76
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.03
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.68
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.23
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.29
p-value of test                       :    0.9958

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.95
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:39.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.28
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.89
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.94
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.74
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.92
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.86
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17629.39
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.58
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.99
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.40
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.77
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.48
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.74
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.04
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.70
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.45
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.55
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.55
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.40
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.81
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.67
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.92
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.45
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.85
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.38
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.34
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.08
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.78
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4908.38
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.32
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.80
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.76
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.45
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.79
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.57
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.93
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.44
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :   0.083
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:21.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.34
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:21.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 2.35e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:46.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.79e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 6.83e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.56
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.37
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:04.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:06.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10125.00
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9926.76
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:04:21.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4723.83
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:46.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4968.78
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4133.94
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.06
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11782.69
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11985.53
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.94
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000142402

Normal statistic for number of bits   :    1.13
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.43
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000058504

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    2.49
p-value of test                       :  7.7e-3

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:02.84

 All tests were passed




Server wird beendet - Lösche Semaphor 17727519.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:49.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5493
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:56.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:42.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4205
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:58.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:05.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:05.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:56.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:04:00.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9920

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:14.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:42.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.88
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.05
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.87
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.47
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.26
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.60
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.28
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.25
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.80
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  395.41
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:42.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1470.78
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:01.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7024.11
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:40.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:03.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.52
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:34.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5124.06
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:59.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45770
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869770
  j =  1                              :        399908463
  j =  2                              :            45764
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45930
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869930
  j =  1                              :        399908144
  j =  2                              :            45922
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:29.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:19.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:58.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:38.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:38.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.81
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.64
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.71
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:42.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.92
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.71
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.39
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  157.42
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17150.63
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.20
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.39
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.07
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.53
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.23
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.63
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.43
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.89
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.57
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.77
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.11
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.90
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.24
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.26
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.07
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.21
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  187.33
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.26
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.95
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.96
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.83
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.03
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4787.90
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.93
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.03
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.78
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.21
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4894.61
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.95
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.18
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.59
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :   -1.13
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:22.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.49
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.71

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.44e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 8.10e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.68
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.38
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.27
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:03.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.03
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:05.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10139.75
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9930.34
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:43.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4849.65
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.38
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:49.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.93
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4275.29
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11756.95
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11488.55
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.38
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999864428

Normal statistic for number of bits   :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.97
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999978617

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 6.10e-3
p-value of test                       :    0.9936

Anderson-Darling statistic = A2       :    4.44
p-value of test                       :  5.6e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.92
p-value of test                       :    0.9982

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:19.70

 All tests were passed




Server wird beendet - Lösche Semaphor 18776095.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:48.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5378
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:57.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:41.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:56.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:58.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7472
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:05.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:06.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:56.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:00.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.81
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.81
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     328
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:12.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:42.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.06
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.75
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.88
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.21
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.85
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.59
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.96
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.24
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:41.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.86
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:01.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7231.98
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:40.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.20
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:02.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.59
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:33.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5014.73
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:56.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46171
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870171
  j =  1                              :        399907663
  j =  2                              :            46161
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45896
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869896
  j =  1                              :        399908209
  j =  2                              :            45894
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:28.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:17.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:44.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:57.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:36.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.05e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 6.20e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 5.02e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:38.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:35.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.44
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   40.95
p-value of test                       :    0.9950

-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.22
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.61
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   59.23
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.71
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:43.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.53
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.71
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.40
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.50
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.66
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17420.96
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.56
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.35
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.09
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.03
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.06
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.79
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.35
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.23
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.66
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.40
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.43
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.47
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.39
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.07
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   49.48
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.93
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.21
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.08
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.57
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.06
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.83
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.11
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5029.53
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.70
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.52
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.99
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.78
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4918.22
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  428.38
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.97
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:34.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.15
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.81
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:22.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :  -0.060
p-value of test                       :    0.52

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.32e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 9.13e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 8.33e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.61
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.04
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.82
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:03.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:05.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10118.30
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10076.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.051
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:41.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4665.66
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:47.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5088.34
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:49.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.82
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4206.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11861.62
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11487.66
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.49
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000098848

Normal statistic for number of bits   :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.60
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999956669

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :  -0.081
p-value of test                       :    0.53

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:12.15

 All tests were passed




Server wird beendet - Lösche Semaphor 19791903.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:48.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997251
  j =  2                              :             1373
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5472
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:55.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7541
p-value of test                       :  4.9e-3


-----------------------------------------------
CPU time used                    :  00:02:42.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:57.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:58.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:06.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7143
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:06.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:56.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:04:01.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     856
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    2.00
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    3.93
p-value of test                       :  9.4e-3

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:14.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:42.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.39
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.03
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.65
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.62
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.28
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.21
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:42.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1434.70
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7155.04
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:40.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.71
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.55
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:01.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.74
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.16
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:33.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4908.71
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:58.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45626
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869626
  j =  1                              :        399908752
  j =  2                              :            45618
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45877
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869877
  j =  1                              :        399908249
  j =  2                              :            45871
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:28.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:18.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:46.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:59.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:56.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:35.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.04
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:39.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:37.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.93
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:50.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.05
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.71
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:49.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.14
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.06
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.51
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:43.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.39
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.49
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.02
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.74
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17109.71
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:50.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.53
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.35
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   42.00
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.33
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.14
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.44
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.91
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.37
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.75
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.38
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.76
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.10
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.01
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.67
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.91
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.92
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.09
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.02
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.82
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.64
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.12
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.35
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4942.12
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.92
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.02
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:33.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.44
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  321.59
p-value of test                       :    0.9909


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4933.47
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.74
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.16
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:33.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.78
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:14.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.46
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:15.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.12

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.29e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.18
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.48
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.29
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:58.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  4.0e-3

Anderson-Darling statistic = A2       :    3.38
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  248.03
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:57.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9954.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10128.70
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:20.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4914.45
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:35.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4831.40
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4129.06
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:10.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4027.05
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11429.15
p-value of test                       :    0.9953

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11893.89
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.57
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000053386

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.48
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  7999935330

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    2.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.65
p-value of test                       :    0.05

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   02:57:44.13

 All tests were passed




Server wird beendet - Lösche Semaphor 20840479.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1245
p-value of test                       :    0.9994    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334365
  j =  1                              :        599997510
  j =  2                              :             1245
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5391
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:43.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:37.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:35.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:55.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:04.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:05.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:00.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:04:03.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:52.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.94
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    3.37
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:10.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:37.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.15
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.68
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.15
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.35
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.07
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.23
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.63
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  201.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.58
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:50.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1489.73
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:13.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6949.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:52.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.62
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   47.87
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.86
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:07.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.80
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.41
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:38.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4932.55
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:20.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45807
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869807
  j =  1                              :        399908391
  j =  2                              :            45797
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46096
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870096
  j =  1                              :        399907819
  j =  2                              :            46074
  j =  3                              :               11
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :  4.1e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    5.39
p-value of test                       :  1.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9987


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:27.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:18.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:46.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:00.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:38.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 4.92e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.36e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:38.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:40.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.44
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   99.56
p-value of test                       :  6.0e-3

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.09
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.32
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.19
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:52.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.20
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.55
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:32.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:35.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:23.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.67
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:39.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17504.81
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.65
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.10
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.45
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.36
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.86
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.99
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.26
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.21
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.90
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.82
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:34.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.74
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.05
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.38
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.47
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.32
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.86
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.80
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.10
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.42
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.92
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.50
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.49
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5161.63
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.76
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.77
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.72
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.94
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4858.65
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.43
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.23
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.55
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :    1.28
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:29.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.68
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :   -0.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:27.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.95e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 6.79e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:47.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.11
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:30.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.38
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.20
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:05.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.47
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:09.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9761.17
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9927

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9989.94
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.02
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:04:13.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4843.80
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:50.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5091.78
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:51.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.83
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4240.41
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11866.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:34.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11694.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:34.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.40
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000039907

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.32
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999921467

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.57

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   0.068
p-value of test                       :    0.47

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:19:03.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           0.9994 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 167903232.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1270
p-value of test                       :    0.9948

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334390
  j =  1                              :        599997460
  j =  2                              :             1270
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1465
p-value of test                       :  3.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334585
  j =  1                              :        599997070
  j =  2                              :             1465
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:48.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:38.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:38.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:55.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:56.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:05.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:05.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:58.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:04:03.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.99
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:50.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     638
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    2.22
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.28
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:17.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.91
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:48.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.03
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.99
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.19
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.46
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.63
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.20
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.26
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.09
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.08
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  470.65
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:53.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1509.10
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:02.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6749.11
p-value of test                       :    0.9943

-----------------------------------------------
CPU time used                    :  00:01:55.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.51
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.95
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:14.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.13
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:46.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.45
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:42.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5024.26
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:59.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45945
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869945
  j =  1                              :        399908113
  j =  2                              :            45939
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46413
p-value of test                       :  6.5e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870413
  j =  1                              :        399907177
  j =  2                              :            46407
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:29.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:19.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:02.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.59e-3
p-value of test                       :    0.9931

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:38.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.87e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:22.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:43.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:44.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.03
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.25
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.79
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.29
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:54.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.96
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:51.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.38
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.49
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.11
p-value of test                       :    0.9901

-----------------------------------------------
CPU time used                    :  00:01:31.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:31.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.36
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17525.61
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:55.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.62
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.32
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.92
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.08
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.25
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.67
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.05
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.25
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.48
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.57
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.84
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.59
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  577.97
p-value of test                       :  8.9e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.02
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.82
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.53
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.23
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  444.92
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.51
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.49
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.83
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.16
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.05
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.51
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.53
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.30
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.43
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.87
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.54
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.79
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.31
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :   -1.09
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:26.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.71
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :   -0.37
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:27.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.16e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:46.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.69e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 8.50e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.24
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.34
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.42
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:09.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:09.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10188.12
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.02
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:04:20.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.23
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4897.03
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:58.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.90
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3924.67
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11613.61
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:31.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11728.54
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:32.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.96
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000027457

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.54
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000164860

Normal statistic for number of bits   :    1.30
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.6e-3

Kolmogorov-Smirnov- statistic = D-    : 4.92e-3
p-value of test                       :    0.9949

Anderson-Darling statistic = A2       :    4.03
p-value of test                       :  8.8e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.73
p-value of test                       :    0.9969

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:12:38.79

 All tests were passed




Server wird beendet - Lösche Semaphor 169771008.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5462
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:53.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:41.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4462
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:57.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:58.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:08.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:09.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:03.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:04.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.91
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    2.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.41
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    2.00
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:15.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:47.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.34
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.57
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.69
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.73
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.70
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.83
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.29
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.49
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:46.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.40
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:03.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7296.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:55.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.41
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.40
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:14.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.38
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.94
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:37.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4971.21
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:53.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45840
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869840
  j =  1                              :        399908321
  j =  2                              :            45838
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45649
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869649
  j =  1                              :        399908703
  j =  2                              :            45647
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:30.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:20.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:48.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :  7.1e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.86
p-value of test                       :  3.5e-3


-----------------------------------------------
CPU time used                    :  00:02:02.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:58.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.17e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:53.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:48.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.44
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.09
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   61.48
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.08
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.02
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.99
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:50.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.92
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.02
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.14
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:29.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.41
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:29.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   11.75
p-value of test                       :  2.8e-3

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.98
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17507.48
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:54.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.35
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.38
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.69
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.96
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.97
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.30
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.52
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.30
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.92
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.41
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.29
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.26
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  423.21
p-value of test                       :    0.9945


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.37
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.12
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.68
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.43
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.50
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.44
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.41
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.48
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.41
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.31
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.28
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.29
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.59
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.08
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4987.67
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.18
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.43
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.41
p-value of test                       :    0.9919


-----------------------------------------------
Normal statistic for number of jumps  :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:25.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.72
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :   -1.15
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:24.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.88

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.47e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 8.25e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 9.03e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.31
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.56
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.09
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:10.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.83
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:09.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9687.85
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10081.19
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.77
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:04:15.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.34
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:53.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.54
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:52.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.99
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.17
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12005.94
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11789.15
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:30.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.02
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000071578

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.28
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000005659

Normal statistic for number of bits   :   0.045
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.51
p-value of test                       :    0.07

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:02.28

 All tests were passed




Server wird beendet - Lösche Semaphor 171016192.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:49.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5477
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:53.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:41.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:58.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:59.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:07.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:08.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:00.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:04:02.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    4.41
p-value of test                       :  5.5e-3

Stat. AD after spacings (mNP2-S)      :    3.29
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:47.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    3.41
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:15.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.25
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:44.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.72
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.59
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.50
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.91
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.96
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.12
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.19
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  195.49
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.61
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:51.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.13
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:02.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7063.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:52.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.32
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.39
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:01.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.80
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.22
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:32.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5139.92
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:11.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:52.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45512
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869512
  j =  1                              :        399908979
  j =  2                              :            45506
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45960
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869960
  j =  1                              :        399908082
  j =  2                              :            45956
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:25.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:17.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.26
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:59.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:57.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:37.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.14e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 3.39e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.58
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 9.62e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:36.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:41.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.24
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.43
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   97.51
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.33
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.54
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   53.24
p-value of test                       :  4.0e-3

-----------------------------------------------
CPU time used                    :  00:01:46.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.93
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.73
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:40.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17406.80
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.89
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.42
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.44
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.37
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.63
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.38
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.03
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.40
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.66
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.49
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.36
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.93
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.23
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.19
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.57
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.55
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.85
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.77
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.09
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.64
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.08
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  441.99
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4880.75
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.67
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.19
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.46
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.82
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5115.46
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.25
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.50
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.10
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :    1.84
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:26.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.94
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :   -2.12
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:25.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.56
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.48
p-value of test                       :    0.9934

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 6.41e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.17e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 5.93e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.23
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.23
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.22
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:06.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.98
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:07.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10102.41
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10026.42
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.099
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:50.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5031.81
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:45.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4746.07
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3975.78
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.04
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11582.99
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11858.25
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   83.03
p-value of test                       :  6.8e-3


-----------------------------------------------
Total number of bits:  7999931451

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.76
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000062878

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.60
p-value of test                       :    0.95

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:38.79

 All tests were passed




Server wird beendet - Lösche Semaphor 172064768.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5471
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:53.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:40.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4194
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:57.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:58.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7153
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:06.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:07.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:02.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:04:02.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:48.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    4.19
p-value of test                       :  7.1e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     328
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:13.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:44.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.54
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.82
p-value of test                       :    0.9972

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.43
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.41
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.70
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.72
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.49
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.78
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:47.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1370.09
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:11.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6938.15
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:52.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.43
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:57.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.42
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.53
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:30.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4985.79
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:57.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45702
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869702
  j =  1                              :        399908599
  j =  2                              :            45696
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45704
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869704
  j =  1                              :        399908598
  j =  2                              :            45692
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:26.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:18.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:46.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:00.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:00.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:40.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 5.87e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.57e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 3.49e-4
p-value of test                       :  7.7e-3

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:33.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.02
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.86
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.67
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.66
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:50.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.41
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.06
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.19
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:29.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  103.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:40.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17638.94
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.67
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.03
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.90
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.70
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.20
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.73
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.16
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.25
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.67
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.88
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:39.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.08
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.57
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.28
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.79
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.06
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.13
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.55
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.95
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.66
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.38
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.31
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.64
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5019.26
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.96
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.42
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.70
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.44
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.60
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.59
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.62
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.35
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:25.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.06
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:24.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.45
p-value of test                       :    0.93

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 3.37e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:46.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.43e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.48
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:31.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.52
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.03
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:08.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.13
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:09.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9945.14
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10021.32
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:50.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.39
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4936.20
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:49.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11916.53
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11626.83
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.62
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999985256

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.80
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999911993

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:36.85

 All tests were passed




Server wird beendet - Lösche Semaphor 173113344.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5285
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:51.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:40.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4442
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:58.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:06.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:06.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7469
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:59.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:03.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    2.89
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.48
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    2.37
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     641
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:14.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.61
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:42.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.34
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.94
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.97
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.59
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.89
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.05
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.42
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.41
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.88
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:46.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.66
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:59.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6984.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:52.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.96
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.34
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:58.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.97
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.71
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:32.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4939.06
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:00.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45790
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869790
  j =  1                              :        399908423
  j =  2                              :            45784
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45368
p-value of test                       :    0.9916


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869368
  j =  1                              :        399909264
  j =  2                              :            45368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:25.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:16.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:45.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:58.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:57.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 6.91e-3
p-value of test                       :    0.9921

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.59e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 2.70e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.64e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.051
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:21.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:31.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:33.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.33
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.19
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.21
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.97
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.31
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   49.26
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:45.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.12
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.70
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.54
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:28.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.54
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.50
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:40.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17108.10
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.67
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.78
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.23
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.91
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.67
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.98
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.74
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.90
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.85
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.20
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.21
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.25
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  170.77
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.39
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:46.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.69
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.85
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.24
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.09
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.81
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.80
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.23
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5095.13
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.67
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.00
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.94
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.57
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4894.84
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  332.90
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.48
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.07
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :   -1.42
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:26.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.10
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :   -1.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:26.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.26e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:46.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 3.30e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.47
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.90
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.10
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:08.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.25
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:08.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10066.82
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9916.30
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:53.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9963

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.97
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:46.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4836.09
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3992.73
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4006.70
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11533.71
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11878.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.63
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000110392

Normal statistic for number of bits   :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.48
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999915365

Normal statistic for number of bits   :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         : 7.44e-3
p-value of test                       :    0.50

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.69
p-value of test                       :    0.05

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:57.77

 All tests were passed




Server wird beendet - Lösche Semaphor 174030848.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:52.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5344
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:52.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:40.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:58.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:06.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:07.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:58.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:02.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.57
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.13
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     854
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     636
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.03
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.34
p-value of test                       :  6.2e-3

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    2.58
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:16.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:44.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.60
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.53
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.72
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.30
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.23
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.44
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:16.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  315.90
p-value of test                       :  2.0e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.07
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:47.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1489.34
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:59.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6946.32
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:51.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.40
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:57.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.38
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.25
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:32.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4888.75
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:00.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45995
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869995
  j =  1                              :        399908013
  j =  2                              :            45989
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45811
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869811
  j =  1                              :        399908380
  j =  2                              :            45807
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:26.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:17.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:01.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:37.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.65e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.052
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:39.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.97
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:39.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.22
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.39
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.35
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.81
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:46.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.17
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.86
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  151.11
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17823.59
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.52
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.41
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   42.69
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.82
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.49
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.14
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.16
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.75
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.75
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.10
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.09
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.05
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.04
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.38
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.03
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.47
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.59
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.40
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.96
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.05
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.02
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.46
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.05
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  325.51
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.83
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.75
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.95
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5248.99
p-value of test                       :  7.0e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.44
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.30
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.42
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:26.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.24
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:26.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  1.0e-2

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.99
p-value of test                       :  9.2e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.52
p-value of test                       :    0.9942

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.65e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:46.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 6.22e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.86
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.75
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:07.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.91
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:09.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10078.79
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9926.69
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.88
p-value of test                       :    0.9980

-----------------------------------------------
CPU time used                    :  00:03:55.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4985.68
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:47.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.74
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:49.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4116.60
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4184.48
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11727.93
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11640.84
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.19
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999924623

Normal statistic for number of bits   :   -0.60
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.34
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000103567

Normal statistic for number of bits   :    0.82
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :   0.083
p-value of test                       :    0.9998    *****

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:41.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 34  Gap, r = 0                      2.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 174915584.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9967


-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5526
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:52.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:40.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:39.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:56.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:58.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:06.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:06.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:59.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:04:02.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.93
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.17
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:14.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:44.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.63
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.95
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.87
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.97
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.83
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.74
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  396.32
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1408.22
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:02.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6917.92
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:51.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.98
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.70
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:58.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.45
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.29
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:31.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5127.60
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:04.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45899
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869899
  j =  1                              :        399908209
  j =  2                              :            45885
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45831
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869831
  j =  1                              :        399908342
  j =  2                              :            45823
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 5.22e-3
p-value of test                       :    0.9936

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:26.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:18.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:46.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:00.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:38.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.24e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 4.67e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.69
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:22.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:35.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:32.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.18
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.64
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.32
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:49.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.50
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.51
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.65
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:48.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.60
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.94
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.81
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:29.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.19
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17684.64
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.55
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.58
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.52
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.06
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.63
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.46
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.74
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.97
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.95
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.29
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.69
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.79
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.92
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.49
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.58
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.95
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.00
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.36
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.87
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.18
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.56
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  316.10
p-value of test                       :    0.9952


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4928.69
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.54
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.59
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.50
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.06
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4903.67
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.43
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.07
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.09
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:26.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.75
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :   0.039
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:25.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 2.99e-3
p-value of test                       :    0.9969

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.15
p-value of test                       :    0.98

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 8.75e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 8.25e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.22
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.95
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.06
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:08.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.30
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:08.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9738.02
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10027.66
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:42.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.50
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:46.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:48.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3907.58
p-value of test                       :    0.9904

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4181.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11710.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11944.72
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.72
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000184216

Normal statistic for number of bits   :    1.46
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.13
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000060205

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   0.092
p-value of test                       :    0.46

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.89
p-value of test                       :    0.97

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.30
p-value of test                       :    0.01

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:15.37

 All tests were passed




Server wird beendet - Lösche Semaphor 175931392.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:40.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5505
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:52.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4199
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:39.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:39.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:57.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:06.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:05.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:58.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:04.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:48.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:14.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    2.57
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:41.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.01
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.27
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.61
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.42
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.57
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:34.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.87
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:34.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.73
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:33.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.14
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.96
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.58
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:09.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7105.86
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:55.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.41
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:40.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.24
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:46.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.29
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:43.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5174.79
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:58.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45658
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869658
  j =  1                              :        399908687
  j =  2                              :            45652
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45625
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869625
  j =  1                              :        399908754
  j =  2                              :            45617
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:31.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:20.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  8.8e-3

Anderson-Darling statistic = A2       :    4.71
p-value of test                       :  4.0e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  2.5e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:01.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:59.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:01:40.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.53e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:22.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:49.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:50.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.39
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.52
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.50
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.13
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:52.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.02
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.40
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.63
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17590.69
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.39
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.15
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.48
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.76
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.60
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.59
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.20
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.77
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.62
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.32
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.00
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.70
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.29
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.11
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.77
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.48
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.65
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.67
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.58
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.93
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.02
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  459.35
p-value of test                       :  4.9e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4926.29
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.49
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.65
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.11
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.49
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5058.00
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.55
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.64
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.91
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :   -1.15
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:25.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.15
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:25.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.98e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.16e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 8.92e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.12
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.36
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.51
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:10.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.19
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:07.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9811.16
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10163.43
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:04:21.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4729.21
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:57.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4942.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4268.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.03
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:29.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11944.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:37.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11714.51
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:39.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.41
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000027946

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.62
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000014575

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:33.28

 All tests were passed




Server wird beendet - Lösche Semaphor 176881664.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:50.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1270
p-value of test                       :    0.9948

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334390
  j =  1                              :        599997460
  j =  2                              :             1270
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.41

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5562
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:55.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:41.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:57.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:58.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:06.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:07.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:01.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:04:03.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    2.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:49.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:15.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    3.58
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:45.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.83
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.74
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.10
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.34
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:12.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.00
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.61
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.15
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.68
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:48.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1527.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:59.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7023.67
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:52.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.96
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.18
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:00.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.97
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.70
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:31.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4984.09
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:55.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45824
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869824
  j =  1                              :        399908355
  j =  2                              :            45818
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45625
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869625
  j =  1                              :        399908753
  j =  2                              :            45619
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:26.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:16.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:00.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.77e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:58.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:37.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.61e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.57e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:24.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:22.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:37.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:40.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.87
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.78
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.56
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.68
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.16
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:44.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.32
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.50
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.87
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:29.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:30.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.86
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17299.83
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.49
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.92
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.05
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.64
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.94
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.69
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.87
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.82
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.83
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.36
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.34
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.94
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.79
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.46
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.27
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.84
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.43
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  442.58
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.71
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.81
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.41
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.02
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4996.98
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.51
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.70
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.98
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.42
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4863.47
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.50
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.26
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.13
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:25.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.15
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  :   0.061
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:26.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 4.71e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.23e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.88
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.63
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.68
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:08.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.42
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:08.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.84e-4
p-value of test                       :    0.9996    *****

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.6e-3

Anderson-Darling statistic = A2       :    4.29
p-value of test                       :  6.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10440.31
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9966.31
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.094
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:48.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.90
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:46.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4959.37
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:47.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.65
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4322.63
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11742.39
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11702.51
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.51
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999913562

Normal statistic for number of bits   :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.23
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999954236

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:12.62

 All tests were passed




Server wird beendet - Lösche Semaphor 178290688.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1228
p-value of test                       : 1 -  9.4e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334348
  j =  1                              :        599997544
  j =  2                              :             1228
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5362
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:53.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4443
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:57.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4525
p-value of test                       :  2.3e-3


-----------------------------------------------
CPU time used                    :  00:01:59.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7465
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:07.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7476
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:08.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:04:00.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:04.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    2.52
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:50.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :   10.25
p-value of test                       :  1.1e-5    *****

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    2.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:17.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:46.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.61
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.23
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.72
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.54
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.58
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.85
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.41
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.31
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  393.72
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:49.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:01.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6975.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:48.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.01
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.43
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:58.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.54
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.63
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:31.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4968.66
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:56.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45916
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869916
  j =  1                              :        399908173
  j =  2                              :            45906
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45950
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869950
  j =  1                              :        399908106
  j =  2                              :            45938
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:25.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:16.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.86e-3
p-value of test                       :    0.9981

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  4.8e-3

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:46.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:00.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:57.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:38.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.59e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:35.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.015
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:36.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.78
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.34
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.71
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.66
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.96
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:55.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.77
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.95
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.75
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:29.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.22
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:29.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  163.26
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:40.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17605.47
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.30
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.96
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.68
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.72
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.23
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.10
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.28
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.78
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.42
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.12
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.76
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.24
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.43
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.93
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.76
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.08
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.81
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.04
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.37
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.16
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.91
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  448.83
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.08
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.01
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.83
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.84
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.90
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.39
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.50
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.99
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.77
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:26.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.46
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:25.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.51
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.52
p-value of test                       :  5.8e-3

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 9.20e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 3.38e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.31
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.94
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:06.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.57
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:07.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.49
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9975.84
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:46.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4955.28
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4746.87
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:48.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4136.69
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4006.06
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11685.54
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11723.23
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.16
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000046678

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.53
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999952121

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   0.058
p-value of test                       :    0.48

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.4e-3

Anderson-Darling statistic = A2       :    4.41
p-value of test                       :  5.8e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.82
p-value of test                       :  2.4e-3

Sample variance                       :    0.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:21.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21          1 -  9.4e-5
 23  ClosePairs mNP, t = 5           1.1e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 179339264.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:51.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997191
  j =  2                              :             1403
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5467
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:56.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7183
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:45.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:57.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:00.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:10.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:11.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:01.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:04.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.88
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.37
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    4.23
p-value of test                       :  6.8e-3

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.68
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    2.25
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:15.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.81
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:43.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.22
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.75
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.54
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.83
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.73
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.42
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.09
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.91
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.74
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:29.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.80
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:46.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1395.75
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:24.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7042.23
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:52.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.79
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.26
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:57.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.17
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.68
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:31.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5047.16
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:56.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46024
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870024
  j =  1                              :        399907958
  j =  2                              :            46012
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46264
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870264
  j =  1                              :        399907476
  j =  2                              :            46256
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:26.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:19.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:45.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9947


-----------------------------------------------
CPU time used                    :  00:01:59.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:58.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 2.71e-3
p-value of test                       :    0.9972

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:37.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.86e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:35.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:37.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.20
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.39
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.01
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.67
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:49.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.02
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.53
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:46.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.41
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.29
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.20
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.16
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17475.47
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.68
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.41
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.61
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.56
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.96
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.86
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.47
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.99
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.20
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.66
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.13
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.66
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.92
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.58
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.78
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.57
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.32
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.32
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.08
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.87
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.52
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4919.32
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.58
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.62
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.36
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.90
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4907.95
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.33
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.05
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.09
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:25.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.84
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :   0.052
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:25.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.60
p-value of test                       :  3.1e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    7.02
p-value of test                       :  3.5e-4    *****

Tests on the sum of all N observations
Standardized normal statistic         :   -3.59
p-value of test                       :    0.9998    *****

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.42e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.60e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.17
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.05
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:07.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.33
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:08.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10057.70
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9836.46
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.040
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:46.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.48
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:46.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4821.41
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:47.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4170.23
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.41
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11783.44
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11901.03
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.57
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000099139

Normal statistic for number of bits   :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.83
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000205228

Normal statistic for number of bits   :    1.62
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.89
p-value of test                       :    0.03

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:11.11
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 82  LempelZiv, r = 0                0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 180322304.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:40.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5470
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:54.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:41.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4223
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:57.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4438
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:58.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7456
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:07.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:07.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:00.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:04:05.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     844
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:48.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.06
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:14.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.15
p-value of test                       :    0.9988

Stat. AD after spacings (mNP2-S)      :    5.96
p-value of test                       :  1.0e-3

-----------------------------------------------
CPU time used                    :  00:02:14.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:43.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.70
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.73
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.62
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.89
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.69
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.09
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.24
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.73
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.00
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:29.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.73
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1408.89
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:06.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7024.15
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:53.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.86
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.21
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:20.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.08
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:47.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.17
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:44.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4997.32
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:53.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46043
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870043
  j =  1                              :        399907919
  j =  2                              :            46033
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46033
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870033
  j =  1                              :        399907940
  j =  2                              :            46021
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:31.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:19.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:48.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:02.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:59.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:48.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:49.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.94
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:55.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.92
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.74
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.54
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:52.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.65
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.88
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:29.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.04
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17568.36
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.08
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.86
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.97
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.67
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.01
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.05
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.05
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.00
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.16
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.47
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.74
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.57
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.09
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.53
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.75
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.91
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.80
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.91
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.80
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.82
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.09
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.02
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.52
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.34
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.58
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.63
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5137.12
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.50
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.28
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.50
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:25.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.12
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :  -0.055
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:25.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.76e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:46.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 5.41e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.58
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.48
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.19
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:08.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9956

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.54
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:11.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10052.14
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9743.18
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.075
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:04:19.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5016.17
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:59.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4976.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:02.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3904.80
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.15
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:29.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11819.35
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:36.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12023.42
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:38.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.48
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999841850

Normal statistic for number of bits   :   -1.25
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.13
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999851429

Normal statistic for number of bits   :   -1.17
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:28.20

 All tests were passed




Server wird beendet - Lösche Semaphor 181305344.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:48.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5369
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:57.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4434
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:42.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:43.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:59.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:59.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:07.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:07.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:59.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:03.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:49.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:15.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:17.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    3.91
p-value of test                       :  9.6e-3

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:48.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.25
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.72
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.04
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.72
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  290.15
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.03
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:45.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1554.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:09.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7050.39
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:47.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.57
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.94
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:57.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.09
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.57
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:31.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4762.92
p-value of test                       :    0.9974


-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:54.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45811
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869811
  j =  1                              :        399908380
  j =  2                              :            45807
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45925
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869925
  j =  1                              :        399908151
  j =  2                              :            45923
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:25.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:18.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:47.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:04.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:57.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:37.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.65e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-5
p-value of test                       :    0.9928

Kolmogorov-Smirnov- statistic = D-    : 3.22e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -2.16e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:39.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:35.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:50.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.56
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.24
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.06
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.50
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.33
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:47.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.86
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.70
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.12
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.91
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17216.80
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.81
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.92
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.91
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.33
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.09
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.86
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.30
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.91
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.69
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.01
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.81
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.77
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.69
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.80
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.88
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.85
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.79
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.16
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.49
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.21
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.76
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.81
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5121.15
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.19
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.59
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.41
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.84
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4984.32
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.04
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.16
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.51
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :    2.05
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:24.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.71
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:25.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9962

Tests on the sum of all N observations
Standardized normal statistic         : 5.43e-3
p-value of test                       :    0.50

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:18.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.77
p-value of test                       :    0.04

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 8.26e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 8.81e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.11
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.50
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:05.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9967

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:07.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10046.19
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9962.37
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.014
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:37.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4964.71
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:46.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.27
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:48.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4245.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4319.59
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:21.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11857.09
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11914.24
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.63
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000067582

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.00
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999971138

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.57

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:46.00

 All tests were passed




Server wird beendet - Lösche Semaphor 182484992.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1269
p-value of test                       :    0.9952

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334389
  j =  1                              :        599997462
  j =  2                              :             1269
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5352
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:55.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:42.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:59.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:59.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:08.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:08.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:59.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:04:03.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     936
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:16.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    3.14
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:50.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.88
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.18
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.23
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.75
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.28
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.97
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.11
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.44
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:46.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1446.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:02.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6869.35
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:49.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.65
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.92
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:58.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.91
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.44
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:31.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5034.50
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:58.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45748
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869748
  j =  1                              :        399908509
  j =  2                              :            45738
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45887
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869887
  j =  1                              :        399908230
  j =  2                              :            45879
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:26.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:17.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:46.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:00.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:58.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:38.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.19e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 3.09e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.54e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:24.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:37.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:37.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.09
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.66
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.30
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.60
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.19
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.98
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.91
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:47.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.01
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.97e-3
p-value of test                       :    0.9926

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.4e-3

Anderson-Darling statistic = A2       :    4.69
p-value of test                       :  4.3e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   72.10
p-value of test                       :  1.4e-3

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.01
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:39.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17243.84
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.89
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.23
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.17
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.48
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.92
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.39
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.05
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.39
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.76
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.33
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.10
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.26
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  544.64
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.99
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.01
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.50
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.48
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.07
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.89
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.30
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.62
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.92
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.44
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.60
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.17
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.86
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.08
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.48
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.02
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.25
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.21
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:24.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.52
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :    1.24
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:24.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.21e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 3.99e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.46e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.28
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.92
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.87
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:07.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.91
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:07.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9933.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9892.27
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:36.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.12
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:47.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4908.54
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:47.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4024.45
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4116.84
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11551.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11725.30
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.39
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999733790

Normal statistic for number of bits   :   -2.10
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.54
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999983462

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:52.57

 All tests were passed




Server wird beendet - Lösche Semaphor 183500800.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:49.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5509
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:55.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4242
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7176
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:42.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4228
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:58.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:59.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:08.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:08.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:04:00.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:04:02.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.04
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.08
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    2.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.63
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    3.25
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:16.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.60
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:47.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.65
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.68
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.75
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.84
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.67
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.44
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.45
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.76
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.39
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:06.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7001.57
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:50.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:17.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.60
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:57.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.60
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  164.60
p-value of test                       :  3.6e-3


-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5191.73
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:00.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45629
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869629
  j =  1                              :        399908745
  j =  2                              :            45623
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45764
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869764
  j =  1                              :        399908479
  j =  2                              :            45750
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:26.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:17.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:46.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:01.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:57.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:37.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.72e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 7.41e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:34.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:32.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.08
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:49.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.17
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.01
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.71
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.80
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:47.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.02
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.96
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.09
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.70
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:40.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17635.39
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.54
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.20
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.99
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.21
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.93
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.21
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.89
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.06
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.53
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.34
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.32
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.43
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.09
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.96
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.77
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.04
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.31
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.10
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.69
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.77
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.14
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.41
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.44
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.15
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.46
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.98
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.26
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5034.24
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.74
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.37
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:34.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.68
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:24.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.60
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :    2.67
p-value of test                       :  3.8e-3



-----------------------------------------------
CPU time used                    :  00:02:24.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.93
p-value of test                       :    0.97

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 5.97e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.82
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.21
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.01
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:08.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.42
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:06.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9964

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10036.91
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10034.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:40.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5003.22
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.08
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:48.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.03
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4172.41
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11994.90
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11798.65
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.98
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999987788

Normal statistic for number of bits   :  -0.097
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.77
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999943694

Normal statistic for number of bits   :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:45.09

 All tests were passed




Server wird beendet - Lösche Semaphor 184516608.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5423
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:56.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4236
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:42.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:43.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:59.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:00.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:09.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:09.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:03.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:06.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.18
p-value of test                       :    0.9944

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:47.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:16.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:44.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.52
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.04
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.18
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.02
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:28.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.25
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  268.42
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.50
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:49.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.11
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:07.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6963.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.59
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.11
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.61
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:17.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.80
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:47.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.79
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:35.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5041.06
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:57.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46142
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870142
  j =  1                              :        399907720
  j =  2                              :            46134
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45693
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869693
  j =  1                              :        399908620
  j =  2                              :            45681
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:29.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:18.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:04.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  8.0e-3

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:59.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:39.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 7.60e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:22.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:49.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.17
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.33
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.93
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.63
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.11
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.32
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.65
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:49.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.07
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.36
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   15.72
p-value of test                       :  1.3e-3

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.45
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:40.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17186.40
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   57.27
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.52
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.66
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.23
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.35
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.22
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.53
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.07
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.19
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.89
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.01
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.88
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.16
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.44
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.68
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.49
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.39
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.71
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.47
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.00
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.64
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.60
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5152.92
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.36
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.31
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.58
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.45
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4947.98
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.47
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.16
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.05
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :  -0.086
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:25.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.67
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :   -0.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:28.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 4.31e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.48e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.78
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.75
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.65
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:04.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.31
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:04.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9916

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10013.76
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9808.77
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.10
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:04:08.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4982.15
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:51.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.70
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:52.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4068.38
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4137.39
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11704.56
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11729.77
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.64
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000053221

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.25
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000066478

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:26.93

 All tests were passed




Server wird beendet - Lösche Semaphor 185499648.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5546
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:55.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:40.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:57.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:58.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:07.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:07.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:59.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:05.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.20
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:49.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.03
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    3.08
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     641
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    2.09
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    2.97
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:17.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.01
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9934

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:48.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.18
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.40
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.44
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.55
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.28
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.54
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.70
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.30
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.89
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.25
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:46.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1404.44
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:02.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6892.68
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:50.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.09
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.04
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:00.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.55
p-value of test                       :    0.9901


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.98
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:32.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5132.71
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:56.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46269
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870269
  j =  1                              :        399907463
  j =  2                              :            46267
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45793
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869793
  j =  1                              :        399908414
  j =  2                              :            45793
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:26.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:16.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:02.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:57.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:39.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.51e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.32e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 4.62e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:38.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:37.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.82
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.84
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.33
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.13
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.77
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.62
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.51
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:46.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.23
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.58
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.89
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17602.96
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.39
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.53
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.72
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.95
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.43
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.80
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.85
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.83
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.82
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.12
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.15
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.45
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.18
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.69
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.44
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.66
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.11
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.88
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.08
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.78
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.23
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.59
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.42
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.80
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.67
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.96
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.99
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.88
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.69
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.94
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.61
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:22.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.88
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:24.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.61e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.01
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.54
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.32
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:08.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.14
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:06.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10054.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10103.01
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:54.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:38.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4914.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:46.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4785.95
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3999.43
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4017.72
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11620.30
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11865.43
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.81
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999976625

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.47
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999960422

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   0.010
p-value of test                       :    0.50

Sample variance                       :    2.55
p-value of test                       :  6.4e-3

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:06.88

 All tests were passed




Server wird beendet - Lösche Semaphor 186580992.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5439
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:55.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4251
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:40.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:58.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4436
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:59.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:07.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:07.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:04:00.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:04:05.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    3.56
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:50.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.90
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:19.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.33
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:46.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.82
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.65
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.81
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.48
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.60
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  394.91
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:46.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.66
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:03.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7202.82
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.29
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.25
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:58.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.18
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.28
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5003.97
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:00.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45591
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869591
  j =  1                              :        399908824
  j =  2                              :            45579
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45589
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869589
  j =  1                              :        399908822
  j =  2                              :            45589
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9979

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:28.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9930


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:18.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:48.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:03.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:58.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:39.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.043
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:36.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.68
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:01:38.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.03
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.70
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   94.69
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.49
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:50.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.48
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.88
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.89
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.21
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.96
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.26
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.16
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:28.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.98
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:39.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17333.90
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.23
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.33
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.53
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.43
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.77
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:39.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.78
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.00
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.12
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.79
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.16
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.83
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.57
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.29
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.18
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.23
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.21
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.31
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.75
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.41
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.94
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.06
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5135.74
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.60
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.93
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  448.19
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.37
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5044.39
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.10
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.99
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:36.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.81
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:25.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.30
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:24.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.35e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.57e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.77
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.39
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.50
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:09.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.66
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:07.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9946.44
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9979

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10020.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:39.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.95
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:46.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.91
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:47.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4266.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11713.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12108.39
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.36
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999917921

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.42
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000042247

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   0.050
p-value of test                       :    0.48

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.08e-3
p-value of test                       :    0.9958

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.22
p-value of test                       :    0.01

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:28.70

 All tests were passed




Server wird beendet - Lösche Semaphor 187596800.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:50.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5296
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:54.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4233
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:40.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:57.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:58.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:06.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7019
p-value of test                       :    0.9998    *****


-----------------------------------------------
CPU time used                    :  00:03:07.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:04:00.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:04.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    5.60
p-value of test                       :  1.5e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.73
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    2.49
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:18.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:50.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.09
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.07
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.99
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.32
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.00
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.01
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.77
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:17.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  278.76
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:46.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1465.26
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:11.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7138.19
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.79
p-value of test                       :  4.0e-4    *****

Kolmogorov-Smirnov- statistic = D-    : 3.97e-3
p-value of test                       :    0.9960

Anderson-Darling statistic = A2       :    6.02
p-value of test                       :  1.1e-3

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   10.31
p-value of test                       :    0.9997    *****

-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.71
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:59.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.25
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.18
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:31.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5036.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:00.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45780
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869780
  j =  1                              :        399908443
  j =  2                              :            45774
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45858
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869858
  j =  1                              :        399908287
  j =  2                              :            45852
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:27.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 3.43e-3
p-value of test                       :    0.9962

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:18.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:01.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:57.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:38.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.04e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.33e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 7.38e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:37.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:37.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.14
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.17
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.81
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.90
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.74
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.25
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:50.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.19
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.13
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.46
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.52
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.36
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:39.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17459.10
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:50.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.66
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.06
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.91
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.28
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   33.68
p-value of test                       :  9.2e-3


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.82
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.91
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.71
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.32
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.30
p-value of test                       :    0.9968


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.16
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.13
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.45
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.10
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.28
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.00
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.41
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.95
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.55
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.85
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:40.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.45
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.57
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5037.44
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  310.14
p-value of test                       :    0.9955


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.72
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.24
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.59
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.46
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.10
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.68
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:33.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.55
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:13.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.00
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :   -2.08
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:12.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.48e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.17e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.05
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:18.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.53
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.70
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:55.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.53
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9920.42
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10089.16
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:29.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4825.12
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4775.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4159.03
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4017.37
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11750.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11802.46
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.77
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  7999977528

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.44
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000063322

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.1e-3

Anderson-Darling statistic = A2       :    3.77
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.60
p-value of test                       :  4.6e-3

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:29.60
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 19  BirthdaySpacings, t = 8         0.9998 
 38  Run, r = 0                      0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 188645376.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1461
p-value of test                       :  4.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334581
  j =  1                              :        599997078
  j =  2                              :             1461
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5546
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:43.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4481
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:36.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:35.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:54.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:55.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:02.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:02.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:55.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:04:01.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    2.84
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.13
p-value of test                       :    0.9995    *****

-----------------------------------------------
CPU time used                    :  00:01:50.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.16
p-value of test                       :    0.9980

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.34
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:11.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.30
p-value of test                       :  6.8e-3

Test on the Nm values of W_{n,i}(mNP1):    2.92
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     126
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:40.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.26
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.09
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.66
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.20
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:33.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.15
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:34.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.70
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:34.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.46
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:46.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.27
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:01.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7049.14
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:44.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.00
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:02.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.89
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.39
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:35.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4878.55
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:07.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45845
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869845
  j =  1                              :        399908315
  j =  2                              :            45835
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45853
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869853
  j =  1                              :        399908300
  j =  2                              :            45841
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:16.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9933

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:28.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:18.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:00.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:53.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:34.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.84e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.49e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 9.24e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:22.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:34.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:37.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:49.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   96.64
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  112.55
p-value of test                       :  4.2e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.80
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.69
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:39.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.34
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.14
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:32.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:32.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.05
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17458.14
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.30
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.30
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.44
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.04
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.73
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.55
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.29
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.85
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.66
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.73
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:39.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.08
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.79
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.75
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.15
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.59
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:47.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.61
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.48
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.11
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.24
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.38
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:47.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.83
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.39
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.53
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.33
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.67
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.12
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4862.42
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.79
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.08
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.59
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:30.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.93
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:15.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 3.31e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.39
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.91
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.53
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:09.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:13.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9997.35
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9954.71
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:55.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4983.20
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:48.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.62
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:49.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4161.97
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.28
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11791.30
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11703.96
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:30.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.79
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000087079

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.06
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000194572

Normal statistic for number of bits   :    1.54
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:29.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9903

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:17:17.30
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP2S, t = 3         0.9995 
 61  WeightDistrib, r = 28           4.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 167936001.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5379
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:43.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4517
p-value of test                       :  3.3e-3


-----------------------------------------------
CPU time used                    :  00:01:37.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:35.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:53.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:54.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:01.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:02.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:52.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:58.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.14
p-value of test                       :    0.9991    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:12.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    2.52
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:37.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.60
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.63
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.30
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.45
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.33
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:11.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.45
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.87
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  200.33
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  381.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1372.92
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:03.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6938.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.49
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.68
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:05.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.91
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.37
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:36.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5002.05
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:06.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45965
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869965
  j =  1                              :        399908072
  j =  2                              :            45961
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45896
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869896
  j =  1                              :        399908213
  j =  2                              :            45886
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

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CPU time used                    :  00:05:14.56

Generator state:




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HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


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CPU time used                    :  00:02:32.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :  7.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


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CPU time used                    :  00:02:19.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


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CPU time used                    :  00:01:46.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20


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CPU time used                    :  00:02:04.67

Generator state:




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HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

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CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

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CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

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CPU time used                    :  00:01:33.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.75e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 9.98e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

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CPU time used                    :  00:00:22.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.47e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

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CPU time used                    :  00:00:22.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
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   N =  1,  n = 2000000000,  r =  0,   k = 1


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Normal statistic                      :   -0.48
p-value of test                       :    0.69

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CPU time used                    :  00:00:21.81

Generator state:




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HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


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Normal statistic                      :   -1.15
p-value of test                       :    0.87

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CPU time used                    :  00:00:21.85

Generator state:




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HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.98
p-value of test                       :    0.98

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CPU time used                    :  00:01:35.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

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CPU time used                    :  00:01:35.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


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Number of degrees of freedom          :   67
Chi-square statistic                  :   67.64
p-value of test                       :    0.46

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CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


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Number of degrees of freedom          :   67
Chi-square statistic                  :   83.63
p-value of test                       :    0.08

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CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


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Number of degrees of freedom          :   67
Chi-square statistic                  :   59.37
p-value of test                       :    0.73

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CPU time used                    :  00:00:54.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.08
p-value of test                       :    0.11

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CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


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Number of degrees of freedom          :   37
Chi-square statistic                  :   40.11
p-value of test                       :    0.33

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CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


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Number of degrees of freedom          :   37
Chi-square statistic                  :   40.13
p-value of test                       :    0.33

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CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
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   N =  1,  n = 500000000,  r =  0,   g = 10


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Number of degrees of freedom          :   29
Chi-square statistic                  :   39.38
p-value of test                       :    0.09

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CPU time used                    :  00:01:44.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.25
p-value of test                       :    0.30

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CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.04
p-value of test                       :    0.21

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CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


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Number of degrees of freedom          :    3
Chi-square statistic                  :    3.59
p-value of test                       :    0.31

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CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.49
p-value of test                       :    0.92

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CPU time used                    :  00:01:29.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


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Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

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CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


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Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

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CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.15
p-value of test                       :    0.36

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CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17121.77
p-value of test                       :    0.95



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CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   56.17
p-value of test                       :    0.02


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Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.17
p-value of test                       :    0.25


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Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.01
p-value of test                       :    0.69


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Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.69
p-value of test                       :    0.82


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Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.35
p-value of test                       :    0.78


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CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.11
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.63
p-value of test                       :    0.44


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Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.43
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.02
p-value of test                       :    0.80


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Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.08
p-value of test                       :    0.38


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CPU time used                    :  00:00:40.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.43
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  202.80
p-value of test                       :  1.3e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.94
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.88
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.44
p-value of test                       :    0.43


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CPU time used                    :  00:00:48.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.63
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.67
p-value of test                       :    0.34


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Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.96
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.97
p-value of test                       :    0.28


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Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.69
p-value of test                       :    0.68


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CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.77
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.94
p-value of test                       :    0.31


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Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5062.62
p-value of test                       :    0.26


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Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.58
p-value of test                       :    0.34


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Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.39
p-value of test                       :    0.29


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CPU time used                    :  00:00:36.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.81
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.35
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5072.04
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.36
p-value of test                       :    0.57


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Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  158.72
p-value of test                       :    0.99


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CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.69
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :    1.57
p-value of test                       :    0.06



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CPU time used                    :  00:02:21.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.06
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :   -0.27
p-value of test                       :    0.60



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CPU time used                    :  00:02:17.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 5.92e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:46.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 2.11e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.08
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.05
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.34
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:08.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.30
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:12.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10250.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9985.08
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : -9.99e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:04:08.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4826.28
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    3.69
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4720.24
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:51.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.82
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4180.41
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11799.29
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11825.62
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:30.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.53
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999962165

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.78
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000004069

Normal statistic for number of bits   :   0.032
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.61
p-value of test                       :    0.05

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:13.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.85

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  6.9e-3

Anderson-Darling statistic = A2       :    3.66
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    3.07
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:01:10.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:53.01
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs mNP1, t = 5          0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 168951809.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:40.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5513
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:45.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:37.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:36.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:55.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:03.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:03.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:54.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:00.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    3.45
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:45.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.69
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:12.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:44.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.03
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.18
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.92
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.90
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.90
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.04
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.55
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.68
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  271.83
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.77
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:43.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1380.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7019.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:44.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.70
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.19
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:59.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.02
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.06
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:34.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5098.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:07.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45539
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869539
  j =  1                              :        399908923
  j =  2                              :            45537
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45670
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869670
  j =  1                              :        399908667
  j =  2                              :            45656
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:32.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:19.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:45.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:01.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:55.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:33.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 6.62e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.84e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:32.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:32.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.86
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.61
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:48.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.00
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.21
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.66
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:40.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.56
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.17
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.10
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.83
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.55
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17367.85
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.71
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.82
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.87
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.49
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.07
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.59
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.29
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.82
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.63
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.49
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:39.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.63
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.87
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.62
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.97
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.61
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.12
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.80
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  566.25
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  177.25
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.91
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.06
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.79
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4849.25
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.20
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.61
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.38
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.18
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4993.84
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.80
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.56
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:34.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.77
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:21.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.41
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:22.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.14e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 9.67e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.69e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.77
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:29.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.27
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:08.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.88
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:08.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10115.28
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9871.53
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : -4.04e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:04:00.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.49
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:48.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4907.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:49.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4208.33
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.42
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12053.07
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11846.11
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:29.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.72
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999962906

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.03
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000102013

Normal statistic for number of bits   :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   0.034
p-value of test                       :    0.49

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:12.61

 All tests were passed




Server wird beendet - Lösche Semaphor 170426369.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:39.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5452
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:45.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:37.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:37.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:57.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:04.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:04.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:04:00.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7185
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:02.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:49.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    2.63
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.58
p-value of test                       :  4.8e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     335
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:15.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.57
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:42.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.00
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.43
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.64
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.46
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.83
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.27
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.17
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.88
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:55.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1462.44
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:08.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7266.67
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:58.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.84
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.17
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:13.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.11
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.68
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:37.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5072.59
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:04.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45835
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869835
  j =  1                              :        399908333
  j =  2                              :            45829
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45832
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869832
  j =  1                              :        399908339
  j =  2                              :            45826
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:34.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:53.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:06.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:57.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:38.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 6.14e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:41.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.82
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.10
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.79
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.89
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.17
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.15
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:50.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.83
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.36
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.96
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.28
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:18.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.18
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.63
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   99.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17262.49
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.93
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.09
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.12
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.15
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.02
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.55
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.34
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.82
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.84
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.50
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.54
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.88
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.55
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.97
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.87
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.94
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.05
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.87
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.53
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.63
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.88
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.42
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5044.02
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.85
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.07
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.85
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.46
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4815.59
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.22
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.80
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.04
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:26.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.33
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :    1.50
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:27.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.049
p-value of test                       :    0.48

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.64e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 4.02e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.78e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.21
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.59
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.89
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:07.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.21
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:07.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 2.64e-3
p-value of test                       :    0.9973

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9745.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10008.45
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:04:26.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4966.40
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.55
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:58.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.28
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.98
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11938.53
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:33.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11671.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:34.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.12
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999989363

Normal statistic for number of bits   :  -0.084
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.69
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000049150

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         : 5.46e-3
p-value of test                       :    0.50

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.30
p-value of test                       :    0.01

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:57.44

 All tests were passed




Server wird beendet - Lösche Semaphor 171278337.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5395
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:47.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:38.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:37.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:54.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:55.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7135
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:04.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7453
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:03.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:54.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:00.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:46.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     645
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:13.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.13
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.52
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:43.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.90
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.28
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.64
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.33
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.13
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  487.54
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:42.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1453.75
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:02.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6950.69
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:43.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9916

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.63
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.47
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:03.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.64
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.22
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:35.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5231.64
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:58.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45542
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869542
  j =  1                              :        399908917
  j =  2                              :            45540
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45945
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869945
  j =  1                              :        399908113
  j =  2                              :            45939
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:29.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:17.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:44.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:59.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:37.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.87e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 8.59e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.12e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:27.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:22.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:33.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:33.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.83
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:47.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.30
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.57
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.14
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.38
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.17
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:39.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.22
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.13
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.92
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17695.39
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.65
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.33
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.32
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.93
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   33.55
p-value of test                       :  9.6e-3


-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.14
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.99
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.21
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.04
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.49
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.08
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.13
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.84
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.87
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.73
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.96
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.69
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.33
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.33
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.46
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:48.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.92
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.77
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5097.76
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.25
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.50
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.07
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.40
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.49
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.91
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.30
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:43.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.83
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:25.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.90
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :  -0.033
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:24.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    2.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.80e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 5.77e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.77
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.68
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.56
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:07.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.24
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:09.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10098.20
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10054.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:49.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:48.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:50.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4042.90
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4228.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11821.64
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11726.52
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.67
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999948773

Normal statistic for number of bits   :   -0.40
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.09
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999962468

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    0.22
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.080
p-value of test                       :    0.47

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.82
p-value of test                       :    0.03

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:19.04

 All tests were passed




Server wird beendet - Lösche Semaphor 172523521.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:49.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:39.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:37.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:55.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:02.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:03.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:53.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:04:00.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.97
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     854
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.24
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:15.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:42.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.03
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.73
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.90
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.58
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.25
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:44.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1398.21
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:02.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7010.19
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:43.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.99
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.73
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:01.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.51
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.21
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5076.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:01.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45649
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869649
  j =  1                              :        399908704
  j =  2                              :            45645
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46168
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870168
  j =  1                              :        399907667
  j =  2                              :            46162
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    4.03
p-value of test                       :  8.6e-3


-----------------------------------------------
CPU time used                    :  00:02:29.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:17.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:59.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:56.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:37.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.14e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 3.20e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:33.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:34.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:48.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.38
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.77
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.82
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:48.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.17
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.29
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:39.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.91
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.55
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.05
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.71
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:29.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.69
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.31
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 2.37e-3
p-value of test                       :    0.9976

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16974.15
p-value of test                       :    0.9930



-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.54
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.59
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.70
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.47
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.25
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.77
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.35
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.63
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.02
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.56
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.40
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.00
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.75
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.57
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.39
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.67
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.70
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.27
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.01
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.88
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.34
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.05
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.94
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.11
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.38
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.58
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  441.56
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5107.37
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.75
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.65
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.17
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :    1.07
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:28.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.79
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:26.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.17
p-value of test                       :    0.99

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 2.26e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 6.08e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.75
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.23
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.00
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:09.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:08.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10199.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9905.47
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:53.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4850.46
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:49.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4934.28
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:50.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11619.01
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11771.19
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:29.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.57
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000034318

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.29
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999946526

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :  -0.051
p-value of test                       :    0.52

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.96
p-value of test                       :    0.97

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:16.48

 All tests were passed




Server wird beendet - Lösche Semaphor 173441025.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:03.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5511
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:56.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:40.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:56.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:02.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:02.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:55.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:01.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:14.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.82
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    2.61
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:43.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.65
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.07
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.59
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.12
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.81
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.25
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.77
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  177.87
p-value of test                       :    0.9966

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.04
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:44.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.09
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:00.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6927.92
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:44.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.43
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.45
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:02.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.22
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.66
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:35.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5051.99
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:02.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46190
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870190
  j =  1                              :        399907622
  j =  2                              :            46186
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45562
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869562
  j =  1                              :        399908880
  j =  2                              :            45554
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:28.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:17.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:44.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:59.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:56.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:38.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.43e-4
p-value of test                       :  9.0e-3

Kolmogorov-Smirnov- statistic = D-    : 4.23e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:22.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.94
p-value of test                       :  1.7e-3

-----------------------------------------------
CPU time used                    :  00:01:34.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.11
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.84
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.14
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.56
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.03
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.83
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.13
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:40.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.81
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.23
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.10
p-value of test                       :    0.9915

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.78
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17573.04
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.74
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.34
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.31
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.99
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.17
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.05
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.12
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.55
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.19
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.72
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  108.59
p-value of test                       :    0.9911


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.99
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.35
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.38
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.47
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.52
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.72
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.96
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.70
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.14
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.31
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.09
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5083.23
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  440.14
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.74
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:36.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.75
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.74
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.86
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.83
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.40
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:25.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.55
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :   -1.17
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:23.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 6.43e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.02e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.65
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.15
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  247.28
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:06.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.50
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:08.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9927.41
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10047.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.046
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.033
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:04:01.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.5e-3

Kolmogorov-Smirnov- statistic = D-    : 7.72e-4
p-value of test                       :    0.9992    *****

Anderson-Darling statistic = A2       :    4.36
p-value of test                       :  6.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4601.15
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:01:49.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4805.46
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:49.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.47
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4214.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11897.71
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:29.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11790.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:30.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.30
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999831578

Normal statistic for number of bits   :   -1.33
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.61
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000057667

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:02.43

 All tests were passed




Server wird beendet - Lösche Semaphor 174456833.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:49.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5492
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:58.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:42.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:58.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:59.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:08.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7624
p-value of test                       :  2.0e-4    *****


-----------------------------------------------
CPU time used                    :  00:03:07.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:04:05.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:08.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.22
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     549
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:13.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:42.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.95
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.27
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.09
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.56
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.26
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.38
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.12
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.25
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.06
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:30.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.72
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:57.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1450.02
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:03.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7066.86
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:55.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.59
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.12
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.19
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:16.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.73
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:47.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.89
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:42.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4966.17
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:57.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45648
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869648
  j =  1                              :        399908705
  j =  2                              :            45646
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45900
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869900
  j =  1                              :        399908203
  j =  2                              :            45894
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:31.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:20.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:51.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:07.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:04.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:47.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.76e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:24.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:27.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:27.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.082
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:42.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.82
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.80
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.41
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.35
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.63
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.06
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:51.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.55
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.82
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.00
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.09
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17419.47
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.05
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.73
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.56
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.64
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.54
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.31
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.29
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.59
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.21
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.75
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.60
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.43
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.45
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.48
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.65
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.33
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.80
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.63
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.41
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:42.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.54
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.25
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.18
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.85
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.08
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.81
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.43
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.35
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.23
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:34.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.81
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:26.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.72
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:27.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.14e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 5.51e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.04
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.88
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:09.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.54
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:07.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10040.42
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10029.89
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.074
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:04:34.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:54.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.3e-3

Anderson-Darling statistic = A2       :    3.87
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5122.08
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:58.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4208.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4116.24
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11717.36
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:33.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11775.11
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:36.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.82
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999909122

Normal statistic for number of bits   :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.88
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  7999976757

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.74
p-value of test                       :    0.04

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:52.19
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 19  BirthdaySpacings, t = 8         2.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 175505409.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5585
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:52.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:39.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:56.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:03.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:03.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:55.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:59.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.61
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.73
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    2.58
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     648
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    3.07
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:13.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.02
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     124
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:44.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.67
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.08
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.84
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.65
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.34
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:31.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.08
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:32.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.35
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:32.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:47.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1401.83
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7149.10
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:46.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.14
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.45
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:03.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.02
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.65
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:35.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5071.29
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:57.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45671
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869671
  j =  1                              :        399908661
  j =  2                              :            45665
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45828
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869828
  j =  1                              :        399908348
  j =  2                              :            45820
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:28.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  1.2e-3

Anderson-Darling statistic = A2       :    4.63
p-value of test                       :  4.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  5.7e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:16.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:46.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:03.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:58.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:35.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.54e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 2.49e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:37.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.51
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.35
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.87
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.55
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.26
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.42
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:44.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.84
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.86
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.81
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.17
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:37.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17520.31
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.69
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.68
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.69
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.08
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.52
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:39.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.41
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.85
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.75
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.65
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.83
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:39.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.41
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.97
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.04
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.96
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.76
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.54
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.60
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.69
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.09
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   50.77
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.17
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.38
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5211.70
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.31
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.18
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.79
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5119.28
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.86
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.33
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.41
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :    0.51
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:26.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.74
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :    1.27
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:26.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.19e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:46.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.43e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 9.79e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.79
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.57
p-value of test                       :    0.9916

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:07.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  240.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:08.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9895.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10006.01
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:04:11.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4801.92
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:50.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.00
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:51.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4222.52
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3926.83
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11896.43
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11905.03
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:30.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.52
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000130648

Normal statistic for number of bits   :    1.03
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.67
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999912083

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.63
p-value of test                       :    0.95

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.48
p-value of test                       :    0.07

Sample variance                       :    1.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:38.06

 All tests were passed




Server wird beendet - Lösche Semaphor 176750593.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5435
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:53.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:40.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:39.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:03.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:04.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:56.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:02.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.14
p-value of test                       :    0.9993    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     560
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:13.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:42.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.53
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.95
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.81
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.92
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:10.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.01
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.96
p-value of test                       :    0.9927

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.96
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.26
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:42.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1462.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:01.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6875.38
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:41.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.24
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:02.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.07
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.79
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:35.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4995.47
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:56.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45993
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869993
  j =  1                              :        399908017
  j =  2                              :            45987
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45807
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869807
  j =  1                              :        399908388
  j =  2                              :            45803
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:29.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:17.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:44.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:00.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:55.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:35.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 9.15e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:31.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:32.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.20
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.12
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.70
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.43
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.85
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.64
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:43.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.85
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.24
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:28.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.63
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.87
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17346.51
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.88
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.65
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   44.85
p-value of test                       :  6.1e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.70
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.55
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.24
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.64
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.76
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.17
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.92
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.18
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  452.53
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.56
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.80
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.08
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.34
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.33
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.24
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.74
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.40
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.02
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.36
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.46
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.42
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.74
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.00
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.64
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.74
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.23
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.97
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :    1.39
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:25.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.19
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:25.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.02e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:47.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.35e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:46.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.73
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.76
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  246.66
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.28
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:07.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9864.46
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10304.89
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:53.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5020.94
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:46.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4836.80
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:49.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4202.22
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.91
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11612.36
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11875.53
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.70
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999967013

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   90.94
p-value of test                       :  1.2e-3


-----------------------------------------------
Total number of bits:  7999914498

Normal statistic for number of bits   :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  1.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    3.31
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -1.98
p-value of test                       :    0.98

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:48.52
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP1, t = 3          0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 177799169.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5331
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:53.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:39.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:39.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4474
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:56.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:04.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:04.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:56.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:00.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     954
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.16
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     646
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:15.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:42.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.09
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.01
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.26
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.40
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.04
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.78
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.04
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.31
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  394.69
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.38
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:00.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6982.50
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:42.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.57
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:00.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.99
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.74
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:34.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5252.81
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:03.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46192
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870192
  j =  1                              :        399907618
  j =  2                              :            46188
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45743
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869743
  j =  1                              :        399908517
  j =  2                              :            45737
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:30.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 6.10e-6
p-value of test                       : 1 -  6.1e-6    *****

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  3.9e-4    *****

Anderson-Darling statistic = A2       :    7.36
p-value of test                       :  2.4e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  5.1e-5    *****


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:18.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:44.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:59.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:55.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:35.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 8.38e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:21.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:22.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.51
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:01:36.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:35.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.09
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.86
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.76
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.35
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.18
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.26
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.32
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:40.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.99
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:28.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  157.22
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:38.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17557.89
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.57
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.46
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.01
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.99
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.64
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.91
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.57
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.88
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.08
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.11
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  108.17
p-value of test                       :    0.9918


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.14
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.02
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.03
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.82
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.19
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.41
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.05
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.29
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.99
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.79
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.16
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.55
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.18
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.65
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.09
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.16
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.42
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.65
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.81
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.52
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:26.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.45
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:26.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:46.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.87e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 7.54e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.12
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.61
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.73
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:07.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  242.86
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:09.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10123.93
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9658.85
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:54.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5000.25
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.77
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:50.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.29
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4022.42
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12367.82
p-value of test                       :  2.5e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11998.32
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:29.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.34
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  8000052495

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.32
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999938036

Normal statistic for number of bits   :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:29.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 47  MaxOft, t = 16                  5.1e-5
 99  HammingIndep, L=1200, r=0       2.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 178716673.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:50.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5343
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:53.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:39.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4435
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:56.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:04.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:04.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:55.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:04:00.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     943
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    3.92
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    2.75
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     552
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.06
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.77
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:14.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.93
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:43.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.61
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.57
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.65
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.55
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.84
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  386.03
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:43.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1397.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:01.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7142.43
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:44.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.90
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.63
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:02.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.82
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.40
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:34.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5148.53
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:56.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45601
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869601
  j =  1                              :        399908804
  j =  2                              :            45589
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46209
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870209
  j =  1                              :        399907584
  j =  2                              :            46205
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:29.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:17.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:44.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:00.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:56.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9965

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:35.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 9.53e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:32.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:33.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.67
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.67
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.22
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.06
p-value of test                       :    0.9936

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.36
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.25
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.89
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:40.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.20
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.61
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:29.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.25
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17265.46
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.36
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.76
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.00
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.43
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.70
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.32
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.02
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.18
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.37
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.60
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.36
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.31
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.19
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.46
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.02
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.58
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.52
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.44
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.72
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  470.96
p-value of test                       :  1.6e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.48
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.90
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.34
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.12
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.93
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.20
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5121.55
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.01
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.73
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.10
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:24.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.40
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :    1.25
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:24.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.40e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 4.84e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.91e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.78
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.62
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.65
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:07.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.39
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:07.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10129.80
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10039.42
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.12
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:04:00.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.02
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4966.23
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4245.49
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4162.82
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11796.38
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11959.20
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:29.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.09
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000073954

Normal statistic for number of bits   :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.13
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000035650

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:00.87

 All tests were passed




Server wird beendet - Lösche Semaphor 179765249.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5501
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:54.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7452
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:39.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4232
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7183
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:05.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:54.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7133
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:04:00.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:47.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.97
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:12.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.04
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:45.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.64
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.79
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.41
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.78
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.26
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.92
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.41
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.09
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.98
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:42.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1395.96
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:00.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7106.89
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.89
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.25
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:01.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.04
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.41
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:32.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5101.42
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:57.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45867
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869867
  j =  1                              :        399908269
  j =  2                              :            45861
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45906
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869906
  j =  1                              :        399908190
  j =  2                              :            45902
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.61e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:29.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:17.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:44.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:58.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:55.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  8.9e-3

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:35.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:35.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:35.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.49
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:49.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.98
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.74
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.32
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.91
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.43
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.95
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:39.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.03
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.37e-3
p-value of test                       :    0.9933

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.00
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.25
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.90
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17673.98
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.73
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.97
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.37
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.13
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.00
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.24
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.53
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.77
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.33
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.39
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.75
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.36
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.85
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.13
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.22
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.20
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.33
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.49
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.04
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.51
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.57
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.13
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5178.10
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  455.19
p-value of test                       :  3.9e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.99
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.47
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.09
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5090.50
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.62
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.88
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.92
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:24.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.92
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :   0.097
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:23.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.28

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 6.88e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:46.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.67e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 8.45e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.19
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.16
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.91
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:07.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.24
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:08.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10032.69
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.8e-3

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10271.68
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:45.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4929.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:48.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4699.02
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:50.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.43
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4257.14
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11785.73
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11992.16
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:29.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.85
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999961001

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.07
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999971024

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :  -0.066
p-value of test                       :    0.53

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:35.97

 All tests were passed




Server wird beendet - Lösche Semaphor 180748289.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5502
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:55.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:40.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:40.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:57.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:05.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:04.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:55.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:00.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.90
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:16.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.56
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:48.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.74
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.22
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.95
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.07
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.02
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.40
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.60
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  481.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:43.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1462.05
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:01.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7043.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.08
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.03
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:02.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.07
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.02
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:33.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5058.64
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:13.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45654
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869654
  j =  1                              :        399908696
  j =  2                              :            45646
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45853
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869853
  j =  1                              :        399908296
  j =  2                              :            45849
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:29.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:18.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:00.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9937

-----------------------------------------------
CPU time used                    :  00:01:56.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:35.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.94e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.28e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:34.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:33.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.16
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:48.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.85
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.24
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.29
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.99
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.96
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.99
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:45.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.69
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.50
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.11
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.90
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17405.01
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.98
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.64
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.71
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.89
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.15
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.81
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.44
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.88
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.50
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.70
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.93
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.67
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.04
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.12
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.78
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.80
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.85
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.56
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.68
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.77
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.79
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.68
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.14
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.14
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.70
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.68
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  459.73
p-value of test                       :  4.7e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.43
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.47
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.94
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.03
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : 7.45e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:24.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.15
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :   -1.21
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:24.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.076
p-value of test                       :    0.47

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 4.89e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.81e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.26
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:29.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.99
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.17
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:06.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.47
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:09.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10105.53
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9915.09
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:44.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.08
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:49.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4981.03
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:50.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4337.75
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4036.99
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11958.51
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:29.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11911.32
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:30.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.97
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999954692

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.73
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000136324

Normal statistic for number of bits   :    1.08
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :  -0.041
p-value of test                       :    0.52

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :  -0.065
p-value of test                       :    0.53

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.12

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:07.98

 All tests were passed




Server wird beendet - Lösche Semaphor 181731329.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1263
p-value of test                       :    0.9971

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334383
  j =  1                              :        599997474
  j =  2                              :             1263
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5378
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:09.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4459
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7085
p-value of test                       :    0.9969


-----------------------------------------------
CPU time used                    :  00:02:54.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:16.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:16.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:39.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:39.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:05:02.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:05:01.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.85
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.63
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     568
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.17
p-value of test                       :    0.9969

-----------------------------------------------
CPU time used                    :  00:01:14.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:15.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.57
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    2.16
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:48.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.17
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.14
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.51
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.56
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.31
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.11
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.47
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  490.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:43.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.20
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:01.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7185.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.33
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:04.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.05
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.21
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:33.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5093.05
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:13.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45860
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869860
  j =  1                              :        399908285
  j =  2                              :            45850
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45660
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869660
  j =  1                              :        399908684
  j =  2                              :            45652
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:28.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:17.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:45.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:59.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:33.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 6.03e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.35e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 9.37e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:35.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.15
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.69
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.17
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.22
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.14
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:43.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.74
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:10.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.17
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.47
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.38
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.97
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17293.29
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.79
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.53
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.39
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.17
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.40
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.14
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.34
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.03
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.31
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.79
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.42
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.31
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.55
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.95
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.97
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.43
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.75
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.81
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.92
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.93
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.15
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.91
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4967.74
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.38
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.23
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.39
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.26
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.31
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.33
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.54
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:23.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.27
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:23.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.74e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.05e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.00
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.51
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.47
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:06.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.40
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:07.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9756.97
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10187.50
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:44.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.75
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:50.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4791.81
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:50.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4170.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4147.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11972.78
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:29.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11708.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   30.28
p-value of test                       :    0.9963


-----------------------------------------------
Total number of bits:  8000019684

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.74
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999896960

Normal statistic for number of bits   :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.90

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:16.97

 All tests were passed




Server wird beendet - Lösche Semaphor 182779905.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:50.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5429
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:58.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:41.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:59.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:01.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:10.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:09.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:59.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:04.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.97
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:50.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.53
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.71
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:18.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:47.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.06
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:55.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.98
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.05
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.07
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.35
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.31
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.62
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.94
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.58
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:51.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1485.66
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:03.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7100.32
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.48
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:08.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.75
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:37.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5007.02
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:10.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46106
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870106
  j =  1                              :        399907791
  j =  2                              :            46100
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45876
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869876
  j =  1                              :        399908253
  j =  2                              :            45866
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:30.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:18.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:04.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:36.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 9.93e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 9.94e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      : -8.33e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:39.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:41.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.41
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:50.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.23
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.58
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.03
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.60
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.17
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.25
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:02.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.26
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.52
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17513.30
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.87
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.34
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.76
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.24
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.32
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.86
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   59.55
p-value of test                       :  6.0e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.78
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.20
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.30
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.00
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.26
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.73
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.95
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.45
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.78
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.56
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  448.27
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  194.73
p-value of test                       :  7.2e-4    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.19
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.89
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  300.25
p-value of test                       :    0.9994    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4972.11
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  431.83
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.73
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.93
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.90
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.38
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.49
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.29
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.61
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :   -1.88
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:22.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.65
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:22.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.73
p-value of test                       :    0.96

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 3.10e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 8.27e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.74
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.92
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.24
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:05.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.18
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:07.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10037.45
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9897.38
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:04:25.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4897.16
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:55.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4868.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:54.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.02
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11786.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:31.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12040.97
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:31.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.35
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000077671

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.42
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000069187

Normal statistic for number of bits   :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   0.037
p-value of test                       :    0.49

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:13.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:11.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:21.52
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 77  RandomWalk1 R (L=1000, r=20)    7.2e-4
 78  RandomWalk1 M (L=10000, r=0)    0.9994 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 183762945.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1476
p-value of test                       :  1.5e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334596
  j =  1                              :        599997048
  j =  2                              :             1476
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5409
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:57.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4175
p-value of test                       :    0.9931


-----------------------------------------------
CPU time used                    :  00:01:43.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:42.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:58.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:59.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:05.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:06.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7494
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:59.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:04:01.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     948
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:50.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    2.22
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:17.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:48.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.71
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.18
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.61
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.80
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.43
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.27
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.79
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.60
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:43.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1433.53
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:02.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6777.28
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:42.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.91
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.64
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:03.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.27
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.93
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:33.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4854.59
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:58.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46035
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870035
  j =  1                              :        399907937
  j =  2                              :            46021
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45668
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869668
  j =  1                              :        399908665
  j =  2                              :            45666
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:28.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:17.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:00.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:33.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.99e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.039
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:35.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.71
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.92
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.24
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.02
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.09
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.98
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:46.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.39
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.60
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.064
p-value of test                       :    0.9958

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.99
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.07
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17539.75
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.41
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.97
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.26
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.54
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.75
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.83
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.58
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.23
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.46
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.69
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.07
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.49
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.90
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.63
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.77
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.61
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.75
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  554.98
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.75
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.98
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.31
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.37
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.99
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.99
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.50
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.17
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.66
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5147.34
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  434.15
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.09
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.35
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :    1.41
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:23.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.03
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :    1.96
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:25.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.89
p-value of test                       :    0.03

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 7.84e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.74
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.25
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.15e-4
p-value of test                       :    0.9992    *****

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  242.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:07.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.92
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:07.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9987.99
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9965.43
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:53.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5014.04
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4963.96
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:50.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4192.58
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4006.84
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11850.99
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11893.82
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:30.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.77
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000019108

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.29
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999929762

Normal statistic for number of bits   :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.37
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    1.86
p-value of test                       :    0.03

Sample variance                       :    2.81
p-value of test                       :  2.7e-3

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:52.56

 All tests were passed




Server wird beendet - Lösche Semaphor 184975361.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:01.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:03.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5402
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:59.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4158
p-value of test                       :    0.9968


-----------------------------------------------
CPU time used                    :  00:01:43.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:43.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:58.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:58.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7136
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:06.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:07.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:58.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:01.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    4.11
p-value of test                       :  7.7e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     843
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:50.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:18.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.75
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:48.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.52
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.53
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.57
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.21
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.62
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.57
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.20
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.12
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  382.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:49.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1413.27
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:01.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7035.32
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.97
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.46
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:04.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.56
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.86
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:35.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4801.18
p-value of test                       :    0.9918


-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:13.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45909
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869909
  j =  1                              :        399908187
  j =  2                              :            45899
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45491
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869491
  j =  1                              :        399909022
  j =  2                              :            45483
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:28.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:18.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:46.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:01.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:54.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:33.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 9.66e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 4.24e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.061
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.062
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:37.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.05
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.25
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.79
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.20
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:48.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.55
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.16
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:45.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.12
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.16
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.68
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:28.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.41
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:40.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17150.90
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.17
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.66
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.66
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.64
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.58
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.54
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.58
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.54
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.10
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.93
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.34
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.78
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.88
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.28
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.34
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.76
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.30
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.80
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.22
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.62
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.36
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.81
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.61
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.51
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.40
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.41
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.38
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.42
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.92
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.23
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:36.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.16
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:23.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.93
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :    1.11
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    1.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.29e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:46.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.02e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.49
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.70
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.82
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:04.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.10
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:06.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9978.78
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9902.83
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.80
p-value of test                       :  2.5e-3

-----------------------------------------------
CPU time used                    :  00:03:46.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.44
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:49.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4831.95
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:50.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3963.11
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3942.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11966.76
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11972.49
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:30.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.94
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999999284

Normal statistic for number of bits   : -5.66e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.94
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999911756

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   0.057
p-value of test                       :    0.48

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 6.23e-3
p-value of test                       :    0.9934

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.36
p-value of test                       :    0.9908

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    2.60
p-value of test                       :  5.3e-3

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:54.68

 All tests were passed




Server wird beendet - Lösche Semaphor 186023937.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:50.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5425
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:00.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:44.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7460
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:44.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4229
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:01.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:01.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:11.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:11.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:08.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:04:09.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.09
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:49.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:17.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:47.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.25
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.81
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.93
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.31
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.43
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.19
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:45.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1397.43
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:01.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7232.99
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:42.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.62
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:04.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.67
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  163.15
p-value of test                       :  4.5e-3


-----------------------------------------------
CPU time used                    :  00:01:33.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4938.08
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:09.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46196
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870196
  j =  1                              :        399907613
  j =  2                              :            46186
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45801
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869801
  j =  1                              :        399908401
  j =  2                              :            45795
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:28.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9961


-----------------------------------------------
CPU time used                    :  00:02:18.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:45.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:00.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:55.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:33.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 7.59e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:34.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.77
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:49.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.68
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.92
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.37
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.79
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.54
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.80
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:10.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.47
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:28.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:39.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17127.82
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.06
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.63
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.07
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.19
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.83
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.07
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.58
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.61
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.48
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.45
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  190.07
p-value of test                       :  8.3e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.53
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  441.52
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.49
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.64
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.14
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.03
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.13
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  170.12
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.81
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.28
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.34
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.81
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.14
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.07
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.50
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.28
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4846.42
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.77
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.13
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.60
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :   -1.17
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:22.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.02
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:23.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.61e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 9.20e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.07
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.54
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.61
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:05.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9987

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.01
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:06.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10056.97
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9999.80
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.089
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:45.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:48.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4813.24
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:50.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4152.86
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4206.64
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11701.72
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:28.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12013.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.33
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999946958

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.15
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000029191

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.36
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.52
p-value of test                       :    0.9941

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:18.84

 All tests were passed




Server wird beendet - Lösche Semaphor 187006977.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1263
p-value of test                       :    0.9971

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334383
  j =  1                              :        599997474
  j =  2                              :             1263
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5448
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:59.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:43.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:58.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:07.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:07.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7480
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:58.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:01.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    4.82
p-value of test                       :  3.5e-3

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:50.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:16.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    2.53
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     121
p-value of test                       :    0.9916

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:51.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.23
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.07
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.58
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.02
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:09.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.72
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.05
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.45
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.24
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  377.93
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:44.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1357.92
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:01.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7021.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:42.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.78
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.47
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:04.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.94
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:46.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  158.24
p-value of test                       :  9.4e-3


-----------------------------------------------
CPU time used                    :  00:01:34.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5155.87
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:13.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45993
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869993
  j =  1                              :        399908019
  j =  2                              :            45983
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45951
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869951
  j =  1                              :        399908104
  j =  2                              :            45939
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:28.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.9999    *****

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    3.65
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  1.2e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:18.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.78
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9955


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:44.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:00.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:55.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9977

-----------------------------------------------
CPU time used                    :  00:01:33.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.71e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.68e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.070
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:37.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:38.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.71
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:48.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.38
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.54
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.82
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.76
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.05
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.53
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:42.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.08
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.25
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.43e-3
p-value of test                       :    0.9909

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  156.83
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:39.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17341.03
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.52
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.12
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.18
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.36
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.29
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.36
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.66
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.99
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.88
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.73
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.37
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.65
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.31
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.15
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.30
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.48
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.05
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.13
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.10
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.42
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.83
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.71
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4917.40
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.89
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.17
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.81
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.66
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4858.10
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.66
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.69
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.19
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:24.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.53
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :   -2.36
p-value of test                       :    0.9909



-----------------------------------------------
CPU time used                    :  00:02:22.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.087
p-value of test                       :    0.47

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.26e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.97e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.10
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.62
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.13
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:04.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.48
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:05.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10248.46
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10065.71
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.076
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:55.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:41.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4980.31
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4968.59
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:50.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.99
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.95
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11485.91
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11912.64
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:29.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.42
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000005470

Normal statistic for number of bits   :   0.043
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.01
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999749654

Normal statistic for number of bits   :   -1.98
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.24

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:40.68

 All tests were passed




Server wird beendet - Lösche Semaphor 188022785.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5486
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:42.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:36.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:35.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:54.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:02.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:02.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:53.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:04:00.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    2.49
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     949
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:51.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:12.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:34.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.92
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.93
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.38
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.41
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.18
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.83
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.67
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.99
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.16
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1466.22
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:59.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7031.54
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:47.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.86
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:02.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.24
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.08
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:36.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5033.02
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:18.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45739
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869739
  j =  1                              :        399908525
  j =  2                              :            45733
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45781
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869781
  j =  1                              :        399908441
  j =  2                              :            45775
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:29.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:18.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:45.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:00.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:52.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9945

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:32.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 8.29e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.61e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:22.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:37.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:39.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.25
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.71
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.89
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.86
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:49.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.46
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.99
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:43.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.56
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.75
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.01
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:32.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:31.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17493.38
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.62
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.57
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.62
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.01
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.37
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.09
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.49
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.70
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.48
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.61
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.30
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.26
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.10
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.29
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.58
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.14
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.60
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.65
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.19
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.28
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:47.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.73
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.96
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.64
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.51
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.64
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.58
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  315.81
p-value of test                       :    0.9953


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4901.23
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.29
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.18
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.44
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:16.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.84
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :    1.71
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:13.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:11.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 6.02e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:46.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.65
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.25
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.43
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:12.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.58
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:11.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10170.45
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10100.04
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:04:01.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4960.65
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:49.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4997.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.26
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4246.35
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11770.12
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11898.26
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:30.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.68
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999978083

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.57
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999897929

Normal statistic for number of bits   :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.034
p-value of test                       :    0.51

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:17:14.31

 All tests were passed




Server wird beendet - Lösche Semaphor 167968770.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997261
  j =  2                              :             1368
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5363
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:44.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:37.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:35.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:53.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:03.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:03.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:57.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:00.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    2.65
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:10.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    2.20
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.14
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.53
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.42
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.86
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.49
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.92
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.91
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.94
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.53
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:48.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1382.87
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:07.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6981.18
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:48.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.69
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:09.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.74
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.96
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:39.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5200.49
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:21.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46026
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870026
  j =  1                              :        399907950
  j =  2                              :            46022
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45832
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869832
  j =  1                              :        399908341
  j =  2                              :            45822
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:31.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:18.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:01.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.94e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    4.15
p-value of test                       :  7.5e-3

-----------------------------------------------
CPU time used                    :  00:01:54.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.05e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.86e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:39.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:39.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   41.75
p-value of test                       :    0.9934

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.57
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.79
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.33
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.45
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.88
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:55.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.28
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.39
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.35
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:33.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.70
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:34.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.14
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17319.32
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.81
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.14
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.95
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.53
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.86
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.57
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.90
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.78
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.50
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.13
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.91
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.85
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.11
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.64
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.17
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.36
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.14
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.45
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.34
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.87
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.66
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5072.04
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.70
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.28
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.31
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.33
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.68
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.78
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.84
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.45
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :  -0.015
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:30.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.79
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :   -0.40
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:26.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.24e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 7.18e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 4.39e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.43
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.52
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.34
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:09.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:09.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9938.18
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10031.14
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:04:23.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.77
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:52.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4902.79
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:54.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.22
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11926.21
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:34.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11699.11
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:32.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.35
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000019549

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.54
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000094087

Normal statistic for number of bits   :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    2.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:13.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         : -2.56e-3
p-value of test                       :    0.50

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:11.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:12:56.20

 All tests were passed




Server wird beendet - Lösche Semaphor 169377794.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:55.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5343
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:51.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:40.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:00.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:09.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:10.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:07.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:14.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.95
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:10.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:37.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.06
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:55.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.89
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.70
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.62
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.01
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.99
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.63
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.97
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.86
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:56.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1391.33
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:57.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7049.85
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:49.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:22.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.24
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:47.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.02
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:41.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5094.58
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:29.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9954


-----------------------------------------------
CPU time used                    :  00:03:01.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46100
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870100
  j =  1                              :        399907801
  j =  2                              :            46098
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45957
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869957
  j =  1                              :        399908089
  j =  2                              :            45951
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:30.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:20.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:53.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:11.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:57.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:39.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.73e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 8.52e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:25.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:25.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:48.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.011
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:50.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.68
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.09
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.78
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.94
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.47
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:51.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.85
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.21
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:29.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.35
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.57
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9958

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17434.72
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.18
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.52
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.14
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.63
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.03
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:39.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   57.17
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.14
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.37
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.58
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.75
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.02
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.30
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.62
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.51
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.49
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.95
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.77
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.79
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.00
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.37
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.98
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.05
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.70
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.61
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.42
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.57
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4978.57
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.27
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.16
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.48
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :   -0.92
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:26.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.66
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:27.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.97e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 7.61e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9929

-----------------------------------------------
CPU time used                    :  00:00:47.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.95e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.04
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.82
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.25
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:08.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    5.31
p-value of test                       :  2.2e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  145.93
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:02:07.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10020.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10034.66
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:04:36.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4804.71
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:53.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.69
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:57.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4265.95
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.64
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11748.94
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11744.80
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:36.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.07
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999974957

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.46
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000036778

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.65
p-value of test                       :    0.95

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:14:17.57

 All tests were passed




Server wird beendet - Lösche Semaphor 170721282.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5298
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:51.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:40.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:38.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4446
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:56.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:58.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:08.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:08.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:02.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:08.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.43
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    2.69
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.64
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    3.30
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     644
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    4.16
p-value of test                       :  7.3e-3

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    2.58
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:15.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:43.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.05
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.20
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.07
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.06
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.95
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.65
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.25
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.34
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  376.77
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:53.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1433.88
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:01.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6884.08
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:54.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.70
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   14.05
p-value of test                       :    0.9941

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.59
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:11.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.98
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.76
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:43.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5154.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:16.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45974
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869974
  j =  1                              :        399908052
  j =  2                              :            45974
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45879
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869879
  j =  1                              :        399908247
  j =  2                              :            45869
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:28.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:17.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:45.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:01.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:55.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:36.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.13e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.96e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.01e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.031
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:42.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:44.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.36
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.21
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.16
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.16
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.13
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.19
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:49.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.46
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.41
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.07
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.03
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:29.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.07
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17178.78
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.42
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.74
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.11
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.39
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.06
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.61
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.71
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.25
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.75
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.19
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.43
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.71
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.38
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.32
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.99
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.63
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.16
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.02
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.40
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.85
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.19
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.84
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5136.58
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.67
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.88
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.47
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.10
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4785.44
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.29
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.65
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.25
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   0.012
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:26.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.06
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :    0.14
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:27.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.15e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 9.71e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.55
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.49
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:08.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.60
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:08.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10085.31
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10034.97
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:04:25.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.75
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:55.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4772.53
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.92
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4206.27
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11780.54
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:29.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11673.84
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:29.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.19
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  7999958433

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.03
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000053278

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    2.37
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :  -0.040
p-value of test                       :    0.52

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:07.57

 All tests were passed




Server wird beendet - Lösche Semaphor 172032002.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5568
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:51.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4208
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:40.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:57.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:06.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:05.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:56.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:00.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:53.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    3.63
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:15.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.87
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:42.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.67
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.67
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.72
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.78
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.56
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   87.80
p-value of test                       :  2.5e-3

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.10
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.46
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:44.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.80
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:00.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7009.19
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:45.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.26
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.22
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:03.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.77
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.54
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:35.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4893.66
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:58.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45728
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869728
  j =  1                              :        399908547
  j =  2                              :            45722
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45639
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869639
  j =  1                              :        399908728
  j =  2                              :            45627
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:27.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:18.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:45.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:01.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:34.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.56e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 8.48e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 7.62e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.097
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:34.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:35.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.59
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.82
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.98
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.58
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.90
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.67
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:44.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.55
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.67
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:29.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.12
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:30.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.08
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17362.65
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.79
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.27
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.29
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.04
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.79
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:38.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.10
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.64
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.62
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.00
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.74
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.63
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.14
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  558.17
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.43
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.24
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.83
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.20
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.06
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.13
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.34
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.78
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.19
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.95
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  457.50
p-value of test                       :  3.1e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  238.81
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.17
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.03
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5118.36
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.96
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.15
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.31
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:26.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.13
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:24.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.01e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:46.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 3.43e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.69
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.76
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:08.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:07.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9935.73
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9984.86
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:56.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.47
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:49.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.56
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:50.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.51
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4097.62
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11854.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11819.87
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.35
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000005506

Normal statistic for number of bits   :   0.044
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.27
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999961442

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  3.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    4.14
p-value of test                       :  7.8e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.56
p-value of test                       :    0.9948

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:25.71

 All tests were passed




Server wird beendet - Lösche Semaphor 173080578.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5323
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:55.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7155
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:43.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:59.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4188
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:01.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:12.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7464
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:13.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:04:12.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:16.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     863
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:48.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.69
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.88
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:15.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.20
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.80
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.96
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.50
p-value of test                       :    0.9939

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.56
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.91
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.07
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  369.46
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:55.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1340.51
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:01.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6991.49
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:54.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.21
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.22
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:09.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.01
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.21
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:40.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5118.27
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:56.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45786
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869786
  j =  1                              :        399908429
  j =  2                              :            45784
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45368
p-value of test                       :    0.9916


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869368
  j =  1                              :        399909267
  j =  2                              :            45362
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:30.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:20.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:52.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:06.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:56.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:38.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 9.05e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:24.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:24.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:24.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:42.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:46.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.82
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.96
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.77
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.68
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.10
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.17
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:49.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.56
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.36
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.42
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:29.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:29.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.57
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17509.26
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.96
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.87
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.77
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.16
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.26
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.33
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.26
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.38
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.38
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.23
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.73
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.87
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.66
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.80
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.93
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.16
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.94
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.12
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.79
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.33
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.69
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.26
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5168.82
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.38
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.81
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  441.06
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.66
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.07
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.03
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.19
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.72
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :    1.45
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:27.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.24
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:26.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    2.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 3.05e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.21
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.64
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.37
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:11.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.59
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:09.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10050.69
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9954.39
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:04:29.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4844.68
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:52.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4843.32
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4173.38
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4078.43
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11803.39
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:35.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11688.05
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:36.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.29
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999971621

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.58
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999993578

Normal statistic for number of bits   :  -0.051
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:15.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:50.07

 All tests were passed




Server wird beendet - Lösche Semaphor 173998082.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:50.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5324
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:59.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:42.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:44.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:00.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:02.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:13.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:07.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:12.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:51.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:16.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:18.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     126
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:49.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.39
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:55.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.43
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.63
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.41
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.28
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.08
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.25
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.59
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.48
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  370.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:51.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.99
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:59.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7180.82
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:54.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.25
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.92
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:16.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.36
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.31
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:39.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5119.58
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:00.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46114
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870114
  j =  1                              :        399907776
  j =  2                              :            46106
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46041
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870041
  j =  1                              :        399907923
  j =  2                              :            46031
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:32.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:20.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:51.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:08.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:56.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:38.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 2.53e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:24.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:24.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:49.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:52.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.97
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:51.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.94
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.31
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.50
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.71
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.10
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:50.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.29
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.15
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.09
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:29.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.84
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17395.84
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.63
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.73
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.50
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.60
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.16
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.90
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.49
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.08
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.13
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.98
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.88
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.57
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.20
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.52
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.83
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.62
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.31
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.50
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.00
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.97
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.32
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.93
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.67
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.93
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.17
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.17
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5115.97
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.08
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.13
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.02
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :    1.65
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:27.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.96
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:28.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.96e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 9.31e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.79
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.54
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.93
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:07.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:05.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10073.10
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9792.21
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:04:15.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4692.13
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:52.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4725.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:54.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.97
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4024.11
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11773.74
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:31.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11787.87
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:32.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.99
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999947768

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.20
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000092080

Normal statistic for number of bits   :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:12.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :  -0.098
p-value of test                       :    0.54

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:58.54

 All tests were passed




Server wird beendet - Lösche Semaphor 175210498.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5321
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:56.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4467
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:41.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:58.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:58.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:06.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7168
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:07.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:04:01.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:01.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.87
p-value of test                       :  3.4e-3

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:49.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:17.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.43
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:44.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.49
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.57
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.02
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:11.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.85
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.95
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.86
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.46
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  470.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:44.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1295.42
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:02:01.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7042.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:40.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.44
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:03.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.23
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   89.57
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:33.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4977.55
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:59.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45950
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869950
  j =  1                              :        399908103
  j =  2                              :            45944
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45752
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869752
  j =  1                              :        399908500
  j =  2                              :            45744
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:29.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:17.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:45.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:00.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:57.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:38.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 7.63e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 7.21e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:39.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:39.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.43
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.50
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.33
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.30
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.76
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.26
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.41
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.60
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.51
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.01
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17058.41
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.67
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.60
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.74
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.48
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.41
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.13
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.69
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.98
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.28
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.20
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.20
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.49
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.15
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.81
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.81
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  192.61
p-value of test                       :  5.9e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.17
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  195.19
p-value of test                       :  6.7e-4    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.19
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.40
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.49
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.85
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.40
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.83
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.81
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.11
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5037.56
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.30
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  239.52
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.80
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:24.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.45
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:25.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.72e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 9.11e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.47
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.58
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.2e-3

Kolmogorov-Smirnov- statistic = D-    : 7.10e-3
p-value of test                       :    0.9924

Anderson-Darling statistic = A2       :    6.24
p-value of test                       :  8.1e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  142.73
p-value of test                       :    0.9992    *****

-----------------------------------------------
CPU time used                    :  00:02:08.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.50
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:07.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9992.25
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10047.36
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:42.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4946.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:48.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4842.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4118.09
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.40
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11796.44
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11922.74
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.04
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999883757

Normal statistic for number of bits   :   -0.92
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.67
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999824087

Normal statistic for number of bits   :   -1.39
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   0.027
p-value of test                       :    0.49

Sample variance                       :    2.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:19.00
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 77  RandomWalk1 R (L=1000, r=20)    6.7e-4
 88  PeriodsInStrings, r = 0         0.9992 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 176259074.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5493
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:56.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4429
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:41.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:58.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:06.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:06.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:55.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:00.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.17
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    2.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:15.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.07
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:47.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.21
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.35
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.93
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.61
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.29
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.06
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.64
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.23
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.70
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:43.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1394.29
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:00.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7021.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:40.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.83
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.20
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:07.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.11
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.65
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:34.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5082.76
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:54.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45843
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869843
  j =  1                              :        399908316
  j =  2                              :            45839
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45836
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869836
  j =  1                              :        399908331
  j =  2                              :            45830
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:27.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:17.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:57.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:36.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.95e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.16e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:37.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.56
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.52
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.61
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.97
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.41
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.65
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.66
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:43.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.84
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.11
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.00
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17011.82
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.61
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.60
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.51
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.94
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.25
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.32
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.12
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.02
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.50
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.68
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.28
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.82
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.34
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.37
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.35
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.72
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.22
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.97
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.62
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.41
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.84
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.71
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4842.49
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.74
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.85
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.27
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.78
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4885.51
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.48
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.11
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.77
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:24.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.58
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :    1.35
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:25.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.88e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.45e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 9.08e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.64
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.08
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.62
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:07.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  157.72
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:08.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9935.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9959.85
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.08
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:41.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.31
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:46.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4889.83
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:49.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.95
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4218.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11899.07
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11860.33
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.08
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999968213

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.95
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999926981

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.22
p-value of test                       :    0.99

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.61
p-value of test                       :    0.95

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:25.25

 All tests were passed




Server wird beendet - Lösche Semaphor 177307650.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5455
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:55.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:43.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:59.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4463
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:00.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:12.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:13.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:04:08.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:11.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:49.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     559
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:16.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:45.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.63
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   43.84
p-value of test                       :  6.1e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.04
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:11.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.36
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.75
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.16
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.05
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.45
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:53.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1360.19
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:01.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7156.17
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:56.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.99e-4
p-value of test                       :    0.9997    *****

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   55.34
p-value of test                       :  3.3e-3

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.67
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:14.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.68
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.38
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:37.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5084.94
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:57.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46004
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870004
  j =  1                              :        399908001
  j =  2                              :            45986
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46055
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870055
  j =  1                              :        399907892
  j =  2                              :            46051
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:30.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:19.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:51.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:06.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:38.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.62e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 7.43e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -3.17
p-value of test                       :    0.9992    *****

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:46.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:48.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.23
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.19
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.09
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.99
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.52
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.45
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.99
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.37
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.44
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17604.65
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.29
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.88
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.73
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.02
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.99
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.17
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.16
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   45.63
p-value of test                       :  7.1e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.76
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.86
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.59
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.83
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.10
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.19
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.96
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.80
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.70
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.22
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.54
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.37
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.41
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.58
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.74
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.86
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.17
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.27
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.61
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4972.76
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.06
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.59
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.70
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :   0.012
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:25.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.60
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:24.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.61e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.62e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.39
p-value of test                       :    0.9944

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.64
p-value of test                       :    0.9901

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.32
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:07.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.02
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:07.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.14
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.63
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.32
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:04:13.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5009.79
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:50.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4975.73
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:53.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4036.15
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4300.03
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11590.90
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:30.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11703.10
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:31.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.32
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999858335

Normal statistic for number of bits   :   -1.12
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.12
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000118216

Normal statistic for number of bits   :    0.93
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:18.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 28  SimpPoker, r = 0                6.1e-4
 56  SampleCorr, k = 2               0.9992 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 178356226.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:48.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5407
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:56.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:43.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:58.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:00.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:08.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:08.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:57.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7199
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:01.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.51
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:49.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     641
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     273
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:18.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.94
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:49.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.37
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.04
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.25
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.54
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   24.26
p-value of test                       :    0.9998    *****

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.65
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.41
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.45
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.19
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:44.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.91
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:00.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7066.54
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.33
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.04
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:03.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.05
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.05
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:35.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5206.99
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:00.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45974
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869974
  j =  1                              :        399908055
  j =  2                              :            45968
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45893
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869893
  j =  1                              :        399908218
  j =  2                              :            45885
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:28.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:18.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:45.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:00.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:56.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:37.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.23e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.52e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.77
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.90
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.14
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.07
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.45
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.01
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.05
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:45.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.19
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.01
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.90
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.96
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.52
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17250.36
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.08
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.44
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.84
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.74
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.11
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:39.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.76
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.60
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.61
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.34
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.22
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:39.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.59
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.58
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.11
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.79
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.72
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.06
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.29
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  574.25
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.87
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.61
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.78
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  303.32
p-value of test                       :    0.9991    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5046.44
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.57
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.53
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.80
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.16
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.62
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.97
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.52
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.77
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :   -1.31
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:24.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.69
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :    2.65
p-value of test                       :  4.0e-3



-----------------------------------------------
CPU time used                    :  00:02:25.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   0.049
p-value of test                       :    0.48

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 6.19e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.58e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 4.07e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.70
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.99
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.30
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:06.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.19
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:07.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10149.68
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10011.80
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:34.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4976.60
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:45.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4762.25
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4026.44
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11809.28
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11846.58
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.78
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999896930

Normal statistic for number of bits   :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.33
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  8000042577

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    2.48
p-value of test                       :  7.8e-3

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:56.68
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 31  CouponCollector, r = 10         0.9998 
 78  RandomWalk1 M (L=10000, r=0)    0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 179404802.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:48.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5214
p-value of test                       :    0.9976


-----------------------------------------------
CPU time used                    :  00:03:57.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:41.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:06.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:06.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:56.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:04:01.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     939
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:49.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.28
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:15.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:44.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.46
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.46
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.65
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.43
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.57
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.02
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.82
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:43.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1393.99
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:00.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7121.82
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:42.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.50
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:03.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.78
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.51
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:32.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5044.02
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:59.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45598
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869598
  j =  1                              :        399908809
  j =  2                              :            45588
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45762
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869762
  j =  1                              :        399908478
  j =  2                              :            45758
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:27.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:18.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:45.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:00.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:56.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.30e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:22.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:40.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.011
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:39.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.74
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.69
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:50.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.28
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:44.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.65
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.46
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.47
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:29.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.21
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17358.63
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.59
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.39
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.57
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.74
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.97
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.76
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.26
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.34
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.46
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.21
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.53
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.81
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.33
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.17
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.78
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.66
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.14
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.30
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.83
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.15
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.54
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  447.75
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5123.73
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.71
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.03
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:36.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.98
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.91
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5117.99
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.38
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.02
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.46
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :    1.58
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:25.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.34
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:26.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :  -0.038
p-value of test                       :    0.52

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 8.42e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.93e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 5.91e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.93
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.36
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.49
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:05.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-3
p-value of test                       :    0.9979

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  251.31
p-value of test                       :  8.0e-3

-----------------------------------------------
CPU time used                    :  00:02:05.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9852.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10204.66
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:38.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5012.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:46.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5042.03
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.37
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3965.13
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11478.40
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11775.17
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.00
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999964460

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.37
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000031843

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  2.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.63
p-value of test                       :  4.6e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.93
p-value of test                       :    0.9983

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    1.85
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:46.36

 All tests were passed




Server wird beendet - Lösche Semaphor 180420610.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1251
p-value of test                       :    0.9990    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334371
  j =  1                              :        599997498
  j =  2                              :             1251
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.74

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5438
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:58.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:46.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:01.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:02.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7199
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:14.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:13.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:11.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:14.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:50.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    2.65
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.87
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.78
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    4.20
p-value of test                       :  6.9e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:17.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:48.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.76
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.48
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.64
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.40
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.44
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.73
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.88
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.52
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.53
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.66
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:57.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:05.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7078.86
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:58.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.93e-3
p-value of test                       :    0.9981

Kolmogorov-Smirnov- statistic = D-    :    0.61
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   52.81
p-value of test                       :  6.2e-3

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.96
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:16.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.10
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:46.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   92.04
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:43.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5056.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:54.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45981
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869981
  j =  1                              :        399908040
  j =  2                              :            45977
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45861
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869861
  j =  1                              :        399908281
  j =  2                              :            45855
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:31.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:21.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:52.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:08.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:59.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:37.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 8.56e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:24.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:24.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.093
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:45.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:45.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.47
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.48
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.83
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.00
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.67
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.79
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.62
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.28
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.60
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:28.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.37
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:29.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.76
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17364.51
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.23
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.33
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.62
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.50
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.74
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.62
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.15
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.79
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.09
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.35
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.62
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.72
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.87
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.10
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.37
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.68
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.76
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.25
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.53
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.90
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.07
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.14
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4996.78
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.36
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.48
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.75
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.54
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4855.67
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.00
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.19
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.70
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :    1.46
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:26.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.02
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:24.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 4.28e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 4.20e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.19
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.41
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.66
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:02.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.32
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:03.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.0e-3

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10214.99
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9878.13
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:04:21.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4943.10
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:56.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:58.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4129.77
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.70
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11621.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:35.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11881.52
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.73
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  7999936329

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.84
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000129670

Normal statistic for number of bits   :    1.03
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.68
p-value of test                       :    0.05

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.59
p-value of test                       :    0.06

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:08.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           0.9990 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 181469186.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:58.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:43.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:44.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:00.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:02.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7511
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:12.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7170
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:04:07.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:10.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:50.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.58
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     640
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.54
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    2.20
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:11.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:44.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   22.92
p-value of test                       :  1.8e-3

-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.31
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.74
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.32
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.29
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.28
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:29.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:54.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1371.75
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:02.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7284.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:55.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.36
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.27
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:11.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.06
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:48.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.58
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:43.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4950.49
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:32.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:57.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46454
p-value of test                       :  3.7e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870454
  j =  1                              :        399907095
  j =  2                              :            46448
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45612
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869612
  j =  1                              :        399908778
  j =  2                              :            45608
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:34.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:24.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:52.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:06.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:58.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  9.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:39.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.83e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.94e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.030
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.043
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:52.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:53.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.94
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.86
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.08
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:53.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.48
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.28
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.85
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.63
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17376.15
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.17
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.43
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.86
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.52
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.55
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.84
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.53
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.77
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.02
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.66
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.97
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.51
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.91
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.74
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.43
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.08
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.66
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.93
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.25
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.35
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.49
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.56
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5095.23
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.77
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.89
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.29
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.37
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4924.56
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  433.78
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.55
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:34.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.45
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:20.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.00
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:20.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    2.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:10.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.69e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.96
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.14
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:10.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.07
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:09.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9923.15
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9909.46
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:12.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:04:33.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:51.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.80
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4170.24
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11536.71
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:32.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11911.38
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:34.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.86
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999944510

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.02
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  7999895664

Normal statistic for number of bits   :   -0.82
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:31.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.93
p-value of test                       :    0.97

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   0.041
p-value of test                       :    0.48

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:02.45

 All tests were passed




Server wird beendet - Lösche Semaphor 182517762.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1267
p-value of test                       :    0.9959

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334387
  j =  1                              :        599997466
  j =  2                              :             1267
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:59.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:42.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:44.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4247
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:00.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:09.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:08.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:57.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:04:02.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     945
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:14.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:43.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.81
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.03
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.63
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.68
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.73
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.97
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.61
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  263.54
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  503.50
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:44.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.65
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:00.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7110.02
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:46.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.57
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:03.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.32
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  149.55
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:35.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5041.94
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:04.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46098
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870098
  j =  1                              :        399907809
  j =  2                              :            46088
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45886
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869886
  j =  1                              :        399908233
  j =  2                              :            45876
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:31.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:17.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:44.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:59.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:37.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.37e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:36.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.037
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:40.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.79
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:49.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.70
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.50
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.01
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.13
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:39.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.02
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.66
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.080
p-value of test                       :    0.9941

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.80
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.64
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17456.64
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.79
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.49
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.59
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.24
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.61
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.54
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.52
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.21
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.00
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.11
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.22
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.69
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.41
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.82
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.33
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.80
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.54
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.75
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.02
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.92
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.60
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.44
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.19
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.74
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.15
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.98
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.54
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5077.11
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.74
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.21
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   28.56
p-value of test                       :  4.6e-3


-----------------------------------------------
Normal statistic for number of jumps  :   -2.15
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:20.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.14
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:18.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 5.70e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.21e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.88
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.68
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.30
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:03.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  160.65
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:03.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10177.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9983.46
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:34.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4889.85
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:46.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4978.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:51.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.73
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4280.67
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11804.32
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:29.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11937.10
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:29.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.87
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000001744

Normal statistic for number of bits   :   0.014
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.25
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000025432

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.96
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:51.12

 All tests were passed




Server wird beendet - Lösche Semaphor 183599106.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:38.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5378
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:01.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:45.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7199
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:46.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:03.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:04.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:17.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:15.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:04:10.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:14.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:50.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:16.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:47.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.00
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.69
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.27
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.42
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.76
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.48
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.23
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.44
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.67
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:30.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.40
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:53.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1434.38
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:01.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7033.61
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:59.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.76
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.89
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:16.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.86
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:46.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.21
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:42.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4944.87
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:31.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:56.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45964
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869964
  j =  1                              :        399908076
  j =  2                              :            45956
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46278
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870278
  j =  1                              :        399907451
  j =  2                              :            46264
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:32.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:23.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:52.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:09.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:59.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 7.36e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.41e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 3.27e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:24.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:42.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.095
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:44.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.27
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.99
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.80
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.30
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.81
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.93
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.68
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.02
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.58
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17440.46
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.25
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.86
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.45
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.05
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.51
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:36.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.40
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.85
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.47
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.33
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.23
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.50
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.89
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.36
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.07
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.83
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.91
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.64
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.27
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.37
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.61
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.74
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4901.97
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.16
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.77
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:34.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  442.89
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.11
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4926.85
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.79
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.12
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.85
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:19.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   27.74
p-value of test                       :  6.0e-3


-----------------------------------------------
Normal statistic for number of jumps  :    1.12
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:20.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    2.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:10.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:10.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 3.43e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.29e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.27
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:36.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.58
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:38.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.84
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:24.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:18.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10065.56
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10114.21
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:10.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:04:36.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.48
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:52.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.38
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.38
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.36
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11721.29
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:35.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11831.46
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:38.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.26
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  7999922958

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.44
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000159283

Normal statistic for number of bits   :    1.26
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:20.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:12:30.54

 All tests were passed




Server wird beendet - Lösche Semaphor 184614914.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5377
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:56.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:42.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:58.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:07.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7484
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:07.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:00.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:05.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    3.13
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:50.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     635
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.97
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:15.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.05
p-value of test                       :  9.0e-3

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    2.13
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:46.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.99
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.24
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.25
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.27
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.88
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.03
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.83
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.22
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  396.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:46.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1411.30
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:00.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7055.95
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:44.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-3
p-value of test                       :    0.9986

Kolmogorov-Smirnov- statistic = D-    :    0.73
p-value of test                       :  1.4e-3

Anderson-Darling statistic = A2       :    4.60
p-value of test                       :  5.0e-3

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   57.29
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:05.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.45
p-value of test                       :    0.9940


-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.03
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:36.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5136.21
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:55.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46200
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870200
  j =  1                              :        399907606
  j =  2                              :            46188
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45913
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869913
  j =  1                              :        399908176
  j =  2                              :            45909
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:30.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:24.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:52.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:06.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:35.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:33.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.67
p-value of test                       :    0.9962

-----------------------------------------------
CPU time used                    :  00:01:33.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.79
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.90
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.02
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:48.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.33
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.51
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.55
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:39.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.18
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.63
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.94
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.88
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17683.40
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.53
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.94
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.04
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.84
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.72
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.84
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.85
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.34
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.49
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.01
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.68
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.96
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.94
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  167.69
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  102.06
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:43.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.06
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.42
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.13
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.26
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.59
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.01
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.53
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4883.01
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.47
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.75
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  315.37
p-value of test                       :    0.9956


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.08
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4930.94
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.87
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.86
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.88
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:20.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.12
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:20.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 9.14e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.52e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 9.53e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.49
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.86
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.50
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:04.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.78
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:05.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9934.44
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9889.16
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:35.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4936.42
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:47.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4947.29
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:51.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4305.85
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4231.87
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11611.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11616.64
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:29.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.09
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999809861

Normal statistic for number of bits   :   -1.50
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.77
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999967562

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.76

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.68
p-value of test                       :    0.05

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:07.01

 All tests were passed




Server wird beendet - Lösche Semaphor 185696258.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5492
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:56.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4186
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:42.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:43.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:59.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:07.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:06.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:58.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:07.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    2.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:50.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.70
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     563
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:16.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.35
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.19
p-value of test                       :    0.9926

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:47.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.57
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.21
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.57
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.38
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.32
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:12.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.78
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.31
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.02
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.77
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.14
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:46.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1351.60
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:00.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7171.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:43.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.42
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.15
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:06.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.53
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.07
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5180.09
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:56.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45854
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869854
  j =  1                              :        399908296
  j =  2                              :            45846
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45900
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869900
  j =  1                              :        399908204
  j =  2                              :            45892
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:29.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:25.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:50.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:05.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:34.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.08e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.75e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:33.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:32.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.86
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.91
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.68
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.53
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:48.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.58
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.56
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.96
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:39.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.43
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.37
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.06
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  151.57
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17411.92
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.47
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.96
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.08
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.21
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.50
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.50
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.43
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.60
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.02
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.48
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.88
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.22
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.07
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.18
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.33
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.32
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.75
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.23
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.53
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.05
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.53
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.38
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4930.02
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.79
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.87
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.27
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.60
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.17
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.92
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.78
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.47
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:21.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.73
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :   0.057
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:20.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.65e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 4.71e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.87
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.84
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.14
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:05.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.09
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:05.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10040.52
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9988.77
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:35.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5018.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:47.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4748.95
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:50.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.52
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.85
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11535.77
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11672.48
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:29.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.31
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999929900

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.15
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999992084

Normal statistic for number of bits   :  -0.063
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 7.87e-3
p-value of test                       :    0.9916

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.85
p-value of test                       :    0.97

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.94
p-value of test                       :    0.97

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:11.12

 All tests were passed




Server wird beendet - Lösche Semaphor 186744834.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5519
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:59.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:43.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:45.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:01.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:02.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7453
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:12.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:13.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:04:08.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:16.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:49.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.95
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:17.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.23
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:44.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.81
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.36
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.57
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.08
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.70
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.69
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.66
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  268.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  473.10
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:53.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1443.32
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:01.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6804.39
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:54.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.37
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:15.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.27
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:46.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.26
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:38.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4955.38
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:17.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45879
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869879
  j =  1                              :        399908243
  j =  2                              :            45877
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45835
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869835
  j =  1                              :        399908340
  j =  2                              :            45815
  j =  3                              :               10
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:36.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:27.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:55.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:11.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:36.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.92e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 9.65e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.85e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 5.34e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:39.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.74
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.80
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.27
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.25
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:50.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.20
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.29
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.88
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:48.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.64
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.78
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.92
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.91
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17525.86
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.97
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.07
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.77
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.66
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.95
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.90
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.52
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.23
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.78
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.06
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:37.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.05
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.38
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.78
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.38
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.54
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  192.64
p-value of test                       :  5.8e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.01
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.87
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.38
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   48.81
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.48
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.90
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5109.54
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.44
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.36
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.31
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.94
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5151.52
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.02
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.90
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:34.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.10
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:21.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.76
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :   -0.63
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:20.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.77e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 6.49e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.99e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.76
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.36
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.29
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:03.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.41
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:03.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10020.11
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10102.03
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.018
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:04:23.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4772.82
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:54.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4968.83
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:56.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12100.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:34.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11848.22
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:35.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.21
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000102061

Normal statistic for number of bits   :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.68
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999970670

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    2.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:18.87

 All tests were passed




Server wird beendet - Lösche Semaphor 187793410.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5434
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:59.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4216
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:45.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:00.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4222
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:00.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:11.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:15.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:08.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:04:09.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.77
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:49.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    3.15
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     265
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:16.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.74
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:43.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.78
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.57
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.13
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.53
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.59
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:11.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.26
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.32
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.71
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.31
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.24
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:49.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1501.70
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:03.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7003.88
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:48.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.41
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.80
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:57.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.77
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.36
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:31.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5006.43
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:42.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45505
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869505
  j =  1                              :        399908994
  j =  2                              :            45497
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46113
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870113
  j =  1                              :        399907778
  j =  2                              :            46105
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:16.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:07.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:56.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:11.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.93e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:21.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.22e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:21.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.00
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.42
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:47.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.47
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.21
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.98
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.87
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.22
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   45.33
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:41.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.19
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9926

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.88
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.14
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.85
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17411.15
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.67
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.79
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.25
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.60
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:33.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.57
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.20
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.93
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.34
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.82
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:32.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.84
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.75
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.30
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.35
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.82
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.61
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.04
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.26
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.85
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.13
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.16
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4921.34
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  434.73
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.38
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:31.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.20
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.20
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5034.21
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.65
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.45
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:30.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.19
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:07.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.75
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :   -0.40
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:08.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 7.44e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:40.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.39e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.69
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.01
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9986

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.67
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:52.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.21
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:52.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10009.17
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9982.05
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:49.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:15.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.12
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:41.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5024.11
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:41.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4228.70
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.38
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11679.61
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11788.18
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.33
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  7999979751

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.15
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999916211

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.72
p-value of test                       :    0.04

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   02:56:34.94

 All tests were passed




Server wird beendet - Lösche Semaphor 188841986.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5486
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:43.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:35.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:54.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:55.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:02.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:02.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:55.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:04:01.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.90
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:51.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    2.11
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:13.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:35.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.79
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.81
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.50
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.93
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.80
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.72
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:50.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.94
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7276.77
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:48.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.11
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   40.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:02.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.87
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.66
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:36.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5067.37
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:18.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45724
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869724
  j =  1                              :        399908556
  j =  2                              :            45716
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46151
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870151
  j =  1                              :        399907701
  j =  2                              :            46145
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:16.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:29.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:18.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:45.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:59.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:52.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:15.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:33.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.14e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 8.47e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9992    *****

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.31e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9934

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.46
p-value of test                       :    0.9931

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:35.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:37.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:55.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.98
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.18
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.50
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.33
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.14
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:43.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.87
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.06
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:32.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.85
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:31.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.16
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17420.04
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.96
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.41
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.46
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.01
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.67
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.48
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.97
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.92
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.43
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.28
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:40.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.49
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.09
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  558.87
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.71
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.49
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:48.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.41
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.46
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.96
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.51
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.54
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:47.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.74
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.85
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5108.32
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.00
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.43
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.37
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.59
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5115.74
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  427.94
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.40
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.51
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :    1.37
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:19.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.80
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    0.51
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:13.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 4.82e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.67e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 8.92e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.18
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.11
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.43
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:10.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.40
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:12.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10042.37
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9966.74
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.082
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:47.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4824.97
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4780.19
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:51.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4005.38
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.31
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11667.70
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11834.86
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:30.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.99
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000027367

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.36
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999917102

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    2.87
p-value of test                       :  2.2e-3

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:29.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    0.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:17:03.48
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 53  SampleMean, r = 0               0.9992 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 168001539.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1461
p-value of test                       :  4.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334581
  j =  1                              :        599997078
  j =  2                              :             1461
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:43.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4225
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:37.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:35.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:55.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:55.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:02.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:02.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:53.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:04:00.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    5.12
p-value of test                       :  2.5e-3

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.75
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:14.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    2.19
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:37.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.50
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.12
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.20
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.62
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.32
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.28
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  269.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  521.20
p-value of test                       :  2.5e-3

-----------------------------------------------
CPU time used                    :  00:01:42.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1450.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:59.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7224.88
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.03
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:03.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.62
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.14
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:35.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5281.91
p-value of test                       :  8.5e-3


-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:05.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45808
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869808
  j =  1                              :        399908386
  j =  2                              :            45804
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46199
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870199
  j =  1                              :        399907604
  j =  2                              :            46195
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:14.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:32.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:19.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:45.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:00.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:54.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:32.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.12e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    3.22
p-value of test                       :  6.4e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:33.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:34.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.59
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.81
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.02
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.66
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:47.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.53
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.76
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.36
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.00
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.03
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:30.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.51
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.65
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17266.97
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:55.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.83
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.31
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.53
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.18
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.87
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   59.57
p-value of test                       :  8.0e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   63.36
p-value of test                       :  2.3e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.38
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.90
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.45
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.23
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.85
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.92
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.12
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.00
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:48.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.17
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.80
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.62
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.60
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.89
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:47.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.65
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.65
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5019.54
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.04
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.24
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.79
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.15
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5060.61
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.32
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.36
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.48
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:26.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.47
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :   -1.12
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:18.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   0.033
p-value of test                       :    0.49

Sample variance                       :    2.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 6.88e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 7.07e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.23
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:29.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.14
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.13
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:07.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.24
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:10.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10093.46
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9838.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:04:04.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5012.19
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:49.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4822.83
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:49.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.81
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4030.98
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11741.35
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11916.12
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:29.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.31
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000024853

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.82
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999970385

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.86
p-value of test                       :    0.03

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:53.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 55  SampleCorr, k = 1               6.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 169213955.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:51.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5287
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:44.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:37.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:36.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:54.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4494
p-value of test                       :  8.9e-3


-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:03.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:58.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7172
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:04:01.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.20
p-value of test                       :  7.1e-3

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:12.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:38.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.28
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.69
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.28
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.45
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:11.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.46
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.94
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  392.99
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:52.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1403.23
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:07.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7008.87
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:53.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.59
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:26.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.63
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.88
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:37.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5044.41
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:09.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46260
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870260
  j =  1                              :        399907485
  j =  2                              :            46250
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46025
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870025
  j =  1                              :        399907956
  j =  2                              :            46013
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:35.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:21.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:04.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:54.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:37.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:26.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.95
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:41.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:41.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.66
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.25
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.41
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.40
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.01
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.87
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.14
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.89
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.12
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.46
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.24
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:40.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17703.46
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.95
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.00
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.19
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.23
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.65
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.56
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.34
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.17
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.52
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.81
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.62
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.79
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.22
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.79
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.63
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.91
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.96
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.95
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.28
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  107.52
p-value of test                       :  6.6e-3


-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.18
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.04
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.20
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.46
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.63
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.69
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.39
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.33
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.45
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.79
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   29.42
p-value of test                       :  3.4e-3


-----------------------------------------------
Normal statistic for number of jumps  :   -1.14
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:27.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.81
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :   -1.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:25.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 8.72e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:46.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.53e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 5.98e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.20
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:32.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.04
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.45
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:05.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.52
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:09.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9910.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9794.61
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.099
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:04:30.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.80
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:55.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5018.15
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:56.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.93
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4001.91
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:28.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11865.91
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12014.07
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:35.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.73
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999988289

Normal statistic for number of bits   :  -0.093
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.07
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999927257

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :  -0.057
p-value of test                       :    0.52

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:17.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:35.47

 All tests were passed




Server wird beendet - Lösche Semaphor 170164227.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5516
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:49.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:38.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:37.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:54.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:03.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:02.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7491
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:53.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:59.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:48.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.25
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:14.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    3.65
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:43.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.14
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.49
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.15
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.83
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:45.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1524.23
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:05.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6862.65
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:47.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.89
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.86
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:06.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.28
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.61
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:37.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5038.83
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:14.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:58.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45670
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869670
  j =  1                              :        399908662
  j =  2                              :            45666
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45895
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869895
  j =  1                              :        399908212
  j =  2                              :            45891
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:30.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:16.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:44.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:59.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:34.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:22.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:38.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:38.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.05
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.90
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.23
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.07
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:44.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.09
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.53
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.53
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:28.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.49
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:29.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.22
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17292.52
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.67
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.65
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.92
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.15
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.74
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.49
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.01
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.37
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.26
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.20
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.64
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.04
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.62
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.76
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.47
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.69
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.29
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  577.95
p-value of test                       :  8.9e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.99
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.56
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.24
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.94
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5117.18
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.26
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.30
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.06
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.55
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5123.01
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.94
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.58
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.13
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:26.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.28
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:25.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 4.22e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 7.38e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.29
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.29
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.80
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:06.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 3.97e-3
p-value of test                       :    0.9959

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.11
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:08.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10017.96
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  6.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    4.54
p-value of test                       :  5.0e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9621.21
p-value of test                       :    0.9966

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:04:15.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4762.39
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:50.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4725.93
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:52.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4010.52
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4159.98
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11852.84
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:29.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11741.94
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:30.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.94
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000022621

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.46
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999889640

Normal statistic for number of bits   :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.1e-3

Anderson-Darling statistic = A2       :    3.46
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    1.95
p-value of test                       :    0.03

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:47.09

 All tests were passed




Server wird beendet - Lösche Semaphor 171606019.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:51.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5457
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:47.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:38.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:37.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:55.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:56.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:03.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:03.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:54.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7475
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:00.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.85
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:13.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:43.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.03
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.24
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.97
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.75
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.12
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.89
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.74
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.24
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  501.49
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:44.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1472.90
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:02.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7140.54
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:45.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.97
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:02.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.09
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.52
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:35.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4842.80
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:02.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45903
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869903
  j =  1                              :        399908199
  j =  2                              :            45893
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45640
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869640
  j =  1                              :        399908724
  j =  2                              :            45632
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:29.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:18.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:44.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:59.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:33.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 8.15e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.12
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:35.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.57
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:47.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.85
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.10
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.88
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:48.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.43
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.62
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.36
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.27
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.05
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.65
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.30
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17287.02
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.52
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.42
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.53
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.07
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.22
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.67
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.02
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.59
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.33
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.44
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.92
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.72
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.14
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.82
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.18
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.74
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.68
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.76
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.84
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.98
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.79
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.02
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4952.76
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.82
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.51
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.29
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.57
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.33
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.94
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.79
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:24.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.60
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :   -1.42
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:24.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.21
p-value of test                       :    0.9928

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 9.67e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.59
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.23
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.69
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:07.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.00
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:09.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9871.10
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9825.75
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:52.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5005.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:51.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.53
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:52.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.46
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4070.30
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11863.07
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11859.54
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:30.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.81
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000106333

Normal statistic for number of bits   :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.05
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999957200

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    2.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:37.70

 All tests were passed




Server wird beendet - Lösche Semaphor 172589083.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:50.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5415
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:50.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:38.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:38.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4239
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:55.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7472
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:03.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:02.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:54.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:00.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:47.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.13
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:13.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.39
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:40.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.87
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:10.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.43
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.12
p-value of test                       :    0.9947

-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.76
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.48
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:42.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1460.21
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:00.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6869.27
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.20
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:15.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.4e-3

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.49
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:03.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.80
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   84.02
p-value of test                       :    0.9937


-----------------------------------------------
CPU time used                    :  00:01:33.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5030.82
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:01.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46065
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870065
  j =  1                              :        399907875
  j =  2                              :            46055
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45922
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869922
  j =  1                              :        399908162
  j =  2                              :            45910
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:28.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:18.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:44.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:58.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:34.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 7.82e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.41e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.95e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:21.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:33.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:33.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.31
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.44
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.31
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.38
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:48.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.85
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.73
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.74
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:37.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.69
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.03
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.22
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.86
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17392.09
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.10
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.61
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.68
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.19
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.03
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.22
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.82
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :    9.15
p-value of test                       :    0.9984


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.42
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.88
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.92
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.69
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.82
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.58
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  100.39
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.58
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.87
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.31
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.91
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.99
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.34
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.81
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.26
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.67
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.05
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.87
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.07
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4938.46
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.77
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.93
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.08
p-value of test                       :    0.9950


-----------------------------------------------
Normal statistic for number of jumps  :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:26.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.89
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:26.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.85e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 9.54e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.14
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.32
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.95
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:09.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.23
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:07.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10074.25
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9997.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:47.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5076.74
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:49.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4818.26
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:51.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4193.77
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11744.59
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11974.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:29.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.63
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999981041

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.31
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  7999994373

Normal statistic for number of bits   :  -0.044
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.43

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:29.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 6.76e-3
p-value of test                       :    0.9928

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.94
p-value of test                       :    0.97

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:01.77

 All tests were passed




Server wird beendet - Lösche Semaphor 173506587.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:39.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5267
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:56.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:06.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7467
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:06.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:02.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:05.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     965
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:51.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.03
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:16.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:18.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:49.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.24
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   18.81
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.90
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.54
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.40
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.05
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.90
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.31
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.81
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:53.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.77
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:59.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7033.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:52.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.10
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.90
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:16.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.39
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.68
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:37.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5008.55
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:02.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46193
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870193
  j =  1                              :        399907620
  j =  2                              :            46181
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45597
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869597
  j =  1                              :        399908812
  j =  2                              :            45585
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:33.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 4.82e-3
p-value of test                       :    0.9945

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:20.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:51.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9956

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:07.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:37.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 9.49e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.36e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:49.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:50.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.02
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.42
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.38
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.96
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.69
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.20
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.80
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:50.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.92
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.36
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.56
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.35
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.38
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17384.86
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.79
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.00
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.71
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.71
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.65
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.17
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.36
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.18
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.47
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.61
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.36
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.42
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.18
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.50
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.49
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  104.40
p-value of test                       :    0.9962


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.58
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.32
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.89
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.30
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.40
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.95
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.37
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.27
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.31
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.39
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.59
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4928.88
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.45
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.08
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.97
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:24.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.64
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :    2.43
p-value of test                       :  7.5e-3



-----------------------------------------------
CPU time used                    :  00:02:27.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   0.071
p-value of test                       :    0.47

Sample variance                       :    1.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 7.63e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:46.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.00e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 9.54e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.91
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.78
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.58
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:08.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.37
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:08.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10118.78
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10312.63
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:11.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.15
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:04:31.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4958.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.45
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:58.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.57
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:28.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11877.03
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:36.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11731.47
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:37.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.45
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999888923

Normal statistic for number of bits   :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.08
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000091744

Normal statistic for number of bits   :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:07.65

 All tests were passed




Server wird beendet - Lösche Semaphor 174489627.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:00.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1269
p-value of test                       :    0.9952

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334389
  j =  1                              :        599997462
  j =  2                              :             1269
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5434
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:50.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:39.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:38.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:55.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:56.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:03.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:04.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:55.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:04:00.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:50.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     565
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:17.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:46.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.65
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.00
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.24
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.77
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.34
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.07
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.96
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.33
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:45.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1524.98
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:00.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7264.72
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:46.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.95
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:03.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.62
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.77
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:35.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4915.96
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:00.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46215
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870215
  j =  1                              :        399907571
  j =  2                              :            46213
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45730
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869730
  j =  1                              :        399908545
  j =  2                              :            45720
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 6.01e-3
p-value of test                       :    0.9924

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:29.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:16.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:44.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:59.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:34.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 5.12e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:22.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:22.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:37.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.069
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:38.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.96
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:50.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.98
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.94
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.78
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.59
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.19
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.88
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.80
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.34
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.93
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17140.54
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.30
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.81
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.84
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.97
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.35
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.83
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.33
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.65
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.88
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.34
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.99
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.47
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.33
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.41
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.38
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.02
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.57
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.05
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.23
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.16
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.29
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.69
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.73
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.53
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  274.33
p-value of test                       :  3.8e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.42
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.16
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5058.64
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.38
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.65
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.03
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:25.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.94
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :    1.21
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:26.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   0.065
p-value of test                       :    0.47

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    1.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 8.72e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:47.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.94
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.13
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:05.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.87
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:07.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9781.49
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.80
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.068
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:04:09.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4958.41
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:50.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5008.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:50.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.93
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.13
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11895.58
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11679.63
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:30.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.99
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000051496

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.42
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999972731

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.45
p-value of test                       :    0.93

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :  -0.017
p-value of test                       :    0.51

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:08.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 C (L=10000, r=0)    3.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 175734811.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5338
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:51.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7167
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:04.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:04.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:56.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7457
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:01.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    3.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:51.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.72
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    2.21
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.65
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:18.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:43.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.64
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.13
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.06
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.41
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.68
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.75
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.93
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  202.35
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.76
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:42.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1437.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:00.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7051.70
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:39.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.08
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.22
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:02.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.61
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  153.86
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:34.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5114.35
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:56.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45972
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869972
  j =  1                              :        399908057
  j =  2                              :            45970
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45778
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869778
  j =  1                              :        399908449
  j =  2                              :            45768
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:28.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:17.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:44.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  9.2e-3

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:58.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:55.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:33.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 5.42e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.59e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 3.10e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:21.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:33.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:34.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.81
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.82
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.47
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.83
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.34
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.82
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.59
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:39.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.58
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.79
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.82
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.61
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17750.53
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.34
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.44
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.40
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.68
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.59
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.70
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.47
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.38
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.47
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.68
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.76
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.77
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.19
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.47
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.22
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.07
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.01
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.85
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.03
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.74
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.17
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.67
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5115.21
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.84
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.84
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.60
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.11
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.95
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.92
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.74
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    0.45
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:26.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.97
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :    1.84
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:26.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :  -0.071
p-value of test                       :    0.53

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 6.86e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 3.19e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.99
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.41
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:07.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.90
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:07.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9934.94
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.95
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:50.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.61
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:48.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.5e-3

Anderson-Darling statistic = A2       :    3.53
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5133.27
p-value of test                       :  7.6e-3

-----------------------------------------------
CPU time used                    :  00:01:50.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4157.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.69
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12010.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11794.06
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:29.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.98
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999765956

Normal statistic for number of bits   :   -1.85
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.34
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  8000040639

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    2.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:36.79

 All tests were passed




Server wird beendet - Lösche Semaphor 176816155.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5524
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:54.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:41.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:40.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:58.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4462
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:58.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7180
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:07.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7462
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:08.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:04:06.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7148
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:04:09.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:43.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:06.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    2.94
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     115
p-value of test                       :    0.9983

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:36.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.58
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.73
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.11
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.41
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.48
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.63
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.25
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.60
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1413.74
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:04.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7027.02
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.68
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:17.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :  9.1e-4    *****

Anderson-Darling statistic = A2       :    4.00
p-value of test                       :  9.1e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.27
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:16.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.91
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.62
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5097.48
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:55.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46076
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870076
  j =  1                              :        399907855
  j =  2                              :            46062
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45903
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869903
  j =  1                              :        399908197
  j =  2                              :            45897
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 6.05e-3
p-value of test                       :    0.9923

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:32.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 9.75e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:20.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:50.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:07.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:56.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:36.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 7.92e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:24.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:24.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.050
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:42.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:50.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.53
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.73
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.55
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.67
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.06
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.33
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.88
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.74
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9902

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.43
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17205.62
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:56.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.11
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.73
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.72
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.23
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.04
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:38.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.78
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.08
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.77
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.71
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.10
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.44
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.68
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.13
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.58
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.76
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.18
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.06
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.27
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.85
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.35
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.33
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.96
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.78
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.94
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.90
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.74
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.46
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.48
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.64
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.37
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.73
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:24.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.33
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:25.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.76e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 6.23e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.22
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.00
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.91
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:09.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.35
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:09.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10030.15
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9908.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:11.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:04:30.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4999.94
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:54.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.76
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:58.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3913.09
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.61
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11789.62
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:34.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11883.23
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:36.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.03
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999838478

Normal statistic for number of bits   :   -1.28
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.02
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999984785

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.55
p-value of test                       :    0.06

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:39.98

 All tests were passed




Server wird beendet - Lösche Semaphor 177733659.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:42.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5503
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:52.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:40.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:40.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4238
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:56.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:05.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:05.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:55.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:01.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    3.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    3.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:15.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.63
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:44.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.58
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.15
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.79
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.10
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.56
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.07
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  472.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:42.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1383.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:58.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7066.10
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.96
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:02.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.53
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.23
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:35.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5066.48
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:57.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45806
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869806
  j =  1                              :        399908392
  j =  2                              :            45798
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45732
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869732
  j =  1                              :        399908537
  j =  2                              :            45730
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:27.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:17.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 7.61e-3
p-value of test                       :    0.9912

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.9903


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:44.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:58.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:00.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.86e-3
p-value of test                       :    0.9922

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:41.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:22.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 4.00e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:35.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:33.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.17
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   37.76
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.72
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.36
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.03
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.82
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.32
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:44.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.71
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.77
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17087.97
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.56
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.87
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.45
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.75
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.23
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.77
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.21
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.81
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.16
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.07
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.07
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.49
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.50
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.45
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.30
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.79
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.64
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.67
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.79
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.26
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.14
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.57
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5025.77
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.84
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.55
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.11
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.11
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.27
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.58
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :   0.034
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:24.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.18
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:24.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.18
p-value of test                       :    0.9965

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 2.41e-3
p-value of test                       :    0.9975

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.96
p-value of test                       :    0.98

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.38e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 9.98e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.73e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.93
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:29.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.53
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.53
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:08.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.83
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:07.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9873.40
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9841.19
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.07
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:48.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.77e-3
p-value of test                       :    0.9928

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5101.55
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:49.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4727.55
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:50.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.65
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4249.94
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11982.73
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:28.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11703.72
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:30.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.61
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000057445

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   33.58
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  7999922319

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:44.86

 All tests were passed




Server wird beendet - Lösche Semaphor 179142683.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5377
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:52.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:39.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:57.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:05.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:04.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:56.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:01.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:49.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:14.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:16.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.97
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:43.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.95
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.40
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.23
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.02
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.51
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.31
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.83
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.16
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.86
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:42.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1434.21
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:00.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6915.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.40
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:03.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.63
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.53
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5005.49
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:01.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45810
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869810
  j =  1                              :        399908384
  j =  2                              :            45802
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45401
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869401
  j =  1                              :        399909204
  j =  2                              :            45389
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:28.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:18.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:45.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:59.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9977

-----------------------------------------------
CPU time used                    :  00:01:55.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:32.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 9.91e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:35.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.98
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.81
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.58
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.54
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.42
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.01
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:44.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.13
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.57
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.86
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.77
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.60
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17366.26
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.40
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.93
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.20
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.42
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.07
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.52
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.24
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.96
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.37
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.82
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:39.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.44
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.57
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.14
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.43
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.58
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.47
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.45
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.30
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.31
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.33
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.48
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.08
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.63
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.88
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.44
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.78
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.65
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.99
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.32
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.86
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.39
p-value of test                       :    0.9921


-----------------------------------------------
Normal statistic for number of jumps  :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:25.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.91
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -1.19
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:26.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.49e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:46.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 8.34e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.07
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.91
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:10.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.56
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:07.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9952.27
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10169.96
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:50.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4789.20
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:48.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4910.47
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:50.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3988.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12036.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11682.24
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:30.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.94
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  7999995255

Normal statistic for number of bits   :  -0.038
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.71
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999959204

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :  -0.012
p-value of test                       :    0.50

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:59.44

 All tests were passed




Server wird beendet - Lösche Semaphor 180092955.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5393
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:51.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:40.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:39.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:57.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:04.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:55.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:01.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.23
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.87
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:49.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:15.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:46.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.46
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.69
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.87
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:10.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.13
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.11
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.90
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.50
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:43.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1414.06
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:00.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7052.55
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.22
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.32
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:03.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.80
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.68
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:35.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5051.40
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:55.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45792
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869792
  j =  1                              :        399908421
  j =  2                              :            45782
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46066
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870066
  j =  1                              :        399907869
  j =  2                              :            46064
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:27.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:17.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:44.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:59.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:55.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.94e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:38.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:36.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.19
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.33
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.68
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.41
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:50.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.26
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.90
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:43.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.26
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.65
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.14
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.90
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17621.95
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.45
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.48
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.37
p-value of test                       :    0.9909


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.94
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.07
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.57
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.88
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.11
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.66
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.94
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.36
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.50
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.02
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.90
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  111.11
p-value of test                       :  3.4e-3


-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.24
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.92
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.57
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.36
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.16
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.12
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.11
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4981.52
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.51
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.90
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.89
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.75
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5207.08
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.61
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.13
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.69
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :  -0.091
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:22.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.82
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :    0.11
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:22.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.28

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.62e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 8.08e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:46.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 5.30e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.21
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.42
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:08.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.18
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:07.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9815.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9760.00
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:47.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4771.29
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5026.17
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:50.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3997.05
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.72
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11708.39
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:28.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11523.72
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:31.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.35
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000031126

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.00
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999972416

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    2.37
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:45.70

 All tests were passed




Server wird beendet - Lösche Semaphor 181141531.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:41.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5509
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:53.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:39.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4447
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:57.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:04.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:04.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:55.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:04:01.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.08
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    4.06
p-value of test                       :  8.1e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     838
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:51.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.82
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     566
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.42
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:18.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.75
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:46.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.19
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.84
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.70
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.34
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.39
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.14
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.88
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  185.84
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.89
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:44.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1393.06
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7134.72
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:40.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.70
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.04
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:02.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.94
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.13
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:35.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4895.06
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:13.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45760
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869760
  j =  1                              :        399908487
  j =  2                              :            45746
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45955
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869955
  j =  1                              :        399908096
  j =  2                              :            45943
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:28.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:18.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:45.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:00.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:54.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:32.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:36.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:35.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.44
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.35
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.48
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.14
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.85
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.73
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.82
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.51
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.27
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17540.57
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.74
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.59
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.82
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.00
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.38
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.68
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.19
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.56
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.87
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.02
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.15
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.44
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.99
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.25
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.86
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.72
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.76
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.26
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.57
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.78
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.72
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.54
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5102.74
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  451.39
p-value of test                       :  5.6e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.38
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:37.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.61
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.20
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.18
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.89
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.91
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.22
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:24.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.95
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:24.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   0.049
p-value of test                       :    0.48

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:10.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:10.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.61e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 5.09e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.94e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 9.56e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.12
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.18
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:05.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.73
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:07.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9894.71
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9841.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.37
p-value of test                       :    0.9911

-----------------------------------------------
CPU time used                    :  00:03:45.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4868.64
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:48.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4793.14
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:50.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.68
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.35
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11769.14
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11855.25
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:29.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.87
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000040048

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.93
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999997454

Normal statistic for number of bits   :  -0.020
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.56
p-value of test                       :    0.06

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:16.55

 All tests were passed




Server wird beendet - Lösche Semaphor 182124571.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5504
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:55.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:40.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4215
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:57.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:04.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:04.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7095
p-value of test                       :    0.9956


-----------------------------------------------
CPU time used                    :  00:03:55.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:01.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    2.57
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:13.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:42.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   21.79
p-value of test                       :  2.8e-3

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.90
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.37
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.62
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.37
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.07
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.71
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.72
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  202.98
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.62
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:44.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1478.88
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:00.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6878.09
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:42.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.88
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.07
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:01.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.01
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.85
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:33.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5013.41
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:06.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45607
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869607
  j =  1                              :        399908789
  j =  2                              :            45601
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46153
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870153
  j =  1                              :        399907695
  j =  2                              :            46151
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:28.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:18.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:46.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:00.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:55.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:33.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.59e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.015
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:21.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:35.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:36.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.21
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.57
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.20
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.73
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.90
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:51.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.00
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.86
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:39.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.54
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.85
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.95
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.32
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.81
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.07
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17411.19
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.02
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.75
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.73
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.01
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.81
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.32
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.91
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.98
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.68
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.12
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.24
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.53
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  424.01
p-value of test                       :    0.9941


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.05
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.33
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.25
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  194.54
p-value of test                       :  4.5e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.79
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.26
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.19
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.05
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.07
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4730.00
p-value of test                       :    0.9970


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.92
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.54
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.74
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.81
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4959.97
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.84
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.76
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.40
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:24.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.47
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :    2.47
p-value of test                       :  6.8e-3



-----------------------------------------------
CPU time used                    :  00:02:24.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    2.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 4.31e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:46.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 5.91e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.18
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.24
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.45
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:06.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.00
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:08.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10161.39
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 6.46e-3
p-value of test                       :    0.9932

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9682.40
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.023
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:45.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4970.03
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5088.46
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:50.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4299.94
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.24
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11822.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11845.50
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:30.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.55
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999876794

Normal statistic for number of bits   :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.32
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999834980

Normal statistic for number of bits   :   -1.30
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    2.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:19.96

 All tests were passed




Server wird beendet - Lösche Semaphor 183009307.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5436
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:56.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:42.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7192
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:41.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:55.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:04.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:04.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:55.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:04:00.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.45
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:46.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:14.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    2.05
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     125
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.80
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:44.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.67
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.93
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.55
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.32
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.04
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.71
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.67
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.55
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:43.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1511.66
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7041.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:42.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.82
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.80
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:00.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.03
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.47
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5024.93
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:06.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46020
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870020
  j =  1                              :        399907963
  j =  2                              :            46014
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45926
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869926
  j =  1                              :        399908155
  j =  2                              :            45912
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:28.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:18.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:46.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:01.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:55.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:34.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 3.05e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 3.40e-4
p-value of test                       :  9.9e-3

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:33.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:35.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.33
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.95
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.51
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.25
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.67
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.42
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:41.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.03
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.51
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.17
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:39.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17241.96
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.36
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.35
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.10
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.46
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.80
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.44
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.27
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.65
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.57
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.96
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.05
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.33
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.72
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.93
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.19
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.18
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.61
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.06
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.15
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.11
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.33
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.69
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.67
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.27
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.47
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.81
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.38
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5106.31
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.78
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.19
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.87
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:24.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.07
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    1.15
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:24.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.88
p-value of test                       :    0.97

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.76
p-value of test                       :    0.96

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.23e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.32
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.15
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.16
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:04.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:06.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9817.73
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9885.49
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.24
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:56.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:44.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:48.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:50.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4025.75
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.51
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11563.01
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11803.69
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:30.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.58
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999970256

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.27
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999887765

Normal statistic for number of bits   :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.85

Sample variance                       :    1.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:05.70

 All tests were passed




Server wird beendet - Lösche Semaphor 183959579.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1269
p-value of test                       :    0.9952

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334389
  j =  1                              :        599997462
  j =  2                              :             1269
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5459
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:57.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:42.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:57.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:06.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:05.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:56.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:01.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     863
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.64
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     650
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.09
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:16.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.54
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    2.40
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     183
p-value of test                       :  5.0e-3

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:38.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.83
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.39
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.95
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.65
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.90
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:44.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1508.84
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:01.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7152.00
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:02.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.29
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  145.04
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4974.11
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:30.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:21.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46196
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870196
  j =  1                              :        399907611
  j =  2                              :            46190
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:13.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45902
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869902
  j =  1                              :        399908201
  j =  2                              :            45892
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:29.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.48
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:24.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:51.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:07.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:55.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:33.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.98e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:33.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.041
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:33.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.56
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.95
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.57
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.04
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.01
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.89
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.71
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:44.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   20.70
p-value of test                       :    0.9950

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.00
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.84
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17315.72
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.76
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.43
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.51
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.55
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.06
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:37.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.02
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.90
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.80
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.25
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.22
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.04
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.39
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.08
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.01
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.74
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.19
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.89
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.03
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.73
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.87
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.96
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4945.27
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.30
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.26
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.80
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.80
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5077.17
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.44
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.95
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.73
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:24.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.96
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :   -1.93
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:23.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.71
p-value of test                       :    0.96

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.34e-4
p-value of test                       :    0.9973

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 8.70e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.80
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.77
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.37
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:06.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.64
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:08.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10034.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9859.12
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:41.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4996.94
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5002.91
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:50.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4290.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4070.34
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12110.48
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11848.36
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:31.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.91
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000161326

Normal statistic for number of bits   :    1.28
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.30
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000026017

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.57
p-value of test                       :    0.94

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.84
p-value of test                       :    0.97

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:39.22

 All tests were passed




Server wird beendet - Lösche Semaphor 185008155.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:50.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:58.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:42.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4413
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:58.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:06.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:05.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:55.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:00.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.74
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     331
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:13.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:41.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.64
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.19
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.20
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.13
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.64
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.99
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.67
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  193.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  505.35
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1504.48
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7107.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.85
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.52e-3
p-value of test                       :    0.9953

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    4.03
p-value of test                       :  8.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   97.72
p-value of test                       :  1.5e-3

-----------------------------------------------
CPU time used                    :  00:03:03.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.24
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.11
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4986.82
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:01.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45744
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869744
  j =  1                              :        399908516
  j =  2                              :            45736
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46317
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870317
  j =  1                              :        399907373
  j =  2                              :            46303
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:29.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:24.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9902


-----------------------------------------------
CPU time used                    :  00:01:53.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:08.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:54.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:33.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.88e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.015
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:33.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:33.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   95.82
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:48.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.99
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.00
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:48.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.27
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.23
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.02
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:43.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.26
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.41
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.56
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.71
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17578.47
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.08
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.02
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.91
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.83
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.52
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.41
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.82
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   44.24
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.50
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.45
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.40
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.94
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.59
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  102.82
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.06
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.32
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.97
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.13
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.36
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.89
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.95
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.01
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5113.02
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.40
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.70
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.27
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.63
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4960.35
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.31
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.91
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:36.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.49
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:22.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.23
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:23.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    2.57
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.87e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 6.27e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 8.23e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.63
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.43
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.13
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:04.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.23
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:07.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10218.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10246.00
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:42.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 8.18e-3
p-value of test                       :    0.9912

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4750.06
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5047.21
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:50.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4123.95
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.70
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11862.80
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:28.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11756.72
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:30.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.33
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000004927

Normal statistic for number of bits   :   0.039
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.71
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000055594

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   0.055
p-value of test                       :    0.48

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    1.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:20.52

 All tests were passed




Server wird beendet - Lösche Semaphor 186056731.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:40.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5382
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:58.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:42.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:41.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:05.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:06.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7124
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:56.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7171
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:04:01.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    5.23
p-value of test                       :  2.2e-3

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    2.76
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    2.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:14.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     129
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:45.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.24
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.24
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.06
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.92
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.92
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.13
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.67
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1346.21
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:00.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7062.78
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:04.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.21
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.39
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:35.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5000.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:00.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45854
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869854
  j =  1                              :        399908294
  j =  2                              :            45850
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45375
p-value of test                       :    0.9908


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869375
  j =  1                              :        399909252
  j =  2                              :            45371
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:30.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:25.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:52.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:07.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:55.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:33.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 9.74e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:34.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:35.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:49.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.99
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.52
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.84
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:48.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.89
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.30
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.99
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.81
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.28
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:29.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.47
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17313.99
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.36
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.54
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.55
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.79
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.11
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.76
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.66
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.70
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.24
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.35
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.73
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.65
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.95
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.81
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.40
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.77
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.94
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.32
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  170.85
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.73
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  323.20
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4993.06
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.54
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  265.71
p-value of test                       :  1.3e-3


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.34
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.59
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5075.82
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.26
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.83
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.59
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :   0.039
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:21.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.65
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :  -0.095
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:22.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.58
p-value of test                       :  5.8e-4    *****

Anderson-Darling statistic = A2       :    4.33
p-value of test                       :  6.3e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.28
p-value of test                       :    0.01

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.44e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 4.18e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   22.83
p-value of test                       :  3.6e-3

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.48
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.03
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:05.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.99
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:07.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9916.35
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9952.15
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:46.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.58
p-value of test                       :  5.8e-4    *****

Anderson-Darling statistic = A2       :    3.74
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5040.58
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4967.85
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:49.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4035.10
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4224.52
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11860.14
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11729.66
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:30.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.38
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000115807

Normal statistic for number of bits   :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.87
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999875861

Normal statistic for number of bits   :   -0.98
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.68
p-value of test                       :    0.05

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:35.51

 All tests were passed




Server wird beendet - Lösche Semaphor 187072539.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5304
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:58.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:42.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4221
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:57.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:06.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:05.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:56.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:04:00.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.72
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:46.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    5.21
p-value of test                       :  2.3e-3

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.88
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:13.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:42.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.37
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.11
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.81
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.75
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.71
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.62
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.95
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.90
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:45.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1393.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:00.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6853.97
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:43.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   49.46
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.24
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:04.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.33
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.97
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:34.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5063.49
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:00.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45748
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869748
  j =  1                              :        399908507
  j =  2                              :            45742
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45794
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869794
  j =  1                              :        399908416
  j =  2                              :            45786
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:28.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:17.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:44.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  5.1e-3

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:04.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:55.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:33.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 9.97e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.44e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:35.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:35.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.95
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:48.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.88
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.21
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.94
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.62
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:39.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.56
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.39
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17659.16
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.60
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.22
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.95
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.58
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.22
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.80
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.17
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.83
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.86
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.51
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.20
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.16
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.32
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.27
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.38
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.61
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.67
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.05
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.97
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.27
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.80
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.05
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.70
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.04
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.54
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.78
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.55
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5115.17
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.87
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.32
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.22
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :   -2.18
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:02:23.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.84
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :    1.63
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:22.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.72

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.42e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.88e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 4.00e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.39
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.29
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:04.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.10
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:05.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9967.85
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10082.34
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:42.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:48.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.80
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:50.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3964.10
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.31
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12085.74
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11738.72
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.33
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999880928

Normal statistic for number of bits   :   -0.94
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.28
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  7999877097

Normal statistic for number of bits   :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.88
p-value of test                       :    0.03

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:00.50

 All tests were passed




Server wird beendet - Lösche Semaphor 188088347.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5394
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:42.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:36.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:35.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:54.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:03.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:03.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:54.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:00.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     867
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:50.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.97
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    3.33
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:13.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.84
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    2.02
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     121
p-value of test                       :    0.9916

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:39.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.40
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.73
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.62
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.26
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.71
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.35
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  194.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:44.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1552.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:59.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7309.36
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:41.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.10
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.94e-3
p-value of test                       :    0.9948

Kolmogorov-Smirnov- statistic = D-    :    0.64
p-value of test                       :  7.2e-5    *****

Anderson-Darling statistic = A2       :    7.04
p-value of test                       :  3.5e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :  105.24
p-value of test                       :  2.8e-4    *****

-----------------------------------------------
CPU time used                    :  00:03:03.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.16
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.25
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:37.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5108.86
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:06.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46052
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870052
  j =  1                              :        399907904
  j =  2                              :            46036
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45921
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869921
  j =  1                              :        399908163
  j =  2                              :            45911
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:29.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:20.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 6.38e-3
p-value of test                       :    0.9928

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:46.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:01.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:52.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9944

-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:32.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.67e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.40e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:22.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.35e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 2.33e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:34.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:38.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.60
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:47.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.25
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:47.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.98
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.87
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.87
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:37.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.27
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.30
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:33.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:31.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.92
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17336.86
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.70
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.80
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.03
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.68
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.92
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.27
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.88
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.52
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.49
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.58
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.49
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.29
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.75
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.08
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.32
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:49.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.23
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.13
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.17
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.36
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.31
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:48.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.37
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.91
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5110.78
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.34
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.41
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.11
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.45
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.45
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.98
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.14
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.59
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:21.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.33
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:14.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.56
p-value of test                       :    0.06

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.35e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.77e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 6.22e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.87
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.88
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.84
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:11.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:12.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10123.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10102.68
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:04:11.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.94
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:49.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4911.46
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4030.74
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4049.62
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11832.06
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11757.61
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.10
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999977045

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.85
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000056989

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.96
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   0.075
p-value of test                       :    0.47

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :  -0.096
p-value of test                       :    0.54

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:16:33.59
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 39  Run, r = 15                     2.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 168034308.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:40.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:52.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5407
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:43.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:37.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:36.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:55.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:03.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:02.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:54.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:04:01.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    6.55
p-value of test                       :  5.5e-4    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     989
p-value of test                       :  1.8e-3

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    2.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    3.87
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:10.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:38.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   20.33
p-value of test                       :  4.9e-3

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.31
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.26
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.98
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.39
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.67
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.04
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.06
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:45.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1524.70
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:59.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7038.23
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:46.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.60
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   14.36
p-value of test                       :    0.9929

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:03.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.18
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   90.32
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:35.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4992.38
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:05.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46293
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870293
  j =  1                              :        399907416
  j =  2                              :            46289
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45723
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869723
  j =  1                              :        399908555
  j =  2                              :            45721
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:32.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:20.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:00.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9994    *****

-----------------------------------------------
CPU time used                    :  00:01:53.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:32.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.50e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 9.74e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 8.39e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:22.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:34.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.04
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:47.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.02
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.65
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.63
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.24
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.54
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.94
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:39.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.85
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.53
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.99
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:30.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:29.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:18.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.90
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17581.71
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.28
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.41
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.42
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.44
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.14
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.42
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.46
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.11
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.06
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.59
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.86
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.40
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  555.44
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.27
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:48.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.60
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.97
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  439.91
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.46
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.92
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:47.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.70
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.93
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4873.04
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.64
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.53
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.45
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.62
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.97
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.08
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.75
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:36.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.50
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:23.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.41
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:17.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.18
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    2.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 6.87e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.22e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.58
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:29.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.03
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.10
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:07.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.69
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  156.81
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:11.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10177.10
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10039.39
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:04:02.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.15
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4987.10
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:50.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4247.93
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.22
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11929.38
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11829.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.13
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000013972

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.81
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999787577

Normal statistic for number of bits   :   -1.68
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:42.73
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP1, t = 3          5.5e-4
 50  SampleProd, t = 8               0.9994 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 169345028.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:40.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5466
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:46.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:38.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:38.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:57.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:58.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:07.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:09.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7498
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:04:07.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7139
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:04:13.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.15
p-value of test                       :    0.9987

Stat. AD after spacings (mNP2-S)      :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.56
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.75
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:15.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    2.40
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     112
p-value of test                       :    0.9993    *****

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:49.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.14
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.52
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.37
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.14
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:10.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.60
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.36
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.23
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.37
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:57.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.44
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:04.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6967.05
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:52.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.57
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.46
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.16
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:10.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.08
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.09
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:41.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5069.73
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:33.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:23.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45997
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869997
  j =  1                              :        399908007
  j =  2                              :            45995
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45639
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869639
  j =  1                              :        399908727
  j =  2                              :            45629
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:30.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:33.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.55e-3
p-value of test                       :    0.9906

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.26
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:21.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:51.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 9.64e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:10.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:56.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  9.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.59
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:39.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 3.19e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.00e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:25.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:49.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:49.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.40
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.92
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.32
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.28
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.23
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.81
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.83
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:52.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.30
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.42
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.21
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:31.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.14
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.32
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.28
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17851.91
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.24
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.56
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.97
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.12
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.33
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.53
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   60.18
p-value of test                       :  5.1e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.99
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.82
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.31
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.79
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.65
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.57
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.32
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.52
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.75
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.06
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.75
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.54
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.01
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.80
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.44
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4891.68
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.12
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.19
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.82
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.99
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.87
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.68
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.35
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.78
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:24.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.77
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :    0.93
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:24.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   0.082
p-value of test                       :    0.47

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 5.08e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 6.79e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.67
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.19
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.86
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:08.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.22
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:08.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10196.88
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10016.97
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:10.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:04:36.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4841.12
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:52.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.70
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.71
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11850.14
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:33.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12022.51
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:35.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.97
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000037180

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.43
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999941837

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :  -0.073
p-value of test                       :    0.53

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :  -0.065
p-value of test                       :    0.53

Sample variance                       :    0.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:15:39.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs NJumps, t = 16       0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 170295300.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:46.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5274
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:50.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:39.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:38.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:56.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:03.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:56.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:00.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.53
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.72
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:48.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:16.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:42.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.09
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.46
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.09
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.60
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.55
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  288.33
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.38
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1489.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:00.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7127.75
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:47.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.42
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.57
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:05.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.08
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  144.78
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:35.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5185.07
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:07.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45687
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869687
  j =  1                              :        399908629
  j =  2                              :            45681
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45569
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869569
  j =  1                              :        399908865
  j =  2                              :            45563
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:27.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 7.32e-3
p-value of test                       :    0.9910

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:18.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:45.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:01.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:54.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:01:31.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.41e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 2.55e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:35.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:37.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.36
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:48.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.45
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.05
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.24
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.08
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:45.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.20
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.60
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:29.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.65
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:28.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.23
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.63
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17725.98
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.54
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.03
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.65
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.72
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.71
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.99
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.63
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.52
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.43
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.99
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.05
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.36
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.44
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.95
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.62
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.03
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.03
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.28
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.71
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.92
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.06
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.70
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5232.93
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.77
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.10
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.90
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.13
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.31
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.15
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.94
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :   -0.96
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:25.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.39
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:26.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:46.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.59e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.23
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.35
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.84
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:08.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.61
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:07.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9916.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9854.83
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:55.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:49.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4962.83
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:50.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4037.18
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4174.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11692.29
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:29.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11694.47
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:31.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.57
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999858422

Normal statistic for number of bits   :   -1.12
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.05
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000004006

Normal statistic for number of bits   :   0.032
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.92

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:27.75

 All tests were passed




Server wird beendet - Lösche Semaphor 171966468.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5426
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:51.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:39.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:38.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4432
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:03.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:04.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:55.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:00.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.08
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     945
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.78
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     650
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     270
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:18.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:46.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.95
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.10
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.46
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.58
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.36
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.84
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.54
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.36
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.40
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.88
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:43.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1495.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:59.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6975.10
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:43.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.64
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.22
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:03.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.42
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.18
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:35.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4978.93
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:57.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45918
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869918
  j =  1                              :        399908166
  j =  2                              :            45914
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45967
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869967
  j =  1                              :        399908069
  j =  2                              :            45961
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:29.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:19.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:46.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:01.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:54.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:32.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 9.48e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.025
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:34.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:35.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.64
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.58
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.14
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.56
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.36
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.71
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.41
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:44.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.43
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.37
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.69
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:28.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.48
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17447.50
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.63
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.60
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.06
p-value of test                       :    0.9926


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.75
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.20
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.98
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.34
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.79
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.01
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.63
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.07
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.82
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.73
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.22
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.54
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.29
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.68
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.86
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.62
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.78
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.46
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.80
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5081.97
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.44
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.38
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.89
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.03
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5062.70
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.04
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.39
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.96
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :   -0.27
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:24.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.50
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :   -0.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:27.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    2.41
p-value of test                       :  1.0e-2

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.26e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.19e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.79
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.59
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.83
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:07.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.96
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:09.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10033.16
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10066.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:04:02.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.73
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:49.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4758.24
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:50.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3948.53
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11592.12
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:29.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11661.27
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:30.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.05
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000186853

Normal statistic for number of bits   :    1.48
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.29
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999930806

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   0.026
p-value of test                       :    0.49

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:12.76

 All tests were passed




Server wird beendet - Lösche Semaphor 172818436.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5401
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:50.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:39.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:38.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:55.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7447
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:04.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:04.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:55.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7499
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:04:01.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:49.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:15.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:44.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.02
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:54.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.65
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   35.39
p-value of test                       :  8.4e-3

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.00
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.24
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.91
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.76
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  186.96
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.72
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:42.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1503.10
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:59.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7157.35
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:42.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.58
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.31
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:02.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.28
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.66
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:35.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5161.76
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:55.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45724
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869724
  j =  1                              :        399908554
  j =  2                              :            45720
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45480
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869480
  j =  1                              :        399909040
  j =  2                              :            45480
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:29.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:16.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:43.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 4.81e-3
p-value of test                       :    0.9947

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:58.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:55.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:35.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.33e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.79e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:21.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:33.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:34.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.19
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:47.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.75
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.83
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:47.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.21
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.11
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:40.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.51
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.03
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.92
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17705.34
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.22
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.95
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.79
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.45
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.13
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.66
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.51
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.84
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.12
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.69
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.05
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.49
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.68
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.79
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.88
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.34
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.81
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.57
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.25
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.09
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.54
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.80
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.33
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.73
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.28
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.60
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.16
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.73
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.20
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.59
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.89
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :   -1.71
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:27.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.07
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:27.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :  -0.092
p-value of test                       :    0.54

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 2.75e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:46.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.54e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 9.70e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.80
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.51
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.19
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:09.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.70
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:08.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9772.24
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10253.32
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.043
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:04:01.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:49.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4842.67
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:50.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3986.89
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.22
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11602.77
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:30.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.93
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  7999952166

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.09
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999994448

Normal statistic for number of bits   :  -0.044
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.43

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:41.79

 All tests were passed




Server wird beendet - Lösche Semaphor 173703172.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:50.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1462
p-value of test                       :  4.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334582
  j =  1                              :        599997076
  j =  2                              :             1462
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5458
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:51.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4451
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:39.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:55.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:57.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7173
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:05.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:06.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:59.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:04:03.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.38
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.84
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:53.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:17.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:45.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.92
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.36
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.72
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.26
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.81
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.08
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.76
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:48.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1521.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7036.65
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.79
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:07.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.30
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.28
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:36.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5190.75
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:02.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45708
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869708
  j =  1                              :        399908585
  j =  2                              :            45706
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45819
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869819
  j =  1                              :        399908367
  j =  2                              :            45809
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:31.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:18.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:46.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:02.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:56.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:36.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 9.67e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 6.99e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:39.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:39.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.50
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.59
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:55.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.98
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.04
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.31
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:45.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.86
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.06
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.39
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:39.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17425.76
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.82
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.10
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.71
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.32
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.33
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.44
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.98
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.10
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.26
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.77
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.20
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.01
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.61
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.98
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.98
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.39
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.59
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.79
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.91
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.80
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.10
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.04
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4903.26
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.63
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.11
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.24
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.99
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4978.93
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.34
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.02
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.24
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:25.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.25
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:23.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 8.63e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 8.31e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.87
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:29.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.29
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.22
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:08.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:09.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.34
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :  9.5e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.19
p-value of test                       :  7.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9645.72
p-value of test                       :    0.9943

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.045
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:04:27.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.48
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:52.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4984.39
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.36
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11566.05
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:32.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11916.44
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:31.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.21
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999953339

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.20
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999863864

Normal statistic for number of bits   :   -1.08
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9983

Tests on the sum of all N observations
Standardized normal statistic         :   0.064
p-value of test                       :    0.47

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   0.021
p-value of test                       :    0.49

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:11.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:19.26

 All tests were passed




Server wird beendet - Lösche Semaphor 174653444.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:50.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5422
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:49.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:39.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:39.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:57.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:05.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:07.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:00.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:04.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.14
p-value of test                       :    0.9990    *****

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    4.54
p-value of test                       :  4.8e-3

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:13.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:44.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   20.23
p-value of test                       :  5.1e-3

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.58
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.44
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.19
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.06
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.33
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.51
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.54
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.32
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.79
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:52.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.19
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6947.96
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:50.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.89
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.85
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:09.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.27
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.89
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:37.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5066.29
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:59.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45554
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869554
  j =  1                              :        399908897
  j =  2                              :            45544
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45775
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869775
  j =  1                              :        399908452
  j =  2                              :            45771
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:30.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:18.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:47.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:04.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:36.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.90e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 3.15e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 8.92e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.034
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:39.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.84
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.53
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.07
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.33
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.72
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.24
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:45.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.54e-3
p-value of test                       :    0.9984

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.20
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.09
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.64
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:28.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.93
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:39.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17479.58
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:54.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.69
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.79
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.86
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.09
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.76
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   64.13
p-value of test                       :  2.7e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.36
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.03
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.07
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.44
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.98
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.45
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.75
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.11
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.15
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.66
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.41
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.85
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.40
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.97
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.32
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  325.30
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4935.44
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.23
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.33
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.79
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.05
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.31
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.05
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  149.67
p-value of test                       :    0.9968


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.81
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:26.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.16
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:25.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.77e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 4.32e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   20.70
p-value of test                       :  8.0e-3

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.34
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.70
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:08.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:09.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9978

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9978.17
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10069.02
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:04:20.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4961.38
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:54.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5007.75
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4212.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.73
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11867.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:32.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11736.12
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:32.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.51
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000062332

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.97
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000046879

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.87
p-value of test                       :    0.03

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:32.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP, t = 3           0.9990 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 175833092.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:40.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1269
p-value of test                       :    0.9952

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334389
  j =  1                              :        599997462
  j =  2                              :             1269
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1209
p-value of test                       : 1 -  9.9e-6    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334329
  j =  1                              :        599997582
  j =  2                              :             1209
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5392
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:52.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4242
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:40.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:39.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4521
p-value of test                       :  2.8e-3


-----------------------------------------------
CPU time used                    :  00:01:57.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:05.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:04.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7179
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:55.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:02.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    2.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    2.03
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:12.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:42.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.01
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.58
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.24
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.45
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.07
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.07
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.01
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.53
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  393.62
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:42.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1371.87
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:59.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6882.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.58
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:03.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.59
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.71
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:31.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5093.04
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:07.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45879
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869879
  j =  1                              :        399908246
  j =  2                              :            45871
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46099
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870099
  j =  1                              :        399907807
  j =  2                              :            46089
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:14.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:27.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:17.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:00.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :  4.7e-3

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:55.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:33.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 8.26e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:21.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:21.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:34.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.81
p-value of test                       :  2.5e-3

-----------------------------------------------
CPU time used                    :  00:01:33.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.99
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.13
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:48.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.94
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.98
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.30
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.93
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.31
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.51
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:29.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.19
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.69
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17313.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.21
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.97
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.45
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.64
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.06
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.02
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.29
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   10.14
p-value of test                       :    0.9963


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.13
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.85
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.83
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.31
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.07
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.08
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.08
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.07
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.44
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.44
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.16
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.73
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  328.24
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5034.34
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.58
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  149.03
p-value of test                       :    0.9972


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.59
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.18
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.93
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.49
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.26
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.39
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :   -2.08
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:24.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.95
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :   -0.27
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:25.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.74
p-value of test                       :    0.96

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.27
p-value of test                       :    0.01

Sample variance                       :    2.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.83e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.18e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 8.99e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.99
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.48
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.90
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:07.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.39
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:09.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9930.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9994.31
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.034
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:47.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4737.66
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:48.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4783.16
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:50.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4129.57
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4002.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11872.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11897.78
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.61
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999858107

Normal statistic for number of bits   :   -1.12
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.30
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000031786

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         : 6.82e-3
p-value of test                       :    0.50

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:34.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21          1 -  9.9e-6
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 176979972.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:40.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5243
p-value of test                       :    0.9923


-----------------------------------------------
CPU time used                    :  00:03:53.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:39.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:39.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:57.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:04.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:03.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:55.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:00.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:14.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.83
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    3.75
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     180
p-value of test                       :  9.4e-3

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:39.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.65
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.53
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.20
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.24
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.41
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.09
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.29
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.79
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:42.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.30
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:00.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6988.10
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:42.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.59
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:02.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.34
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.00
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:35.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5153.29
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:56.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45774
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869774
  j =  1                              :        399908458
  j =  2                              :            45762
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45445
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869445
  j =  1                              :        399909110
  j =  2                              :            45445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:28.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:17.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:44.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:59.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:55.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:34.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.10e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.64e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:35.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   96.79
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.30
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.94
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.52
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:48.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.15
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.80
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:42.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.03
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.00
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.57
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:29.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17440.05
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.71
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.80
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.69
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.29
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.78
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.04
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.57
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.31
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.00
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.61
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.26
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.19
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.03
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.10
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.51
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.35
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.62
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.40
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.02
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.09
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.72
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.13
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.68
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.43
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.34
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  447.91
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.97
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4786.03
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.30
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.36
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.91
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :    1.11
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:27.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.31
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:26.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.95
p-value of test                       :    0.03

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 9.50e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 4.51e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.27
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.69
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:07.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  4.2e-3

Anderson-Darling statistic = A2       :    3.39
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:10.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9935.28
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9801.01
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:48.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.95
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:48.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4924.12
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:49.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3906.94
p-value of test                       :    0.9906

-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4292.69
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11849.09
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11735.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:29.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.96
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000267130

Normal statistic for number of bits   :    2.11
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.54
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000015034

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         : -7.00e-4
p-value of test                       :    0.50

Sample variance                       :    0.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    4.61
p-value of test                       :  4.7e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.71
p-value of test                       :    0.9966

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:55.03

 All tests were passed




Server wird beendet - Lösche Semaphor 177897476.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9954


-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5357
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:51.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4446
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:39.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:38.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:56.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:05.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:04.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:54.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:59.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.09
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.94
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    2.12
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:47.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.08
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    2.81
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:15.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.23
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:43.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.73
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.25
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.24
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.85
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.90
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.37
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.36
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.90
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.89
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1458.33
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:58.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7268.42
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:41.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.22
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.83
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:01.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.01
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.15
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:34.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4881.72
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:13.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:59.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46033
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870033
  j =  1                              :        399907936
  j =  2                              :            46029
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45382
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869382
  j =  1                              :        399909237
  j =  2                              :            45380
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:29.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:17.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:45.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:00.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:57.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:38.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.58e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 5.25e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:34.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:34.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.55
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.38
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.02
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.99
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.76
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.99
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:42.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.06
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.39
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.96
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.59
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.50
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17435.70
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.30
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.74
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.14
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.51
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.45
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.39
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.17
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.17
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.12
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.36
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:39.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.41
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.94
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.31
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.62
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.48
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.36
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.85
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.69
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.13
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.80
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.65
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.48
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.47
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.39
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.61
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.23
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.64
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.57
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.13
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.26
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.05
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:25.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.55
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:25.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 5.40e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.22e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 9.74e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.62
p-value of test                       :    0.9905

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.10
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.19
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:06.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.45
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:08.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10099.36
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10186.70
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.051
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:46.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4908.95
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.68
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:51.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4051.14
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.64
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12012.15
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11882.68
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:29.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.88
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999946229

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.68
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  7999935528

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   0.096
p-value of test                       :    0.46

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:15.84

 All tests were passed




Server wird beendet - Lösche Semaphor 178880516.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:40.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:51.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5376
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:51.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:39.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7181
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:04.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:04.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:54.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:01.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.75
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.00
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:14.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:42.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.35
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.30
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.61
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.46
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.10
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.39
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.42
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.30
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1398.06
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:00.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7125.07
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:43.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.14
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.76
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:03.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.12
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.59
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:35.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4854.02
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:01.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45978
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869978
  j =  1                              :        399908050
  j =  2                              :            45966
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45390
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869390
  j =  1                              :        399909227
  j =  2                              :            45376
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:29.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:18.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:44.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:59.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:34.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.98e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 5.78e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.94
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:34.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:34.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.11
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.01
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  101.47
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.33
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.19
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.43
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:44.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.20
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.72
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.74
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.75
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  166.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17348.66
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.13
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.36
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.83
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.61
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.18
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.26
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.35
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.05
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.35
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.46
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.20
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.98
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.07
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.49
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.43
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.27
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  560.93
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.21
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.08
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.20
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.81
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5127.72
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.12
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.24
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:34.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.40
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.11
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5051.42
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.75
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  162.64
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:34.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.45
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:23.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.26
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:25.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    2.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 7.59e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.30e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 7.70e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9975

-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.88
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.09
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.74
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:08.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9981

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.01
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:07.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9994.33
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9955.59
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:51.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.79
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:49.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4952.27
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:51.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3989.48
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11760.28
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:29.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11659.66
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:30.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.94
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999955604

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.36
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999969296

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   0.045
p-value of test                       :    0.48

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.71
p-value of test                       :    0.96

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:12.71

 All tests were passed




Server wird beendet - Lösche Semaphor 179961860.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:40.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5266
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:52.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:40.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:40.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:03.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:04.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:54.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:04:01.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.18
p-value of test                       :    0.9952

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:13.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:45.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.34
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.89
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.90
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.76
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.88
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:10.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.82
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.61
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.50
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.42
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  475.66
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:44.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.71
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:01.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6988.03
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:41.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.14
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:15.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:02.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.57
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.74
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:35.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5005.37
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:56.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46072
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870072
  j =  1                              :        399907860
  j =  2                              :            46064
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46151
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870151
  j =  1                              :        399907700
  j =  2                              :            46147
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:28.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:17.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:45.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :  1.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.55
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.9900


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:59.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:55.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:33.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.47e-4
p-value of test                       :  8.1e-3

Kolmogorov-Smirnov- statistic = D-    : 2.82e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.27e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.081
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:34.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.58
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.67
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.11
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.62
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.72
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.69
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.88
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.87
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17145.65
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.69
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.30
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.77
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.81
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.35
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:39.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.41
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.86
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   42.28
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.35
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.89
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.31
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.28
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  544.63
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.73
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.75
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.98
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.89
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.02
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.52
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.19
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.02
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.01
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.85
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.65
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.46
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.84
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.92
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4869.92
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.49
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.00
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.06
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:23.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.17
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :    1.12
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:28.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.66
p-value of test                       :    0.95

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   0.043
p-value of test                       :    0.48

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 4.87e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.12e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.65
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   20.22
p-value of test                       :  9.5e-3

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.07
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:07.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:09.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9827.69
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9861.24
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:43.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4697.37
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:49.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4889.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:51.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.67
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4199.24
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11805.37
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12023.82
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.42
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000040645

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:10.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.10
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  7999892850

Normal statistic for number of bits   :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.044
p-value of test                       :    0.48

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:16.62

 All tests were passed




Server wird beendet - Lösche Semaphor 181010436.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:40.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:50.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1472
p-value of test                       :  2.0e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334592
  j =  1                              :        599997056
  j =  2                              :             1472
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5489
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:53.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7173
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:40.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:55.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4238
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7185
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:03.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:04.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:54.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7156
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:04:00.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:47.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.89
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.30
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:13.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.80
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:42.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.01
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.99
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.86
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.28
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.86
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.68
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.56
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.50
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.13
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:43.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1453.02
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:00.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7189.11
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.53
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.95
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:03.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.55
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.81
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:34.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4897.25
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:55.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45975
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869975
  j =  1                              :        399908050
  j =  2                              :            45975
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45632
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869632
  j =  1                              :        399908737
  j =  2                              :            45630
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:29.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 7.02e-3
p-value of test                       :    0.9914

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9904


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:17.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:44.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:58.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:55.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:32.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.63e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.85e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.41e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:34.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:34.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.90
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.45
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.45
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.60
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.00
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.84
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:39.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9915

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.54
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:29.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:17.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.08
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:37.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17540.27
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.73
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.74
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.70
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.57
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.94
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.84
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.06
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.10
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.41
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.96
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.67
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.38
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.65
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.82
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.62
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.40
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.20
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.53
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.78
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.18
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.85
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.98
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4993.89
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.69
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.00
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.30
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.21
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.75
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.49
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.12
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.39
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:24.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.57
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:25.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.83

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:46.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 9.86e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.74
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.74
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.56
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:06.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.28
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:07.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :  9.8e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    7.14
p-value of test                       :  3.1e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9521.09
p-value of test                       :    0.9997    *****

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9821.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:48.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.19
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.85
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:50.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.66
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3998.69
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11915.74
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:28.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11838.47
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:29.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.42
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000054034

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.99
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000075409

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.10
p-value of test                       :    0.98

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:52.31
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 90  HammingWeight2, r = 0           0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 181993503.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1249
p-value of test                       :    0.9992    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334369
  j =  1                              :        599997502
  j =  2                              :             1249
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5266
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:54.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7540
p-value of test                       :  5.0e-3


-----------------------------------------------
CPU time used                    :  00:02:41.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:57.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:05.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:04.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:54.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:01.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    2.07
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:50.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    4.34
p-value of test                       :  6.0e-3

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:17.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:49.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.93
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.79
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.79
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:10.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.79
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.13
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.81
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.03
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:43.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1453.03
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:01.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7138.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.84
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.61
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:03.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.67
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.07
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:33.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5055.42
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:59.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45870
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869870
  j =  1                              :        399908261
  j =  2                              :            45868
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45858
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869858
  j =  1                              :        399908289
  j =  2                              :            45848
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9996    *****


-----------------------------------------------
CPU time used                    :  00:02:29.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:19.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:45.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:00.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:34.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.00e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:34.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:36.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.04
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:48.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.44
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.97
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.42
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:47.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.08
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.20
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.77
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.81
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17303.44
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.08
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.51
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.00
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.51
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.64
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.88
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.40
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.96
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.72
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.52
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.35
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  192.48
p-value of test                       :  6.0e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.52
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.15
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.20
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.63
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.34
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.12
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.58
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.68
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.76
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.90
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4895.78
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.83
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.35
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.17
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.99
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.25
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.63
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.99
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.08
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:24.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.52
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:25.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    0.20
p-value of test                       :    0.9947

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:46.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.39
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.23
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.9e-3

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.52
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:08.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.65
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:05.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9839.52
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9844.04
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:45.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4993.72
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.66
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:50.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3947.70
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3977.13
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11973.61
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12151.59
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:29.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.71
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000082501

Normal statistic for number of bits   :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.80
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999943601

Normal statistic for number of bits   :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:42.40
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14           0.9992 
 46  MaxOft AD, t = 8                0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 182878239.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5336
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:56.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:41.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:57.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:57.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:03.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:04.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:55.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:04:00.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.66
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    2.59
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.38
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9923

Test on the Nm values of W_{n,i}(mNP1):    1.83
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    3.53
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:15.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:46.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.21
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.51
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.95
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.88
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.79
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.18
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.10
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.39
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.95
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.80
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:43.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.19
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:01.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7019.18
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:41.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.82
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.53
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:03.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.79
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.13
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:33.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5042.40
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:04.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45825
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869825
  j =  1                              :        399908353
  j =  2                              :            45819
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46120
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870120
  j =  1                              :        399907766
  j =  2                              :            46108
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 9.59e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:28.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:17.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:59.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:55.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:33.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 4.99e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.026
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:34.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:36.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.10
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:48.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.11
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.36
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:51.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.86
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.12
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:40.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.16
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.72
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.06
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.75
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17367.74
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.69
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.12
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.41
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.78
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.79
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.62
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.97
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.12
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.06
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.81
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.96
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.40
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.37
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.84
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.72
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.45
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.66
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.58
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.28
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.32
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.94
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4747.65
p-value of test                       :    0.9948


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.42
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.48
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.97
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.22
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.18
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  430.77
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.64
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.59
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :   0.043
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:22.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.65
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :    0.14
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:23.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :  2.8e-3

Kolmogorov-Smirnov- statistic = D-    : 5.43e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 3.83e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.58
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.34
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.91
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:08.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.27
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:06.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 5.46e-4
p-value of test                       :    0.9995    *****

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9674.02
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10032.65
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:44.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4995.12
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.70
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:50.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4175.54
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4178.72
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11709.45
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11926.91
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:30.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.12
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000084301

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.08
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999988865

Normal statistic for number of bits   :  -0.088
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:00.01

 All tests were passed




Server wird beendet - Lösche Semaphor 183894047.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:50.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5374
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:56.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:42.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:57.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:06.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:06.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:55.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:04:01.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.24
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    3.64
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:14.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.13
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:47.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.44
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.40
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.69
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.87
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.76
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.72
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.71
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.49
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.98
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:43.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1335.51
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:02.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7214.79
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.33
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.45
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:03.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.20
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.99
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5156.55
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:04.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46088
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870088
  j =  1                              :        399907828
  j =  2                              :            46080
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45650
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869650
  j =  1                              :        399908701
  j =  2                              :            45648
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:29.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:18.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:45.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 5.22e-3
p-value of test                       :    0.9942

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:59.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:33.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.74e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 3.75e-4
p-value of test                       :  3.6e-3

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:37.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:38.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.80
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.63
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:48.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.04
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.10
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.72
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:45.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.33
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.30
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.36
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.14
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17639.81
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.46
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.07
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.87
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.00
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.67
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:38.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.71
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.73
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.14
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.67
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.37
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.82
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.86
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.41
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.77
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.93
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.03
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.98
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  580.91
p-value of test                       :  7.1e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.50
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.82
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.21
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.58
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4976.04
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.03
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.39
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.20
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  449.49
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.24
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.18
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.70
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.34
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:22.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.87
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:24.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:10.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.90e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.08e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 7.69e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.49
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.43
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.18
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:07.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.43
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:06.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9976.54
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9977.53
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:55.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4997.17
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:48.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4991.00
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:50.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.38
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.10
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11635.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11707.24
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:30.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.17
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000090148

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.97
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999915080

Normal statistic for number of bits   :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    2.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:58.80

 All tests were passed




Server wird beendet - Lösche Semaphor 184942623.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5457
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:00.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4219
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:42.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4448
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:58.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:04.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:06.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:55.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:00.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    2.23
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.13
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:15.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:44.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.05
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.41
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.01
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.15
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.42
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.81
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.86
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.86
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.98
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:44.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1460.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:00.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7064.05
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:42.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.51
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.60
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:04.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   14.83
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.57
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:33.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5058.39
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:05.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46006
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870006
  j =  1                              :        399907990
  j =  2                              :            46002
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45683
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869683
  j =  1                              :        399908639
  j =  2                              :            45673
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:28.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:18.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  6.9e-3

Kolmogorov-Smirnov- statistic = D-    : 8.70e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.11
p-value of test                       :  7.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9974


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:01.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:55.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:33.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.48e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:35.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:36.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.17
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.51
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:51.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.95
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.69
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.70
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.99
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.72
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.33
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:18.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  158.18
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17362.51
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.63
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.45
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.88
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.17
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.40
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.47
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.00
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.77
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.16
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.98
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.53
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.88
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.72
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.28
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.32
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.52
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.62
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.65
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.35
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.22
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.12
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.82
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.69
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.97
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.49
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.91
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.20
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.12
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.05
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:23.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.39
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :   -1.22
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:24.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 6.49e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 4.34e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.46
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.66
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:06.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.79
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:04.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10099.39
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9949.08
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:44.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4961.03
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4804.72
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:50.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.01
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4216.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11990.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11692.67
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:30.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.30
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000008260

Normal statistic for number of bits   :   0.065
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.39
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999945572

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:11.72

 All tests were passed




Server wird beendet - Lösche Semaphor 185991199.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5443
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:58.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:43.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:57.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4219
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:06.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:06.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:56.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:04:01.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.16
p-value of test                       :    0.9980


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.18
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    2.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.70
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:14.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.42
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    3.83
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:44.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.15
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.89
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.50
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.50
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.32
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:10.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.73
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.68
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.57
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.53
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:44.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1366.14
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:00.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7193.15
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.01
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.07
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:03.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.99
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.71
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:33.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4869.19
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:06.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45505
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869505
  j =  1                              :        399908998
  j =  2                              :            45489
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46025
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870025
  j =  1                              :        399907953
  j =  2                              :            46019
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:28.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:18.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9964

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:45.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:59.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:15.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:33.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.01e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.79
p-value of test                       :  2.7e-3

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:34.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:35.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.50
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.29
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.67
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:48.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.68
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.01
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.39
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:38.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.55
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.76
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.90
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.36
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:28.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   12.35
p-value of test                       :  2.1e-3

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.78
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17160.69
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.03
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.78
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.37
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.00
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.46
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.63
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.71
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.78
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.90
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.17
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.70
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.76
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.83
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.42
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.52
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.53
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.51
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.15
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.71
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.48
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.41
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.64
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4820.65
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.36
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.95
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.94
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.61
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4986.49
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.32
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.89
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.39
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :    1.23
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:25.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.95
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:25.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 5.62e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.68e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 8.10e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.53
p-value of test                       :    0.9922

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.88
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.26
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:07.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.15
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:05.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10205.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10072.70
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:45.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.9e-3

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5044.68
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.93
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3982.08
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4024.22
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11596.62
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11862.57
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:29.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.96
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000042730

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.22
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999935930

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :  -0.090
p-value of test                       :    0.54

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:12.38

 All tests were passed




Server wird beendet - Lösche Semaphor 186974239.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5336
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:04:03.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4250
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:45.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:47.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4500
p-value of test                       :  7.0e-3


-----------------------------------------------
CPU time used                    :  00:02:03.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:02.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:13.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:14.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:04:12.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:14.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    4.21
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     559
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    5.21
p-value of test                       :  2.3e-3

-----------------------------------------------
CPU time used                    :  00:01:15.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     272
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:14.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     124
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:44.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.65
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.14
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.47
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.72
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.57
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.09
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:33.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.71
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1408.74
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:10.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7101.93
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:03.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.17
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.13
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:14.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.36
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.89
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:40.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5049.56
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:59.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45527
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869527
  j =  1                              :        399908953
  j =  2                              :            45513
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46277
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870277
  j =  1                              :        399907450
  j =  2                              :            46269
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:31.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:22.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:54.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:08.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:59.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:24.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:48.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:51.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.71
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.29
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.27
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.72
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.04
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:54.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.87
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.80
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.26
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.07
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17545.82
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.45
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.91
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.62
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.70
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.71
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.20
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.91
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.40
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.46
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.85
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.81
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.81
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.74
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.30
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.26
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.23
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.35
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.96
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.50
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.36
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.21
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.78
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5023.46
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.16
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.64
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.40
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.56
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4947.77
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.18
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.00
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.60
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :    1.19
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:24.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.69
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:24.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.82e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 6.66e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.02e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 9.36e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.01
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.60
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.45
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:29.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.06
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:31.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9898.78
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9965.20
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:04:39.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.03
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:53.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.7e-3

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4777.98
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:56.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4010.29
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.78
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11945.30
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:33.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11936.78
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:34.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.18
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  7999944684

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.42
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000095644

Normal statistic for number of bits   :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.30
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.31
p-value of test                       :    0.01

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:12:05.39

 All tests were passed




Server wird beendet - Lösche Semaphor 187990047.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5316
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:45.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:37.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:35.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:55.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:03.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:03.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:59.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:01.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    2.63
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:52.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    2.05
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:09.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:40.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.34
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.73
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.82
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.20
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.74
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.97
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.34
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.68
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1393.91
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:08.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6952.74
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:49.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.50
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.93
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:11.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   14.95
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:47.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   93.62
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:40.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5093.96
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:26.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46011
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870011
  j =  1                              :        399907982
  j =  2                              :            46003
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45718
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869718
  j =  1                              :        399908567
  j =  2                              :            45712
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:29.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:18.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:44.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:59.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:54.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:36.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.96e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9973

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:24.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:43.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.87
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.12
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.82
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.89
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.19
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:55.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.05
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:56.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.52
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.03
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.82
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:33.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.32
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:35.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17407.77
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:49.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.52
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.32
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.13
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.09
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.84
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:34.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.53
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.92
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.38
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.44
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.06
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:34.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.38
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.52
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.02
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.10
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.51
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.19
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.65
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.41
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.11
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.84
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.39
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.81
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.12
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  328.35
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.90
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.67
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.57
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4789.52
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.78
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.77
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.09
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:29.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.50
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :   -1.36
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:26.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.89
p-value of test                       :    0.97

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 8.91e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:47.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.24e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:47.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.15
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:31.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.79
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.97
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:07.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.12
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:10.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10001.24
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9808.09
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:04:25.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5080.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:53.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.90
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:54.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4034.73
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4032.03
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11715.38
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:34.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11925.52
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:35.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.66
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000108490

Normal statistic for number of bits   :    0.86
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.69
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000104956

Normal statistic for number of bits   :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:20:20.92

 All tests were passed




Server wird beendet - Lösche Semaphor 168067077.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5577
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:48.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:38.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:38.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:55.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:03.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:03.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7503
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:55.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:59.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.15
p-value of test                       :    0.9988

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    3.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:49.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:18.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.75
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:48.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.92
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.84
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.79
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.18
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.47
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.36
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.04
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.69
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  202.60
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.72
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:47.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1465.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:01.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7297.92
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:42.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.07
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.88
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:04.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.16
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.59
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:35.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5001.64
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:15.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45263
p-value of test                       :    0.9980


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869263
  j =  1                              :        399909478
  j =  2                              :            45255
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45872
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869872
  j =  1                              :        399908262
  j =  2                              :            45860
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:27.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:17.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:44.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:58.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:53.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:34.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 8.33e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:24.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:21.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.088
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:33.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.72
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:48.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.76
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.72
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.64
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.57
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.05
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:44.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.19
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.46
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:28.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17640.63
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.73
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.18
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.58
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.54
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.98
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   56.17
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.97
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.00
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.81
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.52
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.74
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.31
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.62
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.24
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.17
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.83
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.09
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.32
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.20
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.41
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.60
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.25
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5082.05
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.32
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.43
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.78
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  477.44
p-value of test                       :  8.0e-4    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5085.16
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.57
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.92
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.96
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:26.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.49
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:25.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:46.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.72e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.72
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.77
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.03
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:09.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.56
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:09.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10026.13
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9977.83
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:49.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4908.33
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:47.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4841.17
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:48.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3886.67
p-value of test                       :    0.9951

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.81
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11877.84
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:29.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12106.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:31.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.72
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999803024

Normal statistic for number of bits   :   -1.56
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.56
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999952307

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :  -0.082
p-value of test                       :    0.53

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.98
p-value of test                       :    0.02

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:29.14
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 M (L=10000, r=15)   8.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 169803781.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:56.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5328
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:49.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4457
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:39.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:38.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4196
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:55.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7198
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:03.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:03.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7144
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:55.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:04:00.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.84
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    3.81
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:15.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:48.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.43
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.19
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.36
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.67
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.61
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:11.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.25
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.77
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.76
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.56
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.97
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:43.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1492.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:57.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7043.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:39.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.52
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.96
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:01.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.53
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.80
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:35.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4928.15
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:11.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46004
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870004
  j =  1                              :        399907995
  j =  2                              :            45998
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46227
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870227
  j =  1                              :        399907550
  j =  2                              :            46219
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:29.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:18.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:59.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:54.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:32.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.70e-5
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.00
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:22.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:33.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:34.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.45
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:46.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.33
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.37
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.00
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.69
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.58
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.21
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.55
p-value of test                       :  1.0e-3

Anderson-Darling statistic = A2       :    4.87
p-value of test                       :  3.5e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   61.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:29.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.05
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.72
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:39.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17173.38
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.98
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.74
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.66
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.81
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.82
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.21
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.50
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.32
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.00
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.73
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.86
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.46
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.08
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.11
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.16
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.15
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.08
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.91
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.90
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.92
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.36
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.59
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.97
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.51
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.73
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.37
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.03
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4952.06
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.39
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.97
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.95
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :   -2.06
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:27.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.73
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :   0.057
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:25.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.31e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:46.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.08e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:46.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.19
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.29
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.97
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:06.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.53
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  154.74
p-value of test                       :    0.9924

-----------------------------------------------
CPU time used                    :  00:02:07.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9983.26
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:49.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4973.60
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:49.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4193.92
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4313.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12119.18
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:29.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11749.89
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:31.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.16
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999909245

Normal statistic for number of bits   :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.11
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999827039

Normal statistic for number of bits   :   -1.37
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.86
p-value of test                       :    0.03

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:41.30

 All tests were passed




Server wird beendet - Lösche Semaphor 170622981.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1252
p-value of test                       :    0.9989

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334372
  j =  1                              :        599997496
  j =  2                              :             1252
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5321
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:49.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:39.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:38.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4436
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:56.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:57.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:06.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:07.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:01.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:04:06.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.91
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.18
p-value of test                       :    0.9942

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:15.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.91
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.91
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:43.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.80
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.51
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.15
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.46
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   30.82
p-value of test                       :    0.9953

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.75
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.64
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.52
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.94
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:29.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.34
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:57.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1408.30
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:08.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7087.87
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.00
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.22
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:18.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.94
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.05
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4886.21
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:04.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45629
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869629
  j =  1                              :        399908742
  j =  2                              :            45629
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45923
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869923
  j =  1                              :        399908156
  j =  2                              :            45919
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:33.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:21.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:50.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:05.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:37.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.49e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:24.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:24.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:24.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:44.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.71
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.01
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.59
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.25
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.76
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.31
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.49
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:51.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.27
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.79
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.38
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.85
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17497.99
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.77
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.42
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.37
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    8.61
p-value of test                       :    0.9983


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.51
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.73
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.91
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   10.52
p-value of test                       :    0.9950


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.00
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.12
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.62
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.00
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.99
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.43
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.77
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.64
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.04
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.08
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.32
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.78
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.54
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.46
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4875.96
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.20
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.54
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.57
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  460.98
p-value of test                       :  4.2e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.82
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.55
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.88
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.90
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:26.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.06
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:28.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.15
p-value of test                       :    0.9979

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.20e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 7.62e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 6.07e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.79
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.23
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.39
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:08.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.84
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:07.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10062.28
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9925.13
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.016
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:04:31.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4700.34
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:58.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4031.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.92
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11726.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:35.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11718.24
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:37.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.17
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999923756

Normal statistic for number of bits   :   -0.60
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.14
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999867827

Normal statistic for number of bits   :   -1.04
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.34e-3
p-value of test                       :    0.9944

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.47
p-value of test                       :  6.8e-3

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:12:51.73

 All tests were passed




Server wird beendet - Lösche Semaphor 171442181.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5309
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:51.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:39.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4458
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:57.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4176
p-value of test                       :    0.9928


-----------------------------------------------
CPU time used                    :  00:01:57.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:08.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:10.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:07.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7163
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:04:12.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.29
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    1.84
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:50.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.53
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     559
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.28
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    2.38
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     263
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:17.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:46.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.36
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.99
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.01
p-value of test                       :    0.9901

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.79
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.97
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.75
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.61
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.31
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  271.03
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.87
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:54.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1445.85
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:00.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7118.32
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:55.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.69
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.38
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:16.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.33
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.42
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:40.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5157.20
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:15.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45446
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869446
  j =  1                              :        399909111
  j =  2                              :            45440
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46032
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870032
  j =  1                              :        399907938
  j =  2                              :            46028
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:32.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:20.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:49.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:07.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9925

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:38.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.40e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 4.98e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.14e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 3.96e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:24.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:24.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:48.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:50.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.53
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.61
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.57
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.72
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.38
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.32
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:50.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.80
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.18
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.48
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:29.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17076.26
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.48
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.48
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.73
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.22
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.40
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.63
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.62
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.84
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.14
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.41
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.70
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.39
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.16
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.98
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.14
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.20
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.54
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.06
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.98
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.88
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.87
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.41
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5091.85
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.23
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.74
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.87
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.40
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.83
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  321.38
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.33
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.20
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:27.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.90
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :   0.025
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:25.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.43e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 5.37e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.41e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.28
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.71
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.17
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:07.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.86
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:08.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10105.45
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9786.48
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:11.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.087
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:04:34.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4775.80
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:59.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4049.78
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.06
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12030.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:35.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11747.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:35.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.27
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000069772

Normal statistic for number of bits   :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.40
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999988487

Normal statistic for number of bits   :  -0.091
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:12.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:12:39.86

 All tests were passed




Server wird beendet - Lösche Semaphor 172851205.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1255
p-value of test                       :    0.9986

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334375
  j =  1                              :        599997490
  j =  2                              :             1255
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5579
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:53.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:39.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:57.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:58.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7186
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:07.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:09.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:01.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:05.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    5.71
p-value of test                       :  1.3e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     960
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    2.88
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:49.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    2.13
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:16.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9930


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:43.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.88
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.01
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.39
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   34.41
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.16
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.20
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.73
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.96
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  270.55
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  377.86
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:52.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.65
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:00.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6980.29
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.22
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:09.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.34
p-value of test                       :    0.9969


-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.03
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:36.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5111.01
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:00.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46174
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870174
  j =  1                              :        399907657
  j =  2                              :            46164
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45866
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869866
  j =  1                              :        399908277
  j =  2                              :            45848
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:28.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:17.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:45.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:03.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:36.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 6.68e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:24.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:39.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:42.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.07
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.72
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.00
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.84
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.25
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:48.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.68
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17333.92
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.83
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.29
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.22
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.66
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.01
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.46
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.19
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.08
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.79
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.07
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.05
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.68
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.02
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.78
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.56
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.47
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.46
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.21
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   49.30
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.30
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.72
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4941.58
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.21
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.82
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:36.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.32
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.74
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.57
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.75
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.42
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.37
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :   -1.43
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:27.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.23
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:26.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.23

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.98e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 7.43e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.15
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.97
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.00
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:08.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.02
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:09.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9893.86
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10117.73
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:04:21.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4911.43
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:52.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.35
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:53.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.79
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.64
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11871.90
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:30.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11955.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.44
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000143845

Normal statistic for number of bits   :    1.14
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.38
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999938660

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:24.01

 All tests were passed




Server wird beendet - Lösche Semaphor 174063621.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997212
  j =  2                              :             1391
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:55.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4484
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:40.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:41.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:58.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:05.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7184
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:05.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:56.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:00.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:49.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.14
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    2.05
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    2.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:17.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    2.38
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     118
p-value of test                       :    0.9961

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:50.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.80
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.97
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.09
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.56
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.49
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.72
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.90
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.85
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.94
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  375.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:44.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1423.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:59.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6998.25
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:45.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.89
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:03.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.03
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.22
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:34.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4975.72
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:04.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45579
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869579
  j =  1                              :        399908846
  j =  2                              :            45571
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45928
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869928
  j =  1                              :        399908147
  j =  2                              :            45922
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:28.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 3.20e-3
p-value of test                       :    0.9965

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:18.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9905


-----------------------------------------------
CPU time used                    :  00:01:45.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:59.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.61e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:56.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:35.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 5.61e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:22.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:39.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:38.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.66
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.52
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.54
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.05
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.55
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.87
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:45.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.06
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.32
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.66
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:28.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.78e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17599.46
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.95
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.10
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.73
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.77
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.42
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.24
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   60.67
p-value of test                       :  4.5e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.69
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.31
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.30
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.12
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.03
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.36
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.28
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  103.79
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.47
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.33
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  564.25
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.90
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.47
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.82
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.77
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5093.16
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.08
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.66
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.69
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.13
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5052.79
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.10
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.88
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:27.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.69
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :    1.06
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:27.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.62
p-value of test                       :    0.05

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.65e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 9.45e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.71e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 9.16e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.30
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.22
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:08.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.50
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:09.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10076.33
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10201.27
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:51.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4963.44
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:49.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4975.69
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:50.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4249.30
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.92
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11621.13
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11665.89
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.86
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000048841

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.56
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999951824

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   0.069
p-value of test                       :    0.47

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.70
p-value of test                       :    0.96

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   0.023
p-value of test                       :    0.49

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :  -0.056
p-value of test                       :    0.52

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:16.20

 All tests were passed




Server wird beendet - Lösche Semaphor 175177733.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5303
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:53.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:41.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:59.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:07.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7184
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:06.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7524
p-value of test                       :  8.5e-3


-----------------------------------------------
CPU time used                    :  00:04:00.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7198
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:06.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.63
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    2.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:15.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.83
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.65
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:44.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.74
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.27
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.46
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.65
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.55
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:11.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.56
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.16
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.42
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.97
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.62
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:51.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1412.36
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:01.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6958.90
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:50.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.29
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:08.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.43
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.60
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:37.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5011.51
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:03.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46062
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870062
  j =  1                              :        399907880
  j =  2                              :            46054
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45740
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869740
  j =  1                              :        399908522
  j =  2                              :            45736
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 9.45e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:30.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:18.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:46.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:04.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:37.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 7.22e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:40.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:39.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.24
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.85
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.17
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.97
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.91
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.68
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:46.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.39
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.58
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.06
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17353.13
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.90
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.78
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.72
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.15
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.99
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.83
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.49
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :    9.41
p-value of test                       :    0.9980


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.79
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.70
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:39.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.89
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.39
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.59
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  178.33
p-value of test                       :  8.7e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  104.96
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.26
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.15
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.63
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.33
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.92
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.89
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.49
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4982.47
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  452.35
p-value of test                       :  5.1e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.79
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:36.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.27
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.19
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.53
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.19
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.69
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.32
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:25.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.69
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:24.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.83
p-value of test                       :    0.97

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.94e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:46.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.50e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.50
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.04
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.39
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.61
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:08.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9936.25
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10158.88
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.029
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:04:21.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4915.40
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:53.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.84
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:53.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.90
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4256.08
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11905.31
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11658.44
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.43
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000141472

Normal statistic for number of bits   :    1.12
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.36
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000078913

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:50.28

 All tests were passed




Server wird beendet - Lösche Semaphor 176193541.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:41.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:52.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5550
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:52.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:41.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7015
p-value of test                       :    0.9998    *****


-----------------------------------------------
CPU time used                    :  00:03:05.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:06.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7539
p-value of test                       :  5.2e-3


-----------------------------------------------
CPU time used                    :  00:03:56.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:00.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    2.11
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     860
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.29
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:17.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.79
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:44.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.91
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.02
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   37.96
p-value of test                       :  3.9e-3

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.27
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.25
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.32
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.42
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  453.78
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:43.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1479.93
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:59.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7138.94
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.55e-3
p-value of test                       :    0.9974

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.77
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   56.49
p-value of test                       :  2.4e-3

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.45
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:02.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.09
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.80
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:32.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4986.62
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:57.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46063
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870063
  j =  1                              :        399907878
  j =  2                              :            46055
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46085
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870085
  j =  1                              :        399907835
  j =  2                              :            46075
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:27.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:16.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 7.01e-3
p-value of test                       :    0.9920

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.9931


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:44.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:58.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:32.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 6.37e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 2.60e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.39
p-value of test                       :  8.5e-3

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:34.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:35.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.76
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.27
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.61
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.92
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.43
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   48.66
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:44.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.27
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.96
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.05
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.72
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17082.80
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.15
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.44
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.77
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.99
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.87
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.29
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.89
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.15
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.54
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.77
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.30
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.80
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.90
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.37
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.79
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  110.64
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.05
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.94
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  102.70
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.37
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.88
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.22
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5130.84
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.99
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.41
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.78
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.34
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.94
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.16
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.55
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.36
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :   -0.40
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:24.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.01
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:26.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.85e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.82
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.98
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.06
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:08.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.06
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:06.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.57
p-value of test                       :  7.0e-4    *****

Anderson-Darling statistic = A2       :    4.29
p-value of test                       :  6.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10343.94
p-value of test                       :  8.0e-3

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10048.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:49.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4980.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4803.92
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:50.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4078.16
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.20
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12082.07
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11577.10
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.20
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000004120

Normal statistic for number of bits   :   0.033
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.18
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999889145

Normal statistic for number of bits   :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   0.067
p-value of test                       :    0.47

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:42.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 18  BirthdaySpacings, t = 8         0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 177242117.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:52.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5477
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:52.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4484
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4431
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:57.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:05.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:05.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:54.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:01.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:48.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.92
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     553
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.87
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    3.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:16.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:43.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.34
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.00
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.25
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.07
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.31
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.92
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.78
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.16
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  275.23
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.64
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:44.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.62
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:00.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6923.52
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:44.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.70
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.34
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:02.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.15
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.77
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:33.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5004.49
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:12.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:57.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46021
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870021
  j =  1                              :        399907962
  j =  2                              :            46013
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46216
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870216
  j =  1                              :        399907570
  j =  2                              :            46212
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 5.16e-3
p-value of test                       :    0.9937

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:28.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:17.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:44.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:58.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:32.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.47e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 3.17e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.037
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:34.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.51
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.33
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.43
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.10
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:54.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.82
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.07
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:44.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9948

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.91
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.15
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:28.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.31
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:38.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17372.38
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.45
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.44
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.89
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.05
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.69
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.28
p-value of test                       :    0.9938


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.83
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.43
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.18
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.14
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.50
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.48
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.16
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.32
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.55
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.44
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.32
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.08
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.77
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.53
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.26
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.80
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5171.25
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.44
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.43
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.79
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.15
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.33
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.91
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.49
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.43
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:28.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.94
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :   -0.60
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:27.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.79
p-value of test                       :    0.04

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 8.38e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.62e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 7.33e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.70
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.14
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.91
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:07.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.57
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:07.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9761.76
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10018.17
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.016
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:50.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4776.61
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:49.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.88
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:50.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.85
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.06
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12029.57
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11602.06
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.53
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999953120

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.82
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000001942

Normal statistic for number of bits   :   0.015
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.63
p-value of test                       :    0.95

Sample variance                       :    1.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.00
p-value of test                       :    0.98

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:18.75

 All tests were passed




Server wird beendet - Lösche Semaphor 178257925.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1217
p-value of test                       : 1 -  2.6e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334337
  j =  1                              :        599997566
  j =  2                              :             1217
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:54.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:40.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4244
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4455
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:57.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7180
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:05.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:05.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:55.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:02.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    2.25
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:50.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    2.90
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     659
p-value of test                       :  9.2e-3

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.01
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:17.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:45.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.52
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.90
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.22
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.81
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.71
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.19
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.13
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.89
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.79
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:43.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1344.04
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:57.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7045.04
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:45.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.22
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:01.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.31
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.30
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:34.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5001.20
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:57.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45601
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869601
  j =  1                              :        399908801
  j =  2                              :            45595
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45557
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869557
  j =  1                              :        399908889
  j =  2                              :            45551
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:28.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:17.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:44.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :  1.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    4.28
p-value of test                       :  6.6e-3


-----------------------------------------------
CPU time used                    :  00:02:00.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:56.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:34.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 6.42e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 7.27e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.039
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:37.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:39.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.98
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.44
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.35
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.57
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:45.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9996    *****

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.50
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.68
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17559.69
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.85
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.59
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.72
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.88
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   37.34
p-value of test                       :  3.0e-3


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.86
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   57.90
p-value of test                       :  8.8e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.54
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.46
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.42
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.74
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.05
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.79
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.73
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.38
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.92
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.06
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  429.78
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.61
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.54
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.04
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.68
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5119.60
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.80
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.40
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.48
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.26
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4984.43
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.02
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.79
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.77
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:25.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.00
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:25.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   0.027
p-value of test                       :    0.49

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.07e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:46.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.77e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.93
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.04
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.11
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:06.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.76
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:09.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9817.88
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9882.53
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.24
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:47.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4911.13
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:49.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4831.11
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:50.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.54
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.11
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12117.42
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11739.28
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.28
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000064909

Normal statistic for number of bits   :    0.51
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.10
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999896120

Normal statistic for number of bits   :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:06.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  8  CollisionOver, t = 7           1 -  2.6e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 179273733.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5512
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:53.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:39.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:55.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:57.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:04.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:05.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:58.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:01.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    2.43
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:16.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:45.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.25
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.87
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.91
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.42
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.02
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.70
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.39
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  384.86
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:45.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1481.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:00.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7017.62
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:48.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.92
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:02.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.48
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.93
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:35.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4938.47
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:02.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45726
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869726
  j =  1                              :        399908551
  j =  2                              :            45720
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45690
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869690
  j =  1                              :        399908623
  j =  2                              :            45684
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:28.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:18.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:46.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:59.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:56.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:36.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:22.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:21.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.10
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:44.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.09
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.61
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.66
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.00
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.24
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.77
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:45.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9942

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.03
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.29
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.016
p-value of test                       :    0.9995    *****

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.49
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:29.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.63
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  156.14
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:38.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17453.82
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.58
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.94
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.82
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.62
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.67
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:39.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.01
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.81
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.04
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.75
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.66
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.47
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.45
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.93
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.51
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.06
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.00
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.72
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.09
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.51
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.12
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  439.88
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.50
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5121.65
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.17
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  155.51
p-value of test                       :    0.9914


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.63
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.92
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4820.46
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.61
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.83
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.14
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:25.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.25
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:25.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.35

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.04e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 8.71e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.13e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.52
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.22
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.24
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:08.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.18
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:06.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9971.85
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9950.29
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:04:08.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.07
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:49.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5060.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:50.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.42
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4213.83
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11839.40
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11768.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:29.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.50
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999950297

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.15
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000122572

Normal statistic for number of bits   :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:57.78
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 68  MatrixRank, L=1000, r=0         0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 180289541.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5557
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:54.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:39.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4230
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:56.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:57.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:05.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:04.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:56.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:01.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.78
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     854
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:14.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.05
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:42.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.61
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.35
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.46
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.25
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.98
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.75
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   92.64
p-value of test                       :  8.4e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.82
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.62
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:44.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1410.92
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:00.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7050.23
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:45.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.66
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.05
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:03.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.97
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.51
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:33.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5057.91
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:58.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45860
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869860
  j =  1                              :        399908284
  j =  2                              :            45852
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45799
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869799
  j =  1                              :        399908404
  j =  2                              :            45795
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:27.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:18.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:44.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:58.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:55.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:33.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.14e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 7.00e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:21.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:21.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:39.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:38.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.49
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.81
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.31
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.08
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.52
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.33
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.18
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:42.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.06
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:28.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.80
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17550.62
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:54.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.41
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.30
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.23
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.83
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.23
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.37
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.24
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.98
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.03
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.64
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.23
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.69
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.46
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.07
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.05
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.76
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.29
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.06
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.53
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.71
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.85
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.28
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.92
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.67
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.88
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  329.53
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.02
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.13
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.50
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.05
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.55
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:24.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.60
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :   -1.57
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:25.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.12e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.04
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   20.68
p-value of test                       :  8.0e-3

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.98
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:07.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.54
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:07.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9752.19
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10137.64
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:52.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.29
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:49.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4781.96
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:50.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.42
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.04
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11636.31
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11934.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.94
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  7999989651

Normal statistic for number of bits   :  -0.082
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.78
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000016669

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.57

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:35.77
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 32  CouponCollector, r = 20         8.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 181272581.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5344
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:55.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:44.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:00.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:01.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:12.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:13.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:10.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:16.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.79
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:14.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     172
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:41.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.43
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.83
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.97
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.06
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.79
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.34
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.65
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.58
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.96
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:55.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1433.55
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:01.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6828.35
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:54.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.13
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.88
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:16.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.55
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.05
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:44.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4817.58
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:53.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46045
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870045
  j =  1                              :        399907913
  j =  2                              :            46039
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45961
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869961
  j =  1                              :        399908083
  j =  2                              :            45951
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:30.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:20.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:54.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:08.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:56.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:37.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.49e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.48e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:24.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:24.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.018
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:47.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.97
p-value of test                       :    0.9902

-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.47
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.86
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.43
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.96
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:49.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.65
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.71
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.79
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:29.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.53
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17266.83
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.87
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.33
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.74
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.65
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.22
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.40
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.23
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.48
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.40
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.52
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.96
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.25
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.79
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.74
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  107.38
p-value of test                       :  6.8e-3


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.40
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  188.11
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.45
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.35
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.24
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:43.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.14
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.60
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4981.74
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.38
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.33
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.89
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.22
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4987.18
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.18
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.92
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.41
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :   -1.34
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:24.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.25
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :   -1.33
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:24.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 4.95e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 4.74e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.99
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.58
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.45
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:06.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:06.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9835.00
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10222.09
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.34
p-value of test                       :    0.9904

-----------------------------------------------
CPU time used                    :  00:04:29.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:55.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.28
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:59.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.72
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.10
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:29.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11819.89
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:36.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11861.71
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:39.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.64
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999998429

Normal statistic for number of bits   :  -0.012
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.04
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000131131

Normal statistic for number of bits   :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:17.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   0.085
p-value of test                       :    0.47

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:57.70

 All tests were passed




Server wird beendet - Lösche Semaphor 182321157.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997225
  j =  2                              :             1386
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5450
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:56.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:43.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:45.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4218
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:01.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4245
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:02.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:13.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:13.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:09.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:13.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.06
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.77
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:15.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:44.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.75
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.02
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   34.92
p-value of test                       :  9.7e-3

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.23
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.55
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.42
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.41
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  266.22
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.20
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:55.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1404.36
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:03.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7030.04
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:57.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:15.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.97
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.46
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5193.35
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:57.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45658
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869658
  j =  1                              :        399908687
  j =  2                              :            45652
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45692
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869692
  j =  1                              :        399908619
  j =  2                              :            45686
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:31.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 9.25e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:20.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:53.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.16e-3
p-value of test                       :    0.9977

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9942


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:09.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:57.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:38.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.94e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.45e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.15e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 2.47e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:24.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:47.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.37
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.23
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.62
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.90
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:50.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.27
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.07e-3
p-value of test                       :    0.9968

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   62.53
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.56
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17399.46
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.46
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.10
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.36
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.59
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.29
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.27
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.82
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.69
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.04
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.98
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.90
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.67
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.32
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.46
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.81
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.24
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.33
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.58
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.45
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.15
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.56
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.06
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4863.92
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.19
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.17
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.56
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.41
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.88
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.81
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.75
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.29
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:23.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.20
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:24.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.88e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 9.07e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 4.30e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.78
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.17
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.12
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:06.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  8.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  156.63
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:04.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10011.52
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10199.63
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:04:22.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9983

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.24
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:56.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5030.24
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:55.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4240.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3938.33
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12077.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:34.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11699.44
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:34.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.19
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000088852

Normal statistic for number of bits   :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.60
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  7999960017

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:15.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:16.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:59.52

 All tests were passed




Server wird beendet - Lösche Semaphor 183468037.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:27.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5541
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:57.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:41.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:58.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:06.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:05.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:56.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:02.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     944
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:50.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.00
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.87
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:17.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:46.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.73
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.35
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.17
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.63
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.85
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.73
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:42.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1500.49
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:00.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7092.67
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.82
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9981

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.36
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:03.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.73
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.06
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:34.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5131.38
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:01.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45481
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869481
  j =  1                              :        399909042
  j =  2                              :            45473
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45550
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869550
  j =  1                              :        399908905
  j =  2                              :            45540
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:28.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:19.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:45.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:00.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.10e-3
p-value of test                       :    0.9938

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:55.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:37.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.73e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 6.21e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9969

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.13e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 2.34e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.044
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:39.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:41.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.72
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.78
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.64
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.26
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.65
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.82
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.50
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.17
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.88
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17576.48
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.68
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.72
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.91
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.64
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.57
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.74
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.92
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.06
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.58
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.95
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.04
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.82
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.35
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.22
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.03
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.34
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.05
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.90
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.76
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.40
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.12
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.95
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.05
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.33
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.03
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.57
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.37
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.66
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.40
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.29
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.42
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:24.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.83
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :    0.82
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:24.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    2.85
p-value of test                       :  2.3e-3

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 6.68e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.58e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 9.76e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.86
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.73
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.87
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:03.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.95
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:05.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9863.14
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10228.70
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:39.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.33
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4924.66
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:49.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4181.83
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.40
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12106.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11738.74
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.00
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000005350

Normal statistic for number of bits   :   0.042
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.49
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999989351

Normal statistic for number of bits   :  -0.084
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:29.43

 All tests were passed




Server wird beendet - Lösche Semaphor 184549381.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1260
p-value of test                       :    0.9978

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334380
  j =  1                              :        599997480
  j =  2                              :             1260
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5404
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:57.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:42.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7176
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:42.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:58.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:59.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7457
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:09.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:10.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:04:05.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:04:13.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    1.76
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:51.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    2.20
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:18.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9938


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.60
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:46.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.59
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.04
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.81
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.76
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.40
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.00
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.98
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.62
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.38
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.31
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1399.29
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:01.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6960.23
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:50.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.63
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.82
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.47
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:09.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.99
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.79
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:37.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5104.72
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:02.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45980
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869980
  j =  1                              :        399908043
  j =  2                              :            45974
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45807
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869807
  j =  1                              :        399908391
  j =  2                              :            45797
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:32.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:21.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:49.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:06.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:57.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:38.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.09e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:24.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:46.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.30
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.71
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.56
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.58
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.95
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.69
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.83
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.72
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:48.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.53
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.81
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.67
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:29.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.58
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.22
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:40.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17369.24
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.09
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.60
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :    9.28
p-value of test                       :    0.9982


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.66
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.89
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.84
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.28
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.69
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.22
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.72
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.79
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.42
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.51
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  181.46
p-value of test                       :  5.6e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.92
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.09
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.77
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.37
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.18
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.58
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.95
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.30
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4984.39
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.34
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.29
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.91
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.58
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.70
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.76
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.94
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:34.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.22
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:22.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.87
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:22.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.92

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 8.36e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.35e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 8.23e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.10
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.63
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.86
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:06.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :  1.4e-3

Anderson-Darling statistic = A2       :    4.74
p-value of test                       :  4.0e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  257.46
p-value of test                       :  3.8e-3

-----------------------------------------------
CPU time used                    :  00:02:05.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.61
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10050.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.01
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:04:11.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5079.97
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:52.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4739.90
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:53.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4019.36
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4256.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11852.22
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:29.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11742.28
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.20
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000033115

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.24
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000024040

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.35

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.076
p-value of test                       :    0.47

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:46.55

 All tests were passed




Server wird beendet - Lösche Semaphor 185597957.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1257
p-value of test                       :    0.9983

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334377
  j =  1                              :        599997486
  j =  2                              :             1257
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1478
p-value of test                       :  1.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334598
  j =  1                              :        599997044
  j =  2                              :             1478
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5279
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:56.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:42.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4454
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:00.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:10.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:12.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:07.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:04:11.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    4.87
p-value of test                       :  3.3e-3

Stat. AD after spacings (mNP2-S)      :    2.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:49.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    2.10
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:17.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:45.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.65
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.55
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.87
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.81
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.24
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  198.75
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  488.39
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:50.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.26
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:03.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7206.58
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.51
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:09.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.52
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.00
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4981.36
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:01.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45428
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869428
  j =  1                              :        399909148
  j =  2                              :            45420
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45977
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869977
  j =  1                              :        399908050
  j =  2                              :            45969
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:31.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:20.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:08.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:57.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:36.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 3.84e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:48.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.84
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.03
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.30
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.47
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.28
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.11
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.00
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.50
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.95
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.24
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:39.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17407.26
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.17
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.91
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.67
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.98
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.77
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.12
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.79
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.89
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.98
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.54
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.26
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.87
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.76
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.09
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.41
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.83
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.61
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.68
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.42
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  105.67
p-value of test                       :  9.2e-3


-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.32
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.54
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5062.13
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.61
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.16
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.32
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.58
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5176.79
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.16
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.90
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.28
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:22.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.95
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :   -1.48
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:22.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.47e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 6.35e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.42
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.46
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.47
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:02.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.43
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:04.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10285.84
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9974.33
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:04:12.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.64
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:52.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4835.29
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:53.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.51
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3977.28
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11744.87
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11574.79
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:31.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.44
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000046024

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.31
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000071749

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.99e-3
p-value of test                       :    0.9980

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.48
p-value of test                       :  6.6e-3

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9923

Tests on the sum of all N observations
Standardized normal statistic         :  -0.033
p-value of test                       :    0.51

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:10.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:53.77

 All tests were passed




Server wird beendet - Lösche Semaphor 186679301.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5466
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:56.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:41.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:42.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:57.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:59.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:08.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7450
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:07.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:57.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:01.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.15
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:49.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:14.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    2.37
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     174
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.72
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:44.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.37
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.28
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.27
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.01
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.50
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  193.02
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  495.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:42.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.08
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:00.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6930.58
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:46.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.01
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.25
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:03.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.75
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.69
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:34.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4928.08
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:02.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45426
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869426
  j =  1                              :        399909152
  j =  2                              :            45418
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46125
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870125
  j =  1                              :        399907751
  j =  2                              :            46123
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:29.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:18.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:44.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:58.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:35.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.22e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:22.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:38.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.10
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.00
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:49.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.90
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.49
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.02
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:42.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.61
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.92
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.79
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17626.31
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.43
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.13
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.95
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.80
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.62
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.80
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.81
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.22
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.87
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.32
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.78
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.94
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.36
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.42
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.90
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.08
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.52
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.28
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.99
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.23
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5142.34
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.87
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  162.52
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.47
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.42
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.38
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.45
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  158.11
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.02
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:23.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.59
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:23.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.08

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 9.74e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 5.15e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.06
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.37
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.92
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:02.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:06.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10188.82
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9734.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:55.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:38.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.26
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.73
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:49.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4201.36
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11966.26
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11924.40
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.16
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999848414

Normal statistic for number of bits   :   -1.20
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.41
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999981773

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:58.23

 All tests were passed




Server wird beendet - Lösche Semaphor 187727877.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:39.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:50.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5450
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:56.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4484
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:42.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:57.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:58.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:07.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:08.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:57.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:04:02.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     860
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.78
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:13.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.35
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:43.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.44
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   18.33
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.35
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.44
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.68
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.76
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.15
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.79
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:42.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1338.29
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:00.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7023.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:46.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.91
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.61
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:04.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.01
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.67
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:33.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5064.18
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:00.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45773
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869773
  j =  1                              :        399908457
  j =  2                              :            45767
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45549
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869549
  j =  1                              :        399908903
  j =  2                              :            45547
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 7.59e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9904


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:28.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:18.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:45.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:01.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:54.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:35.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 9.11e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:33.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:35.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.25
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:47.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.72
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.49
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.63
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:48.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.36
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.89
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:46.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.26
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.10
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.46
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:10.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 3.91e-3
p-value of test                       :    0.9959

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  101.68
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17412.66
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:48.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.84
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.50
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.66
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    4.47
p-value of test                       :    0.9989


-----------------------------------------------
CPU time used                    :  00:00:34.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.47
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.23
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.58
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   44.52
p-value of test                       :  6.6e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.53
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.42
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.87
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.79
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.61
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.44
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:40.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.62
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.45
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  554.16
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.16
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.87
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.87
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.28
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.08
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  319.92
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.59
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:32.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.36
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  452.11
p-value of test                       :  9.4e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4909.71
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.80
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.54
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:32.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.55
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:10.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.64
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:10.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.01e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.63e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.06
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.11
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:15.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 4.74e-3
p-value of test                       :    0.9950

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.39
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:54.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.67
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:54.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9945.47
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10006.46
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:48.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:18.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4911.94
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:34.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4868.49
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11725.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11837.12
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.37
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000029452

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.99
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  7999971924

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.88
p-value of test                       :    0.97

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.19
p-value of test                       :    0.12

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.20
p-value of test                       :  7.3e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.75
p-value of test                       :  3.0e-3

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.06
p-value of test                       :    0.98

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   02:57:04.73

 All tests were passed




Server wird beendet - Lösche Semaphor 188776453.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1221
p-value of test                       : 1 -  4.2e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334341
  j =  1                              :        599997558
  j =  2                              :             1221
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:43.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:36.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:36.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:54.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:55.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:02.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:02.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:54.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7494
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:59.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:50.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.61
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.94
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:12.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    2.23
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:35.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.83
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.31
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.53
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.07
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.38
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.91
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.64
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.72
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.46
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:45.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1468.72
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:59.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6916.87
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.72
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.04
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:02.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.37
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.89
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5285.09
p-value of test                       :  7.8e-3


-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:07.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46028
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870028
  j =  1                              :        399907948
  j =  2                              :            46020
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46063
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870063
  j =  1                              :        399907877
  j =  2                              :            46057
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 5.42e-5
p-value of test                       : 1 -  5.4e-5    *****

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    3.29
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  1.7e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:30.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:19.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:45.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:01.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9984

-----------------------------------------------
CPU time used                    :  00:01:52.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.86e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 3.08e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:38.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.76
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:47.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.00
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.47
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.82
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:47.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.31
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:37.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.32
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.94
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.75
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:32.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.00
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:32.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.00
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:37.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17330.19
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:55.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.32
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.77
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   43.41
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.00
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.86
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.02
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   57.54
p-value of test                       :  9.5e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   45.01
p-value of test                       :  8.3e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.13
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.26
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:40.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.00
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.74
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.44
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.42
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.62
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:48.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.67
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.86
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.80
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.40
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.36
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:48.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.90
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.16
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5029.11
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.75
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.93
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.57
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.97
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4996.33
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  426.58
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.48
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.07
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -0.82
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:22.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.56
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:13.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 8.31e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.16e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 6.03e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.44
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:29.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.40
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.99
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:10.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.07
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:12.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10214.53
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10187.21
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:04:09.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4841.52
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:49.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5038.82
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:49.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4178.51
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.78
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11813.50
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12031.80
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:29.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.96
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999908651

Normal statistic for number of bits   :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.74
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000047275

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    1.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:29.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:16:23.46
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14          1 -  4.2e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 168099846.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:43.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:37.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:36.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:55.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4213
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:03.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:02.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:53.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:00.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.53
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:12.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:36.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.84
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.02
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.68
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.48
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.95
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.91
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.53
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.19
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.09
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  502.39
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1545.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:02.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7048.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:49.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.70
p-value of test                       :  2.7e-3

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.63
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:02.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.22
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.71
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:35.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5146.47
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:05.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45907
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869907
  j =  1                              :        399908191
  j =  2                              :            45897
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45596
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869596
  j =  1                              :        399908811
  j =  2                              :            45590
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:13.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :  3.4e-3

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:32.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:20.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:46.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:59.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:54.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:33.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 7.77e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:22.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:34.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:34.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:48.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.92
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:51.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.23
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.10
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.02
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:39.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.08
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.99
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.84
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:30.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.27
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.42
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17307.21
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.15
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.48
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.02
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.93
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.85
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.14
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.31
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.89
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.04
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.90
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:39.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.07
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.86
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.00
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.59
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.74
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:47.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.15
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.97
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.53
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.93
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.28
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:47.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.01
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.42
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4890.92
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  327.71
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.25
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.75
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.70
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.28
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.10
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.63
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.26
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :  -0.033
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:26.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.64
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:18.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   0.033
p-value of test                       :    0.49

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.27e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.56e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 8.68e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.02
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:29.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.17
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.96
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:07.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.55
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:10.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9906.68
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9928.65
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:04:00.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4913.19
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5052.41
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:49.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4229.75
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4071.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11954.21
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11855.82
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:28.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.47
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000072691

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.98
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999939014

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.47
p-value of test                       :    0.07

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:45.28

 All tests were passed




Server wird beendet - Lösche Semaphor 169181190.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:39.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1485
p-value of test                       :  6.5e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334605
  j =  1                              :        599997030
  j =  2                              :             1485
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5423
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:43.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:37.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:35.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:54.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:55.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:02.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:03.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7115
p-value of test                       :    0.9914


-----------------------------------------------
CPU time used                    :  00:03:53.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:59.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.12
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     853
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    2.26
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     561
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:13.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:40.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.21
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   19.84
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.95
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.01
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.46
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.58
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.50
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.90
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.26
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:42.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1453.23
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:58.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7030.38
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:42.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.85
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.49
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:01.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.36
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.82
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:34.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4982.14
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:04.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45874
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869874
  j =  1                              :        399908257
  j =  2                              :            45864
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45662
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869662
  j =  1                              :        399908679
  j =  2                              :            45656
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:32.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:20.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:59.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:54.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:22.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.043
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:33.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:34.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.42
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:47.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.81
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.38
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:47.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.98
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.52
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.63
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:43.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.32
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.62
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.72
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17205.76
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.80
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.22
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.32
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.81
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.53
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.89
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.60
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.47
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.92
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.65
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.33
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.42
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  557.08
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.88
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   48.17
p-value of test                       :    0.9914


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.24
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.25
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.49
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.39
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.12
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.21
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.52
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4905.03
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.82
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.77
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.38
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.38
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5084.01
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.25
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.34
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.48
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :    1.97
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:25.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.71
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :   -0.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:22.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.36
p-value of test                       :  9.0e-3

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.71e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 9.14e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 7.12e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.46
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.14
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.27
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:06.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.30
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:09.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10041.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10026.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.041
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:04:03.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4813.53
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:50.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5018.55
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:50.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4024.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3985.01
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11711.56
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11536.98
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:29.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.13
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999860831

Normal statistic for number of bits   :   -1.10
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.14
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999887096

Normal statistic for number of bits   :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:20.88
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           6.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 170131462.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:50.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5485
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:44.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:36.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:35.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:53.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:55.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7508
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:01.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:01.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:52.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:58.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.82
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.90
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     859
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.80
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:44.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.73
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     331
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:10.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.59
p-value of test                       :  5.0e-3

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:37.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.27
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.46
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.96
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.61
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.91
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.57
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.78
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:45.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1481.77
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:03.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6971.23
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.59
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.26
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.86
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:06.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.18
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:47.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5011.68
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:57.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45880
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869880
  j =  1                              :        399908245
  j =  2                              :            45870
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45661
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869661
  j =  1                              :        399908685
  j =  2                              :            45647
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:31.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:19.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:02.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:57.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.60e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:34.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.66e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:35.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:35.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.82
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.82
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.71
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.62
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.55
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.99
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:40.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  8.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    4.56
p-value of test                       :  4.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.91
p-value of test                       :    0.9911

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.31
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.01
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.97
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.88
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17136.00
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.52
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.65
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.63
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.70
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.41
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.88
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.86
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.36
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.11
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.09
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.76
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.05
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.75
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.47
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.71
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.26
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.43
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.54
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.84
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.00
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  448.38
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.71
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4882.77
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  302.83
p-value of test                       :    0.9982


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.82
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.13
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.54
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4864.39
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.59
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.53
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.58
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :   -1.67
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:22.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.48
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   -1.65
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:22.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.38e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:46.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.89e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 9.19e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.83
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.90
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.60
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:06.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.06
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:08.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10261.52
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.19
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:04:12.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.60
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:51.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.35
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:51.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3943.60
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4090.37
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11897.49
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11668.12
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.01
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000166420

Normal statistic for number of bits   :    1.32
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.44
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000142609

Normal statistic for number of bits   :    1.13
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.20

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.90
p-value of test                       :    0.97

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:36.88

 All tests were passed




Server wird beendet - Lösche Semaphor 171212824.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5513
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:51.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:37.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:54.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4445
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:54.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:59.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7459
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:00.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:52.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:58.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9921

Stat. AD after spacings (mNP2-S)      :    3.92
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    1.66
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:12.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    3.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:40.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.88
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.65
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.28
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.34
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.29
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.59
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:43.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.98
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:01.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6945.11
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:40.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.36
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:03.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.13
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.31
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:33.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4856.32
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:56.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46114
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870114
  j =  1                              :        399907777
  j =  2                              :            46104
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45364
p-value of test                       :    0.9920


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869364
  j =  1                              :        399909274
  j =  2                              :            45360
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:28.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:17.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:44.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:59.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :  4.0e-3

Anderson-Darling statistic = A2       :    4.34
p-value of test                       :  6.0e-3

-----------------------------------------------
CPU time used                    :  00:01:57.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:35.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.92e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.05e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.95e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:34.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:34.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.38
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.23
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.25
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:48.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.37
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.41
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.17
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:38.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.51
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.67
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.032
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.69
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  160.06
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:39.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17359.36
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.22
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.24
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.91
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.91
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.25
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.08
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.69
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.50
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.47
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.62
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.94
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.72
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.30
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.25
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.64
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.18
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.93
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.03
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.70
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.77
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.54
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.05
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.46
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.38
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.49
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.86
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.42
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.99
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.18
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.59
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.31
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:22.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.56
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :    0.57
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:21.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  2.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.02
p-value of test                       :    0.98

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.67e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 7.28e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.87
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.41
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.37
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:08.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.87
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:06.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9979.42
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10022.92
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.05
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.090
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:54.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4973.87
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:49.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4999.02
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:52.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.43
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.77
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11966.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:29.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11875.95
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:29.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.52
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999972263

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.99
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999930974

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :  -0.086
p-value of test                       :    0.53

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:58.43

 All tests were passed




Server wird beendet - Lösche Semaphor 172195864.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5451
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:57.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:40.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:57.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:03.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:01.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:51.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:56.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:50.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:15.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.54
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.73
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.65
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.41
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.86
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.48
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.31
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.78
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.48
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:44.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.27
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:03.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7132.18
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.07
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:05.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.43
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.02
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:36.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5172.44
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:00.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45559
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869559
  j =  1                              :        399908882
  j =  2                              :            45559
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45817
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869817
  j =  1                              :        399908367
  j =  2                              :            45815
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:29.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:16.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:44.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:00.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:56.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:36.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.56e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:40.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:39.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.18
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.00
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.95
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.91
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.05
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.85
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.83
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:41.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.28
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.46
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.26
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.06
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17421.35
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.22
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.29
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.80
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.97
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.62
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.10
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.96
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.93
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.90
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.83
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.54
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.50
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.05
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.32
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.12
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.67
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.64
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.45
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.00
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.59
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.07
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.69
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.28
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.11
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.22
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.93
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.61
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.00
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.41
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.80
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.41
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:23.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.40
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:22.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 4.38e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.25
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.26
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.33
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:04.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.32
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:06.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10075.58
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10024.78
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : 7.34e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:04:14.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.98
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:51.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.54
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:50.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.52
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.40
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12061.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11928.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:30.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.82
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000118588

Normal statistic for number of bits   :    0.94
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.30
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000000310

Normal statistic for number of bits   : 2.45e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.43
p-value of test                       :    0.08

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:04.79

 All tests were passed




Server wird beendet - Lösche Semaphor 173178904.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5372
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:01.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4205
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:43.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:44.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:59.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:00.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:08.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:07.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7177
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:56.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:58.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.55
p-value of test                       :  4.8e-3

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:49.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    1.57
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:15.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:15.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:46.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.48
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.60
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.66
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.18
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.63
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.32
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.49
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  393.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1491.55
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:02.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7133.44
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:49.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.05
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:08.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.09
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.75
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:39.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4993.22
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:03.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46165
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870165
  j =  1                              :        399907674
  j =  2                              :            46157
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46046
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870046
  j =  1                              :        399907912
  j =  2                              :            46038
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :  5.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    4.75
p-value of test                       :  3.8e-3


-----------------------------------------------
CPU time used                    :  00:02:30.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:19.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:47.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:05.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:35.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.57e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 4.08e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.010
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:37.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:38.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.91
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.16
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.43
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.16
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:45.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    5.00
p-value of test                       :  3.0e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   17.46
p-value of test                       :    0.9993    *****

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.16
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.37
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.98
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17263.15
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.93
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.29
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.53
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.77
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.10
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.16
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.44
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.43
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.96
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.09
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.96
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.66
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.95
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.86
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.11
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.25
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.49
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.34
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.96
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.31
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.87
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.32
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5051.95
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.21
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.01
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:36.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.00
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.75
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.86
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.88
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.56
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:34.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.54
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :   -0.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:23.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.07
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :    2.56
p-value of test                       :  5.2e-3



-----------------------------------------------
CPU time used                    :  00:02:25.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :  -0.027
p-value of test                       :    0.51

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.06e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 8.20e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.77e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.52
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.13
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:06.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.83
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:06.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9939.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.11
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:10.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:04:24.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4965.69
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:55.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4774.94
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:57.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.62
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4027.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11828.34
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:31.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11697.34
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:31.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.62
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000163660

Normal statistic for number of bits   :    1.29
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   86.07
p-value of test                       :  3.6e-3


-----------------------------------------------
Total number of bits:  7999935915

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.79
p-value of test                       :    0.96

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.27e-4
p-value of test                       :    0.9991    *****

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.60
p-value of test                       :    0.05

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:53.47
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 66  MatrixRank, L=30, r=0           0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 174260248.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.49

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5482
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:57.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4244
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:42.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:57.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7141
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:04.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:03.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:52.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7464
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:59.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.54
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    5.06
p-value of test                       :  2.7e-3

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:12.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    2.09
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:41.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.80
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.18
p-value of test                       :    0.9913

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.93
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.44
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.51
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.91
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.85
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.91
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:44.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1536.78
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:01.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7007.13
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:41.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.06
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:03.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.52
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.81
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:34.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5135.49
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:55.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45982
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869982
  j =  1                              :        399908040
  j =  2                              :            45974
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45997
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869997
  j =  1                              :        399908011
  j =  2                              :            45987
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:28.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.06e-3
p-value of test                       :    0.9989

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:28.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:17.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:43.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:58.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :  4.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    5.42
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.60e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.89e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:35.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.076
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.95
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.39
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.11
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.37
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:49.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.00
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.99
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.73
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:38.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.66
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.10
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.92
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.75
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.99
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17009.61
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.08
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.53
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.04
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.57
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.76
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.59
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.27
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.65
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.84
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.25
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.52
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.42
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.52
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.72
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.82
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.81
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.79
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.27
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.92
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.34
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.40
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.49
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.91
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.47
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.06
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.30
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.41
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4824.03
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.52
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.56
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.30
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    1.07
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:22.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.86
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :   -1.05
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:21.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    2.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 7.55e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.83e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 6.51e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.04
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.28
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.11
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:06.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.76
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:07.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9916

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10017.30
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9942.89
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      : 6.83e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:54.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.85
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4989.24
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:52.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.97
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.94
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11889.36
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:29.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11787.62
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:30.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.88
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000065593

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.89
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000019036

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    2.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:46.98

 All tests were passed




Server wird beendet - Lösche Semaphor 175407128.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5409
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:02.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:44.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:45.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:59.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:00.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:05.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:05.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:58.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:59.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    3.92
p-value of test                       :  9.6e-3

-----------------------------------------------
CPU time used                    :  00:01:46.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    2.76
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:12.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.98
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:40.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.60
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.43
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.60
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.72
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.43
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.99
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.55
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.79
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.71
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.11
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:05.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6775.36
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:49.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 3.27e-3
p-value of test                       :    0.9966

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.03
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:09.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.47
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.35
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:37.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5016.84
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:55.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46004
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870004
  j =  1                              :        399907995
  j =  2                              :            45998
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46296
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870296
  j =  1                              :        399907411
  j =  2                              :            46290
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:30.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:18.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:06.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:56.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:39.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:41.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.13
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.44
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.71
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.88
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.84
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.37
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  156.72
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17180.71
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.10
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.08
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.60
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.08
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.47
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.92
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.57
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.53
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.60
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.77
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.94
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.28
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.19
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.27
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  101.88
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.69
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.21
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.49
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.75
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.94
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:43.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.58
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.93
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.85
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  475.83
p-value of test                       :  4.6e-4    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.20
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.56
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  457.72
p-value of test                       :  5.7e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.52
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.92
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.66
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.77
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :  -0.091
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:24.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.09
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:23.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.60

Sample variance                       :    2.49
p-value of test                       :  7.7e-3

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.23

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.38e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 8.70e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 7.57e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.23
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.93
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   41.00
p-value of test                       :  2.3e-3



-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.27
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:07.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.47
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:05.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10190.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10096.77
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.021
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.07
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:04:25.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4969.13
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:52.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 3.82e-3
p-value of test                       :    0.9960

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4691.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:54.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4147.81
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3978.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11545.46
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:34.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11693.71
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:33.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.96
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000081442

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.54
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000108049

Normal statistic for number of bits   :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  8.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.25
p-value of test                       :  6.9e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.82
p-value of test                       :    0.9976

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:25.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 R (L=10000, r=0)    4.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 176390168.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1505
p-value of test                       :  9.2e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334625
  j =  1                              :        599996990
  j =  2                              :             1505
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5393
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:00.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:40.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:57.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7454
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:04.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7450
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:03.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:54.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:58.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    2.98
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:46.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     333
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:11.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.63
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.24
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.20
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.89
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.43
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.45
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.67
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.79
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.05
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.95
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:43.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1414.73
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:00.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7101.96
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:43.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.34
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.01
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:04.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   17.67
p-value of test                       :  3.4e-3


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.39
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:35.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5132.31
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:58.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45831
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869831
  j =  1                              :        399908341
  j =  2                              :            45825
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45981
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869981
  j =  1                              :        399908041
  j =  2                              :            45975
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:28.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:17.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:44.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9989


-----------------------------------------------
CPU time used                    :  00:01:59.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:36.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.51e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 3.53e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.05e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.41e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.45
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:34.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:35.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.72
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.76
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.49
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.24
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:39.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.80
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.62
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.65
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.29
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17257.27
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.85
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.93
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   46.45
p-value of test                       :  5.7e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.47
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.89
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.03
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.50
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.96
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.28
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.37
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:37.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.66
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.22
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.19
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.45
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.91
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.36
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  192.64
p-value of test                       :  5.8e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.51
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.60
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.79
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.78
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.75
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5079.80
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  317.57
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.96
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.89
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.70
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4904.76
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.30
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.20
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.93
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:22.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.60
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:22.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    2.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.95e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.70e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 5.61e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9997    *****

-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.69
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.20
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.58
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:06.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.53
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:07.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10035.51
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10057.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:57.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4745.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:51.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4838.97
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:50.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.00
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4227.75
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11719.39
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11926.21
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:31.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.75
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999792794

Normal statistic for number of bits   :   -1.64
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.56
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000016384

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  8.3e-3

Anderson-Darling statistic = A2       :    4.50
p-value of test                       :  5.2e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.61
p-value of test                       :  4.5e-3

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.63
p-value of test                       :    0.05

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:56.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           9.2e-5
 85  Fourier3, r = 27                0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 177438744.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:50.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5541
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:02.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:43.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7057
p-value of test                       :    0.9989


-----------------------------------------------
CPU time used                    :  00:02:42.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:01.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:03.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7500
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:51.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:57.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     860
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:13.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:42.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.05
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.76
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.15
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.51
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.50
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  282.85
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:43.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1421.77
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:00.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6975.73
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:43.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.47
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.49
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:02.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.01
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.82
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:34.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5049.62
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:59.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45936
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869936
  j =  1                              :        399908130
  j =  2                              :            45932
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46060
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870060
  j =  1                              :        399907881
  j =  2                              :            46058
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:28.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:17.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:43.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:58.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:57.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:37.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.98e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:21.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:34.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:35.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.63
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:48.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.24
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.56
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.51
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:47.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.76
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:51.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.37
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.89
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:41.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.78
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.05
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.29
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.48
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:39.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17424.83
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   13.89
p-value of test                       :    0.9997    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.17
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.41
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.88
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.47
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.34
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.61
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.00
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.39
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.95
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.45
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.69
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  557.11
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.47
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.74
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.83
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.80
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.62
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.02
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.58
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.69
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.93
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4936.33
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.05
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.17
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.52
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.91
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5096.39
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.85
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.20
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.67
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :   -0.82
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:23.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.41
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :   -1.21
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:22.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.05
p-value of test                       :    0.02

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.5e-3

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.20
p-value of test                       :    0.9946

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.10e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 9.33e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.62e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 9.20e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.42
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.10
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.09
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:03.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:06.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9789.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10116.01
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:53.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4772.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:49.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4731.47
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:51.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.46
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4070.24
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12068.65
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11952.68
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:31.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.41
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000083281

Normal statistic for number of bits   :    0.66
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.80
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999981953

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9938

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:58.78
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 H (L=50, r=0)       0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 178487320.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:39.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5367
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:04:03.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:45.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:46.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:01.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:02.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7465
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:11.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:11.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7165
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:04:07.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:10.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.05
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     834
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:49.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    2.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:14.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.19
p-value of test                       :    0.9929

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:40.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.18
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.58
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.58
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.22
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.91
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:12.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.23
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.77
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.28
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.30
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:30.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  395.69
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:58.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1544.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:07.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7013.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:57.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.92
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   40.02
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:19.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.26
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:46.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.05
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:42.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5213.50
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:54.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46362
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870362
  j =  1                              :        399907284
  j =  2                              :            46346
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45797
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869797
  j =  1                              :        399908409
  j =  2                              :            45791
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  8.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:31.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:21.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:53.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:10.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:56.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:37.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.57e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.32e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.18
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:42.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:43.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.88
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.70
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.48
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.82
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:50.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.54
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.77
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.98
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17659.45
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.58
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.30
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.59
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.42
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.73
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.49
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.33
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.00
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.45
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.47
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.71
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  206.03
p-value of test                       :  7.9e-4    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  443.83
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.53
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.14
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.55
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.72
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.12
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.26
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.74
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.46
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.23
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5069.12
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.27
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.66
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:36.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.43
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.17
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5019.73
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.76
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  238.80
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.25
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:23.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.40
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:24.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 8.03e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.98e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 6.30e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.95
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.15
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.13
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:06.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.20
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:07.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9924.76
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10108.65
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:04:37.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.80
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:53.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.33e-3
p-value of test                       :    0.9955

Kolmogorov-Smirnov- statistic = D-    :    0.57
p-value of test                       :  6.5e-4    *****

Anderson-Darling statistic = A2       :    5.16
p-value of test                       :  2.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5202.56
p-value of test                       :  9.6e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.03
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.14
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11675.28
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:33.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11978.13
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:35.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.06
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999978515

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.27
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000008182

Normal statistic for number of bits   :   0.065
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:30.13
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 M (L=1000, r=0)     7.9e-4
 96  HammingIndep, L=30, r=27        9.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 179535896.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5516
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:55.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:41.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:39.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4445
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:55.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:04.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7133
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:03.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:54.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:59.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.23
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.69
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:15.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:40.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.53
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.48
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.48
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.16
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.14
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.42
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.12
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.23
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  469.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1427.40
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:02.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6836.90
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:45.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.01
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.05
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:02.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.41
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.66
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:34.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5086.63
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:02.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45648
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869648
  j =  1                              :        399908710
  j =  2                              :            45636
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46124
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870124
  j =  1                              :        399907755
  j =  2                              :            46118
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:29.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:16.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9920

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:44.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:58.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.96e-3
p-value of test                       :    0.9907

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 2.54e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.88e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:22.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:38.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:38.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.64
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:49.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.15
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.76
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.45
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.20
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.13
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.92
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.72
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.63
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.67
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  157.37
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17646.12
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.26
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.68
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.97
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.16
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.20
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.80
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.18
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.09
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.48
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.11
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.89
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.45
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.16
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.03
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.06
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.56
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.57
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.55
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.67
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.37
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.67
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.47
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4894.52
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.50
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.38
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.43
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.01
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.02
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.90
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.22
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   33.58
p-value of test                       :  7.9e-4    *****


-----------------------------------------------
Normal statistic for number of jumps  :   -1.24
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:25.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.56
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:26.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:15.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 9.12e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 8.51e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.13
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.57
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.61
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:08.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.90
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:06.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10228.06
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10223.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:04:10.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5033.68
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:51.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.21
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:53.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.42
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4072.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11740.04
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:31.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12024.25
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:31.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.84
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999941249

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.70
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999956192

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:12.34
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0               7.9e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 180715544.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:40.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  3.5e-3


-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5430
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:55.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4172
p-value of test                       :    0.9939


-----------------------------------------------
CPU time used                    :  00:01:40.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7577
p-value of test                       :  1.3e-3


-----------------------------------------------
CPU time used                    :  00:02:41.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4231
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:59.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:59.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:08.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:08.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:04.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:04:07.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:49.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.80
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.62
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:12.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:40.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.36
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.14
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.77
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.79
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.36
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.89
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.79
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.90
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.35
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1461.13
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:07.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6883.69
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.44
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 2.20e-3
p-value of test                       :    0.9978

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   40.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:16.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.01
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:46.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.32
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5194.42
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:18.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45767
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869767
  j =  1                              :        399908469
  j =  2                              :            45761
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46254
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870254
  j =  1                              :        399907495
  j =  2                              :            46248
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:33.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:20.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:52.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:08.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:57.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:38.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 9.51e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.56e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:24.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:24.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:50.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:51.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:51.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.31
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.05
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.46
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.15
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.36
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.2e-3

Anderson-Darling statistic = A2       :    4.02
p-value of test                       :  8.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.60
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.69
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:30.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.21
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:29.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.48
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17378.35
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.74
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.91
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.38
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.89
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.58
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.95
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.13
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.12
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.93
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.28
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.09
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.11
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  453.21
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.45
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.50
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.23
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.06
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.82
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.23
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.34
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.12
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.79
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4972.99
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.21
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.22
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.78
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.52
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4960.91
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.73
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.10
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.51
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:24.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.39
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:24.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.08

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 6.72e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.50e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 5.16e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.31
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.56
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.65
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:06.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.18
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:07.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9881.07
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10062.62
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.014
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:11.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:04:31.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4954.95
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:55.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4753.12
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:58.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4205.11
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.84
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11684.13
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:35.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11581.80
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:36.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.20
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000101935

Normal statistic for number of bits   :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.74
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000047776

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:11:50.69

 All tests were passed




Server wird beendet - Lösche Semaphor 181829656.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997223
  j =  2                              :             1387
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5519
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:53.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:40.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:40.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:04.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:05.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:55.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:01.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:47.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.19
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:02:14.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.12
p-value of test                       :    0.9998    *****

Stat. AD after spacings (mNP2-S)      :    2.51
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:42.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.69
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.53
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.26
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.84
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.30
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.64
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.47
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.82
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.66
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:44.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1445.12
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7145.14
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:41.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.66
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.07
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:02.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.16
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  142.13
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5105.98
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:04.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46299
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870299
  j =  1                              :        399907408
  j =  2                              :            46287
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45858
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869858
  j =  1                              :        399908289
  j =  2                              :            45848
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 9.60e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:28.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:18.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:45.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:00.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:54.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.89
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.03
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.20
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.09
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.01
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.22
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:51.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.20
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.74
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.99
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.94
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.91
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.18
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.87
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17393.79
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.03
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.69
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.65
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.73
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.41
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.98
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.66
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.86
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.72
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.04
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.42
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.92
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.13
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.68
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.88
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.93
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.37
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.60
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  105.25
p-value of test                       :  9.9e-3


-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.53
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.41
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5052.28
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.92
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.16
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.60
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.71
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5215.12
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  330.63
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.40
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.95
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :    1.21
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:25.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.91
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:24.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 5.23e-3
p-value of test                       :    0.9945

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.78e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 8.80e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.01
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.02
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.67
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:07.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.72
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:07.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9974.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9897.19
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:42.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5034.90
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:51.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4035.25
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4133.33
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11732.06
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11974.04
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.99
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000006844

Normal statistic for number of bits   :   0.054
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.02
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000013729

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.20
p-value of test                       :    0.9937

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:38.34
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs mNP2, t = 16         0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 183140376.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5373
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:52.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:39.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7183
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:40.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:57.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:05.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:04.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7459
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:55.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7470
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:01.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:46.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.18
p-value of test                       :    0.9954

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.75
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:12.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:42.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.18
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.28
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.32
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.33
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.32
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.42
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   30.23
p-value of test                       :    0.9964

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.11
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  395.20
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:43.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.30
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6989.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.38
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:02.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.00
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.89
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:33.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4862.60
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:00.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46075
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870075
  j =  1                              :        399907856
  j =  2                              :            46063
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45769
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869769
  j =  1                              :        399908467
  j =  2                              :            45759
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:27.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:18.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:45.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:58.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:16.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:35.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 6.43e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.51e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.49e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:22.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:36.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.06
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.76
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.65
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.20
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:49.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.43
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.14
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.26
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:38.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   61.54
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.26
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.75
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17530.94
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.33
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.06
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.65
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.71
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.22
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.33
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.64
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.00
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.27
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.21
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.63
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.53
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.89
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.02
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.51
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.37
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.68
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.69
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.45
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.64
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.49
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.87
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5119.08
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.79
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.28
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.60
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.50
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4859.75
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.85
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  239.95
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.25
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :   -0.11
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:26.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.86
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :   -1.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:23.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.07e-3
p-value of test                       :    0.9958

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    2.03
p-value of test                       :    0.02

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.72e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 5.24e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 6.28e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.19
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.15
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.41
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:07.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.01
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:07.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9881.57
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10022.46
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:45.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5044.69
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:49.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  3.5e-3

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4708.96
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:51.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4316.71
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11782.55
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11916.50
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:29.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.31
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999985856

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.80
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000119665

Normal statistic for number of bits   :    0.95
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    2.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.56
p-value of test                       :    0.94

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.45

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:22.54

 All tests were passed




Server wird beendet - Lösche Semaphor 184090648.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:39.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5384
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:57.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:41.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:58.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:57.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:06.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:05.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:00.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:01.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.31
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     562
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:13.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.56
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.65
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:40.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.03
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:55.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.64
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.29
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.58
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:11.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.54
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.95
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.98
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.73
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.95
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:45.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1409.87
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7101.43
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:40.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.07
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.16
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:01.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.66
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.85
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:34.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5103.92
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:03.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45518
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869518
  j =  1                              :        399908967
  j =  2                              :            45512
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45651
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869651
  j =  1                              :        399908703
  j =  2                              :            45641
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:28.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:19.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:01.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:55.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.60e-3
p-value of test                       :    0.9984

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:33.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.069
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:37.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.24
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.72
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.45
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.25
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.10
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   14.28
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:41.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.49
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.56
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17829.94
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.55
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.22
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.09
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.24
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.57
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.40
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.09
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.45
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.54
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.28
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.25
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.95
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  446.64
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.74
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.61
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.77
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.90
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.61
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.37
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.90
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.62
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.45
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.44
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  329.13
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.50
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.59
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.58
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4923.87
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.55
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.68
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.59
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:25.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.64
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :    1.34
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:24.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.09
p-value of test                       :    0.98

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.85e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 9.71e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 8.70e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.00
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.21
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.23
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:08.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  248.65
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:09.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9848.35
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10244.56
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:46.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.62
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.98
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:52.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.79
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4226.41
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12173.58
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12108.16
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:30.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.92
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999935168

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.13
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000081220

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 3.57e-3
p-value of test                       :    0.9963

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -2.09
p-value of test                       :    0.98

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:29.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:43.87

 All tests were passed




Server wird beendet - Lösche Semaphor 185106456.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5439
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:58.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:41.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:57.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:06.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:05.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:55.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:00.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.69
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    2.28
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     957
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.31
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    2.00
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     328
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:13.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     175
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    2.28
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:39.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.77
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.69
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.48
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.10
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.56
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.96
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  274.14
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  389.85
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:45.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1414.26
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:00.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7036.41
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.01
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.73e-3
p-value of test                       :    0.9961

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   88.98
p-value of test                       :  8.9e-3

-----------------------------------------------
CPU time used                    :  00:03:02.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.93
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.49
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:34.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5175.92
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:04.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45870
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869870
  j =  1                              :        399908266
  j =  2                              :            45858
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45956
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869956
  j =  1                              :        399908090
  j =  2                              :            45952
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:28.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:18.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:45.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:00.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:55.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:35.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 8.42e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 7.85e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:37.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.97
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:48.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.23
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.86
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.45
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.15
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.03
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.86
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:42.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.83
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.38
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.50
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.19
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.94
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17205.42
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.25
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.16
p-value of test                       :    0.9916


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.44
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.41
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.85
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.87
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.13
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.58
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.28
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.73
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.68
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.69
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.40
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.02
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.38
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.83
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.28
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.77
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.63
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.77
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.39
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.05
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4984.90
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.47
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.41
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.01
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.72
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.67
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.80
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.88
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.82
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    1.89
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:26.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.16
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:23.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 5.12e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 8.07e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.05
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.78
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.73
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:05.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.79
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:06.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9769.13
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9723.54
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:43.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.03
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:48.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4984.41
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:51.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4207.73
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4042.25
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11641.29
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11878.77
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.50
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000115087

Normal statistic for number of bits   :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.59
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000054493

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    1.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:11.52

 All tests were passed




Server wird beendet - Lösche Semaphor 186155032.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5400
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:56.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4195
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:43.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4197
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:00.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:00.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:11.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:11.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:04:05.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:09.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.71
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     865
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    2.74
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     546
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.61
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:13.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.99
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    2.34
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:44.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.73
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.51
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.27
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.06
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.90
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.99
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.11
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.50
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.68
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  389.89
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:51.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.73
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:06.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6938.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:58.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.14
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:17.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.43
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.61
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:37.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5017.52
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:00.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45678
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869678
  j =  1                              :        399908647
  j =  2                              :            45672
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45859
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869859
  j =  1                              :        399908283
  j =  2                              :            45857
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:30.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:19.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:06.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:56.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:43.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:45.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.58
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.06
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.66
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:51.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.17
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.43
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.94
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.53
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.40
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.80
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.62
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17632.34
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.34
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.16
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.79
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.65
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.80
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.89
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.41
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.10
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.19
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.81
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.95
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.46
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.64
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.10
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.48
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.86
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.61
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.94
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.12
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.24
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.78
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  474.48
p-value of test                       :  1.1e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.67
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.32
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.59
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.49
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5231.70
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.80
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.38
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.13
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :   -0.86
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:25.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.00
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :    2.54
p-value of test                       :  5.5e-3



-----------------------------------------------
CPU time used                    :  00:02:26.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.86
p-value of test                       :    0.97

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.82e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.61e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.74
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.32
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.41
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:07.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.77
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:06.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10106.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10151.97
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:04:29.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5056.25
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4942.95
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:58.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.05
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11861.68
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:35.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11674.51
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:35.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.97
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999987803

Normal statistic for number of bits   :  -0.096
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.10
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000111814

Normal statistic for number of bits   :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 9.41e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.91
p-value of test                       :    0.97

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:49.35

 All tests were passed




Server wird beendet - Lösche Semaphor 187170840.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5407
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:56.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:42.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:43.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4471
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:58.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:58.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:08.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:07.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:04.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:04:07.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     953
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    2.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:13.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.66
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:42.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.00
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.02
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.92
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.65
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.57
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.83
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.50
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  469.45
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1393.55
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:02.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7007.57
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:50.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 2.02e-3
p-value of test                       :    0.9980

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.43
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:15.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.71
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:09.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.86
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.08
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:37.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5029.37
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:01.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46200
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870200
  j =  1                              :        399907604
  j =  2                              :            46192
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45404
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869404
  j =  1                              :        399909193
  j =  2                              :            45402
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:30.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 3.03e-3
p-value of test                       :    0.9967

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:18.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:47.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:03.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:36.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 7.97e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:50.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:57.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.00
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.09
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.62
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:50.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.02
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.23
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.99
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:45.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.25
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.6e-3

Anderson-Darling statistic = A2       :    3.55
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.73
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.65
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.33
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17513.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.61
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.62
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.20
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.91
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.94
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.26
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.65
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.18
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.87
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.57
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.41
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.53
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.55
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.68
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.57
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.37
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.19
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.57
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  180.03
p-value of test                       :  6.8e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.86
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.85
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.09
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.78
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.56
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.00
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.68
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.68
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.66
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.78
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.44
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.03
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :   -0.24
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:23.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.44
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:23.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.17e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 5.34e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.28
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.04
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.33
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:04.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.35
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:04.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10260.73
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10122.24
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:04:09.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.63
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:47.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.78
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:47.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4271.19
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.72
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11857.72
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12057.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.26
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  8000048238

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.60
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999876122

Normal statistic for number of bits   :   -0.98
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :  -0.096
p-value of test                       :    0.54

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:21.95

 All tests were passed




Server wird beendet - Lösche Semaphor 188317720.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:47.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5313
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:42.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:34.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:54.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:03.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:04.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:57.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:04:02.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:50.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    3.95
p-value of test                       :  9.2e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     560
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:12.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    3.12
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     336
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:07.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:40.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.53
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.94
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.19
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.29
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.88
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1452.13
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:05.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6908.00
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:49.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.26
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.27
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:12.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.40
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:47.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  150.60
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:39.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5036.85
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:28.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:23.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45275
p-value of test                       :    0.9976


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869275
  j =  1                              :        399909451
  j =  2                              :            45273
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46410
p-value of test                       :  6.7e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870410
  j =  1                              :        399907183
  j =  2                              :            46404
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:30.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:17.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:44.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:58.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:36.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.08e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : -7.88e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:43.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.02
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.99
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:55.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.97
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.90
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.17
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.38
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.54
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:52.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.23
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.76
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:33.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.39
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:35.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17551.85
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.16
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.20
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.32
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.22
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.16
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.37
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   56.98
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.18
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.13
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.24
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.01
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.60
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.06
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.97
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.45
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.74
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.01
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.13
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.20
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   50.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  325.74
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.04
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4965.00
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.29
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.44
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.91
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.59
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4891.02
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  427.14
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.51
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.24
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:29.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.88
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :  -0.037
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:27.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.41e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 9.52e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:47.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.67
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:31.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.43
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.69
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:06.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.81
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:09.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9851.96
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10111.11
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:11.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:04:23.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5110.19
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:52.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5039.93
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:53.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3964.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4197.00
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11605.27
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:36.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11777.96
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:34.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   81.59
p-value of test                       :  9.0e-3


-----------------------------------------------
Total number of bits:  7999936440

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.93
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000039514

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:19:32.05

 All tests were passed




Server wird beendet - Lösche Semaphor 168132615.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5392
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:48.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4523
p-value of test                       :  2.5e-3


-----------------------------------------------
CPU time used                    :  00:01:38.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:38.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:55.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7148
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:03.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7121
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:04.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:55.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:58.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.18
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    2.39
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.46
p-value of test                       :  5.5e-3

Test on the Nm values of W_{n,i}(mNP1):    1.73
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:17.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    2.39
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    2.00
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:48.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.83
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.75
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.19
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.95
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.97
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.05
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:20.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.03
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.57
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1353.85
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:03.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7232.99
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.48
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.90
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:05.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.61
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.62
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:35.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5056.28
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:11.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45881
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869881
  j =  1                              :        399908241
  j =  2                              :            45875
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46043
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870043
  j =  1                              :        399907917
  j =  2                              :            46037
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.59
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9957


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:27.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:17.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:44.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:59.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:54.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:35.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.78e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.13e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.68e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.58
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:00:21.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:33.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:33.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.36
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:48.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.66
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.67
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.71
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.08
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.46
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.84
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:44.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.56
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:31.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.06
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17673.03
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.12
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.55
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.61
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.11
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.37
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.74
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.19
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.54
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.25
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.40
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.83
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.84
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.77
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.20
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.66
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.62
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.92
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.01
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.04
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.24
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.24
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5075.02
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.18
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.25
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:37.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.16
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.74
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5164.47
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.66
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.24
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.90
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :    2.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:26.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.20
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:26.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.17

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 3.87e-3
p-value of test                       :    0.9960

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.35
p-value of test                       :    0.9906

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.49e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:47.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.89e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 9.78e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:46.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.48
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.17
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.47
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:09.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.93
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:09.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9909.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10107.57
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.082
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:49.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5017.71
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4814.64
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:48.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3939.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.54
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11808.61
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:29.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12021.24
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:31.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.17
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000141055

Normal statistic for number of bits   :    1.12
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.75
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999813617

Normal statistic for number of bits   :   -1.47
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.80

Sample variance                       :    0.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.060
p-value of test                       :    0.48

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:10.37

 All tests were passed




Server wird beendet - Lösche Semaphor 169836551.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5456
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:48.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4482
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:38.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7183
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:37.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:55.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4251
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:03.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:03.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:53.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7541
p-value of test                       :  4.9e-3


-----------------------------------------------
CPU time used                    :  00:04:00.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.97
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:15.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.54
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    2.19
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:45.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.57
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.98
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.24
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.15
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.00
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.33
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.98
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.73
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.53
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:45.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.81
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:58.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6974.19
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:39.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.06
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.07
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:02.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.34
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  149.59
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:35.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5140.69
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:09.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45751
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869751
  j =  1                              :        399908502
  j =  2                              :            45743
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45668
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869668
  j =  1                              :        399908668
  j =  2                              :            45660
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:29.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:18.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:58.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:53.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:33.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 7.28e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.58e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:22.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:41.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:40.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.03
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.62
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.68
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:50.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.90
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:55.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.90
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.99
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:41.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.08
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.16
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.32
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:29.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.52
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.27
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17280.32
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:54.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.56
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.13
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.36
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.07
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.60
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.91
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.06
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.94
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.11
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.70
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.28
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.59
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.22
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  104.17
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.12
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.10
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.37
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.10
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.71
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.90
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.38
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.91
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.28
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.07
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.23
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.19
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4848.47
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.19
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.94
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.02
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:26.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.16
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :   -1.44
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:25.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.02
p-value of test                       :  8.9e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.66
p-value of test                       :    0.9961

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 7.61e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:46.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 5.30e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.32
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.06
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.46
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:05.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.53
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:08.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    3.61
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9715.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10226.87
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.69
p-value of test                       :    0.9964

-----------------------------------------------
CPU time used                    :  00:03:45.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.50
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:49.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5079.16
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:50.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.72
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4263.84
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11596.93
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:29.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11883.96
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:30.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.52
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000000931

Normal statistic for number of bits   : 7.36e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.83
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000090931

Normal statistic for number of bits   :    0.72
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:48.42

 All tests were passed




Server wird beendet - Lösche Semaphor 170655751.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1274
p-value of test                       :    0.9929

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334394
  j =  1                              :        599997452
  j =  2                              :             1274
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5370
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:50.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:39.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:39.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:58.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:09.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:09.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:06.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:12.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.13
p-value of test                       :    0.9994    *****

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:14.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:42.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.81
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.86
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.89
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:11.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.37
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:31.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.66
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:59.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1486.32
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:08.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7082.63
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:56.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.28
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.80
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:13.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.67
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.39
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5157.21
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:29.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:07.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45883
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869883
  j =  1                              :        399908238
  j =  2                              :            45875
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45786
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869786
  j =  1                              :        399908430
  j =  2                              :            45782
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:32.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:21.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:51.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:11.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:57.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:39.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.30e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 2.87e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.69e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 5.55e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:24.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:25.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:52.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:53.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.91
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.84
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:50.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.71
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.12
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.49
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.53
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.34
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.82
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:30.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.98
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17153.43
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.01
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.09
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.84
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.52
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.20
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.81
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.86
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.12
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.89
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.86
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:39.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.67
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.62
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.54
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.48
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.91
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.96
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.07
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.37
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.36
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.23
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.43
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.37
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5205.79
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.53
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.03
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  324.53
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.67
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5117.20
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.27
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.46
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.41
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:25.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.27
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :   -2.73
p-value of test                       :    0.9968



-----------------------------------------------
CPU time used                    :  00:02:26.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.96e-4
p-value of test                       :    0.9993    *****

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.26
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.68
p-value of test                       :  3.7e-3

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 7.48e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:46.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.35e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 7.32e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.90
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.09
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.56
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:07.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.70
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:07.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.6e-3

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10306.35
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10142.85
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:13.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:04:35.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5031.24
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:53.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4954.14
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:56.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4293.49
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11681.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:34.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11729.01
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:35.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.15
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999949898

Normal statistic for number of bits   :   -0.40
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.07
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000022876

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.40

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:40.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs mNP2, t = 5          0.9994 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 171474951.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5451
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:51.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:39.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:38.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:54.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:57.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7477
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:06.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:06.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7456
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:00.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:04:05.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     863
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:48.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     332
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:14.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:37.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.47
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.63
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.15
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.23
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.33
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.79
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   86.02
p-value of test                       :  3.6e-3

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.46
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.64
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:48.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.51
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:00.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7188.96
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.21
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.68
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:09.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.94
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.81
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5058.92
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:57.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46194
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870194
  j =  1                              :        399907614
  j =  2                              :            46190
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45876
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869876
  j =  1                              :        399908252
  j =  2                              :            45868
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:28.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:17.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:44.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:00.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.52
p-value of test                       :    0.9941

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:41.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.57
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.17
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.86
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.19
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.44
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.74
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.77
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:45.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.79
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.25
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.97
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.71
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.91
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17444.84
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.08
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.93
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.50
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.06
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.50
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.76
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.60
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.09
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.51
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.07
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.12
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.35
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.60
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.10
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.81
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.46
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.53
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.62
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.93
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.83
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.42
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.17
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.81
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.29
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.54
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4899.14
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.95
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.39
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.48
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :    0.93
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:25.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.27
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:27.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.45

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 7.70e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.77
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.32
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.68
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:09.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.40
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:08.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9874.73
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9890.06
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:04:18.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4934.83
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:53.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:55.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.42
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4182.40
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11693.04
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:29.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11684.20
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.66
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999994292

Normal statistic for number of bits   :  -0.045
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.23
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999968036

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    2.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:52.72

 All tests were passed




Server wird beendet - Lösche Semaphor 172949511.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5485
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:51.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:40.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:39.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4187
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:04.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:04.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:56.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7164
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:04:01.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:15.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    4.08
p-value of test                       :  8.0e-3

-----------------------------------------------
CPU time used                    :  00:02:45.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.51
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:54.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.04
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.65
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.39
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.31
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.42
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.43
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.22
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:43.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1468.11
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:00.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7044.68
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:44.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.85
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:15.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.97
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:03.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.71
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.63
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5010.01
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:57.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45966
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869966
  j =  1                              :        399908072
  j =  2                              :            45958
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46345
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870345
  j =  1                              :        399907313
  j =  2                              :            46339
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:29.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:27.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:17.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:44.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:00.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:55.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:32.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 2.70e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 7.90e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:35.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:33.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.90
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.38
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.38
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.45
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.60
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.83
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.76
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.36
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17551.56
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.86
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.99
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.90
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.74
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.93
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.94
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.07
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.70
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.59
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.46
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.20
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.19
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.62
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.62
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.47
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.51
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.77
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.47
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.33
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.90
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.33
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.62
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.63
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.70
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.66
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:36.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.26
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.14
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.74
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.32
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.99
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.28
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :    1.61
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:27.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.79
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :   -2.54
p-value of test                       :    0.9945



-----------------------------------------------
CPU time used                    :  00:02:26.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.67e-3
p-value of test                       :    0.9962

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.99
p-value of test                       :    0.02

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.81e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:46.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.65e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.23
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.43
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.06
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:08.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.58
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:08.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10179.19
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10136.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.18
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:56.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5080.45
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4790.39
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:51.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4277.55
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.01
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11806.68
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11583.24
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:29.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.14
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999975641

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.57
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  7999766403

Normal statistic for number of bits   :   -1.85
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:02.11

 All tests were passed




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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5499
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:53.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:40.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:57.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:05.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:06.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:56.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:00.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.84
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    3.02
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     954
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.99
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     558
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.77
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:15.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:43.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.64
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.84
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.45
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.88
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.12
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.92
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.26
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1478.68
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:57.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6870.12
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.23
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.84
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:02.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.56
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.07
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:34.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5077.46
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:02.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45759
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869759
  j =  1                              :        399908489
  j =  2                              :            45745
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45939
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869939
  j =  1                              :        399908123
  j =  2                              :            45937
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:28.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 6.61e-3
p-value of test                       :    0.9920

Anderson-Darling statistic = A2       :    3.92
p-value of test                       :  9.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9976


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :  5.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    4.01
p-value of test                       :  8.8e-3


-----------------------------------------------
CPU time used                    :  00:02:18.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 6.16e-3
p-value of test                       :    0.9931

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:45.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:34.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.11e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.40
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:35.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:37.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.38
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.96
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  102.08
p-value of test                       :  3.7e-3

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.01
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.99
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.98
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.48
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:46.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.48
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:28.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:29.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.04
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17743.02
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.19
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.20
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.37
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.65
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.42
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.48
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.87
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.83
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.98
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.03
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.15
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.60
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.66
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.45
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.24
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.86
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.85
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.03
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.44
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.83
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.72
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.04
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4826.91
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.87
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.57
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:36.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.21
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.03
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5118.86
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  327.51
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.34
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:36.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.02
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :    1.58
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:28.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.27
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:28.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 8.62e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 4.14e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.46
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.68
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.98
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:06.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.37
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:07.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9903.03
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:48.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.52
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:50.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.51
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:51.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4170.94
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11914.76
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11819.48
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:29.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.28
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000074899

Normal statistic for number of bits   :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.97
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000127009

Normal statistic for number of bits   :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 3.86e-4
p-value of test                       :    0.9996    *****

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.64
p-value of test                       :    0.9958

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:43.52

 All tests were passed




Server wird beendet - Lösche Semaphor 174882823.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:50.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5471
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:54.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:42.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:54.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:02.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:15.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:39.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:38.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:25.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7108
p-value of test                       :    0.9931


-----------------------------------------------
CPU time used                    :  00:05:07.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:47.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.93
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.29
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:13.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     127
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:43.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.70
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.61
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.65
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.18
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.67
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:09.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.11
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  263.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  471.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:30.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1517.15
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:31.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6846.08
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:38.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.46
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.71
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:02.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.54
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.25
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:34.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4959.27
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:02.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46003
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870003
  j =  1                              :        399907997
  j =  2                              :            45997
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45915
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869915
  j =  1                              :        399908177
  j =  2                              :            45901
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:32.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 9.59e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:25.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:53.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:08.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:55.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:34.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 7.53e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.063
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:35.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.65
p-value of test                       :  4.0e-3

-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.67
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.62
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:33.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.20
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:32.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.01
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.47
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:32.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.41
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:32.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.61
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:40.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.48
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.82
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.86
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.64
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17123.95
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.42
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.81
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.32
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.54
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.84
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.75
p-value of test                       :    0.9921


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.99
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.90
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.06
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.50
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.25
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.33
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.97
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.52
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  115.90
p-value of test                       :  1.3e-3


-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.20
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.79
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.03
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.64
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.56
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.55
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.70
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.49
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.65
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.53
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.01
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.85
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4862.37
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.74
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.10
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:36.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.89
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    1.75
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:27.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.28
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:28.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.76e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.61e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 9.78e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.47
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.52
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  160.91
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:07.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.36
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:08.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9914.48
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9855.47
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:45.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.17
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:48.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4984.73
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:50.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4070.26
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4222.06
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11675.71
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11919.42
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.48
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000050329

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.34
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  7999951434

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.35

Sample variance                       :    2.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:26.37

 All tests were passed




Server wird beendet - Lösche Semaphor 175898631.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:50.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5334
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:51.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:40.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:39.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:56.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:04.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:04.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:55.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7184
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:00.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.35
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:47.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.82
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    4.37
p-value of test                       :  5.8e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     331
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:12.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:43.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.83
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.25
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.83
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.36
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.40
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.86
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.88
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1473.90
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:01.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6869.74
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:39.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.17
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.03
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:02.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.82
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.28
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:34.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5052.81
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:59.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46435
p-value of test                       :  4.8e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870435
  j =  1                              :        399907134
  j =  2                              :            46427
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45842
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869842
  j =  1                              :        399908317
  j =  2                              :            45840
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:28.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:17.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:44.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:59.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:55.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:32.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.80e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.97e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 3.24e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:22.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.36
p-value of test                       :  9.2e-3

-----------------------------------------------
CPU time used                    :  00:01:35.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:36.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.34
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.20
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:51.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.73
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:49.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.41
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.86
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:40.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.76
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.93
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.26
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.43
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17207.56
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.50
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.72
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.35
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.83
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.42
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.66
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.08
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.86
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.44
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.31
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.71
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.46
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  600.85
p-value of test                       :  1.3e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.65
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.92
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.09
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.37
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.68
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.57
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.23
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.87
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.12
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4894.22
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  312.55
p-value of test                       :    0.9939


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.46
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.39
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.58
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5132.11
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.11
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.54
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.22
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:24.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.41
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:26.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    2.55
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.61e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.39e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.38
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.77
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.99
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:08.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.37
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:06.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9951

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9956.02
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9812.71
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:45.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4991.43
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:50.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.75
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:51.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.04
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11766.78
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11643.87
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.71
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000026014

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.45
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000029239

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.24

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:55.57

 All tests were passed




Server wird beendet - Lösche Semaphor 176848903.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5579
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:53.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:39.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4480
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:03.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:04.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:55.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:04:01.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.07
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.91
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.23
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    2.04
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.33
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:13.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:44.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.29
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.48
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.11
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.75
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.53
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.59
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.74
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.45
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.84
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:42.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1516.86
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:01.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7279.45
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:40.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.76
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:03.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.41
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.78
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:35.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5058.31
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:01.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46105
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870105
  j =  1                              :        399907793
  j =  2                              :            46099
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46037
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870037
  j =  1                              :        399907930
  j =  2                              :            46029
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:29.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:18.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:59.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:55.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:33.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 7.70e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.94e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 4.74e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:21.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:34.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.13
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.55
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.69
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.05
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.63
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.90
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:43.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.10
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.22
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.50
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.14
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17346.08
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.52
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.73
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.16
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.11
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.65
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:38.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.81
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.44
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.01
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.69
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.91
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.30
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.35
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.26
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.29
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.51
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:46.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.65
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.79
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.23
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.71
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.95
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.27
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.84
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.09
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.87
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.29
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  329.89
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5102.64
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  426.38
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.52
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.50
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :    1.21
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:25.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.41
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:25.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.83
p-value of test                       :    0.03

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:47.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.19e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:46.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.36
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.11
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.35
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:06.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.08
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:07.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9749.10
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10044.21
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -3.21
p-value of test                       :    0.9993    *****

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:52.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4835.14
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5047.09
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.72
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4118.18
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12072.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:33.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12146.47
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:31.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.10
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000134047

Normal statistic for number of bits   :    1.06
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.48
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000022609

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:28.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    0.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:46.31
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 93  HammingCorr, L = 300            0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 177831943.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5528
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:52.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:39.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:55.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4238
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:56.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:03.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:04.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7168
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:54.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:04:00.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.18
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.82
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     548
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.89
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.15
p-value of test                       :    0.9986


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:14.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:44.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.20
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.20
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.07
p-value of test                       :    0.9959

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.36
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.45
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.48
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.53
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  391.92
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:43.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1371.03
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:00.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7193.52
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:42.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.64
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.16
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:01.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.13
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.38
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:46.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5088.70
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:33.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:34.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45741
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869741
  j =  1                              :        399908524
  j =  2                              :            45729
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:16.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45551
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869551
  j =  1                              :        399908902
  j =  2                              :            45543
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:29.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:18.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:44.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:59.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:55.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:34.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.34e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 8.98e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.073
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:35.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.27
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:49.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.23
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.91
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.69
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:39.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.98
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.22
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.54
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.11
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17365.65
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.45
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.09
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.04
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.06
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.44
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.49
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.13
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.85
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.54
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.20
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.67
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.31
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.42
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  178.40
p-value of test                       :  8.6e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.45
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.35
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.69
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.33
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  170.65
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.03
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.77
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.12
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4850.36
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.20
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  244.38
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.52
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.97
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4902.23
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.54
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  247.34
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.43
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :   -1.02
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:23.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.46
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   -0.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:24.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.96e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 4.15e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.19
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.20
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.59
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:08.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.28
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:08.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10075.99
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 4.46e-3
p-value of test                       :    0.9954

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9719.53
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:58.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4988.03
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4842.65
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:50.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4045.68
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4118.14
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11789.74
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11993.26
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:29.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.66
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000015850

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.51
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999818027

Normal statistic for number of bits   :   -1.44
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    2.76
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :  -0.059
p-value of test                       :    0.52

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.11
p-value of test                       :    0.02

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    2.47
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:49.84

 All tests were passed




Server wird beendet - Lösche Semaphor 178749447.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:51.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5390
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:54.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:39.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:40.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4202
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4452
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:59.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:09.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:09.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:57.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:01.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.53
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     643
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:13.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   22.66
p-value of test                       :  2.0e-3

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.61
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.25
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.20
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.55
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.93
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:29.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  479.10
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:24.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1313.22
p-value of test                       :    0.9910

-----------------------------------------------
CPU time used                    :  00:02:14.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7161.16
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:30.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.59
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:01.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.25
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.70
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:33.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5029.80
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:01.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46136
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870136
  j =  1                              :        399907728
  j =  2                              :            46136
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46121
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870121
  j =  1                              :        399907761
  j =  2                              :            46115
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:29.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:18.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:44.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:58.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:34.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 2.08e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.030
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:35.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:34.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.24
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:48.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.96
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.81
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:49.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.90
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.51
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.98
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:02.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.01
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.83
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.55
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:29.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.27
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.09
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.29
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:48.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17374.59
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.68
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.86
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.31
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.53
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.73
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.36
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.21
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.78
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.93
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.62
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.10
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.22
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.69
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.03
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.41
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.17
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.17
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.26
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.70
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.29
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.19
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.97
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.30
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.88
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.38
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.39
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.89
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.35
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.35
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.93
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.38
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:25.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.84
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :  -0.078
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:24.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   0.087
p-value of test                       :    0.47

Sample variance                       :    0.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.32e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 8.09e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.70e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.91
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.17
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:08.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.9e-3

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  247.60
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:09.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10057.36
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9943.90
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.066
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:52.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4959.36
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:49.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4918.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:50.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4228.67
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.65
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11849.76
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:29.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12341.56
p-value of test                       :  4.6e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:30.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.39
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999931076

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.44
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000022657

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    1.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:55.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 100  HammingIndep, L=1200, r=25      4.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 179798023.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:51.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5312
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:53.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:39.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:04.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:03.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:54.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:04:00.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    2.16
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.47
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:13.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:42.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.23
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.37
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.62
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.12
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.11
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.67
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.28
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.16
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.52
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:43.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.30
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7058.01
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.00
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.50
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:03.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.10
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.58
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5109.49
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:09.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45922
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869922
  j =  1                              :        399908161
  j =  2                              :            45912
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45972
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869972
  j =  1                              :        399908062
  j =  2                              :            45960
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:29.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:17.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:44.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:59.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  8.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:55.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:34.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.54
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:48.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.68
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.76
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.87
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.73
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.32
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.98
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:39.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.34
p-value of test                       :    0.9932

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.02
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.63
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.19
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.22
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17248.60
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.18
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.84
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.89
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.84
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.50
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.37
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.44
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.22
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.23
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.92
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.73
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.61
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.48
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.45
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.60
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.75
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.82
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.11
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.38
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.46
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.96
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.29
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.42
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.85
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.72
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.23
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.38
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.50
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.93
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :   -0.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:24.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.41
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :  -0.024
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:25.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:11.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.97e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.27e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 7.23e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.14
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.16
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.63
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:08.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:04.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10302.89
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9973.01
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:51.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5025.16
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:49.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4774.63
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.85
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11871.55
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11802.04
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:30.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.00
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000055609

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.49
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000041875

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.15
p-value of test                       :    0.9980

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    2.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:23.54

 All tests were passed




Server wird beendet - Lösche Semaphor 180813831.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:51.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5402
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:54.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:40.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:40.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:04.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:03.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:54.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:59.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    2.15
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     547
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.87
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.28
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:15.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    2.30
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:44.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.84
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.80
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.77
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.69
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.85
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:11.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.70
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.99
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.17
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.52
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:43.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1412.16
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:01.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6955.42
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:43.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.08
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.20
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:04.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.95
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.83
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:34.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5079.36
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:00.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45757
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869757
  j =  1                              :        399908491
  j =  2                              :            45747
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45555
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869555
  j =  1                              :        399908891
  j =  2                              :            45553
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:29.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:19.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:45.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:59.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 2.07e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:34.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.18
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.10
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.64
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.23
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.62
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.79
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.10
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:39.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.66
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.23
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.80
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.00
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-3
p-value of test                       :    0.9980

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  163.72
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17185.38
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.53
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.56
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.85
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.26
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.47
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.28
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.06
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.51
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.91
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.65
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.51
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.64
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.50
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.71
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.37
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.89
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.51
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.24
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.15
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.50
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.73
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.50
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5129.96
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.27
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.62
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.21
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.18
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.66
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.10
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.10
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.72
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:26.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.71
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:28.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.2e-3

Kolmogorov-Smirnov- statistic = D-    : 7.70e-3
p-value of test                       :    0.9918

Anderson-Darling statistic = A2       :    3.79
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.69
p-value of test                       :    0.9964

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.46e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.54e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 4.61e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.78
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.93
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.94
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:08.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.93
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:05.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10181.68
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9864.81
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.084
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:45.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4842.54
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:48.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4769.88
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:51.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4030.82
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4203.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11810.79
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11866.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.24
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999879674

Normal statistic for number of bits   :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.71
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999969764

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -2.02
p-value of test                       :    0.98

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:49.13

 All tests were passed




Server wird beendet - Lösche Semaphor 181796871.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5448
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:53.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7497
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:41.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:57.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:05.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:04.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:55.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:59.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    2.72
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.53
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:13.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    2.25
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     174
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:40.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.63
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.81
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.45
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.12
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:10.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.83
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.23
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.04
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.85
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  453.92
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:43.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1433.86
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:01.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7050.90
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.16
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.16
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:05.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.98
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   91.67
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:33.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4970.92
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:56.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45840
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869840
  j =  1                              :        399908325
  j =  2                              :            45830
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45703
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869703
  j =  1                              :        399908598
  j =  2                              :            45695
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:28.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:18.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:44.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:34.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 7.39e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:34.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:34.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.76
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.67
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.05
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.84
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.64
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:38.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.84
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.34
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.91
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.17
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17072.74
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.10
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.92
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.21
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.75
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.59
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.00
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.18
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.83
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.28
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.80
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:37.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.38
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.99
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.25
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.24
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.68
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.07
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.44
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.24
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.92
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.14
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.82
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.53
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5142.65
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  318.67
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.80
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.82
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.13
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4942.55
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  429.19
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.73
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.15
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:22.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.52
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  :    1.69
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:24.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.55e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 7.26e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.83e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.16
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.90
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.15
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:06.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 2.59e-3
p-value of test                       :    0.9973

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.09
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:06.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10002.03
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9911.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:51.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9917

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:48.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.78
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:51.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4170.09
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4277.02
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11546.04
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11918.27
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:30.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.97
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999965429

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.64
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999942857

Normal statistic for number of bits   :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.23

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:25.71

 All tests were passed




Server wird beendet - Lösche Semaphor 182812679.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5338
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:55.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:40.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:42.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:58.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4452
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:07.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:03.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:55.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:01.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     647
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:13.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    2.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:43.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.29
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.82
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.85
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.66
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.57
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.54
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.49
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.23
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.07
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:43.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1273.52
p-value of test                       :    0.9992    *****

-----------------------------------------------
CPU time used                    :  00:02:01.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7220.15
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:42.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.35
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.33
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:04.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.66
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  142.14
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:34.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4847.33
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:56.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45971
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869971
  j =  1                              :        399908062
  j =  2                              :            45963
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46235
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870235
  j =  1                              :        399907533
  j =  2                              :            46229
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:28.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:18.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:44.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:00.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:34.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.099
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:34.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:34.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.11
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.51
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:49.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.74
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.32
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:57.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.67
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.70
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.064
p-value of test                       :    0.9958

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.89
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17455.92
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.92
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.59
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.43
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    8.82
p-value of test                       :    0.9980


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.47
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.65
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.40
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.07
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.77
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.40
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.40
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.12
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.37
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.13
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.04
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.94
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.05
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.21
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.79
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:49.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  320.57
p-value of test                       :    0.9919


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.60
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.36
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.08
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.99
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.64
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.26
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4794.89
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.82
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  242.15
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:40.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.47
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :  -0.055
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:23.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.94
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :   -1.58
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:23.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.63e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 9.87e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.59e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.92
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.60
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.18
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:07.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.03
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:06.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9955.84
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9796.07
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.13
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:54.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.40
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:49.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4985.79
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:51.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.79
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.79
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11810.44
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:28.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11843.48
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:30.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.86
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000115153

Normal statistic for number of bits   :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.09
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999863750

Normal statistic for number of bits   :   -1.08
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         : -2.46e-3
p-value of test                       :    0.50

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:23.42
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 36  Gap, r = 0                      0.9992 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 183795719.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5487
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:57.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:42.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:58.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:58.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:06.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:05.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:56.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:04:00.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:49.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    3.33
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:13.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.72
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:41.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.14
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.85
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.72
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.92
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.75
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.53
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.14
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.15
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.46
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:44.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1453.22
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:01.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7120.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.60
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.49
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:04.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.74
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   83.62
p-value of test                       :    0.9942


-----------------------------------------------
CPU time used                    :  00:01:33.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4946.99
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:59.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46102
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870102
  j =  1                              :        399907802
  j =  2                              :            46090
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45953
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869953
  j =  1                              :        399908096
  j =  2                              :            45949
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:29.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:18.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:44.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9958


-----------------------------------------------
CPU time used                    :  00:02:00.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:34.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 7.25e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:34.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.04
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.61
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.52
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.96
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.55
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:42.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.44
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.20
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.13
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.87
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17633.66
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.91
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.42
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.55
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.80
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.20
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.21
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.48
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.91
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.74
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.18
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.14
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.98
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.27
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.73
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.88
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.46
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.86
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  427.40
p-value of test                       :    0.9917


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.26
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.39
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.61
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.05
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5107.32
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.24
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.42
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.29
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.42
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5161.69
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.45
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.49
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.16
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -2.12
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:23.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.99
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:24.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.55e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 3.63e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.54
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.65
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.36
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:06.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.97
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:06.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10026.45
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10048.02
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:55.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:46.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5018.80
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:50.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.20
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:50.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4289.24
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4208.65
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11955.76
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12175.79
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:29.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.93
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999816827

Normal statistic for number of bits   :   -1.45
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.52
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999972248

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.38

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:45.15

 All tests were passed




Server wird beendet - Lösche Semaphor 184844295.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5524
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:59.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:45.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:59.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:59.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:07.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:06.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:57.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7149
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:04:00.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.11
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:48.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.47
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    3.35
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:14.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:41.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.37
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.50
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    4.47
p-value of test                       :    0.9995    *****

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.37
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.30
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.96
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  469.44
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:45.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1389.80
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:02.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6924.73
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:43.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.63
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.83
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:03.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.91
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.65
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5018.30
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:59.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45660
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869660
  j =  1                              :        399908682
  j =  2                              :            45656
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45893
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869893
  j =  1                              :        399908219
  j =  2                              :            45883
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:29.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:18.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:46.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 6.80e-3
p-value of test                       :    0.9923

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:01.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.10
p-value of test                       :  7.9e-3

-----------------------------------------------
CPU time used                    :  00:01:56.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:33.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:34.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:35.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.21
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.01
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.83
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.59
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.73
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.26
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.40
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.95
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17401.95
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.86
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.76
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.11
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    8.80
p-value of test                       :    0.9980


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.12
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.82
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.52
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.78
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.05
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.55
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.71
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.99
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.43
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.37
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.20
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.82
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.63
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.92
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.99
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.04
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.49
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.07
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.75
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.74
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.59
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.79
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5140.46
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.49
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.22
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.33
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:23.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.65
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :   -1.37
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:24.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 8.25e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.11e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.46
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.14
p-value of test                       :    0.9972

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.09
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:06.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:08.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9860.25
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10094.20
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.037
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.041
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:46.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4734.85
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:50.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:50.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.04
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.21
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11678.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:29.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11893.81
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:30.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.54
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999856514

Normal statistic for number of bits   :   -1.13
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.02
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000104383

Normal statistic for number of bits   :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.96
p-value of test                       :  9.5e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.63
p-value of test                       :    0.9957

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:26.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 29  SimpPoker, r = 25               0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 185860103.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:50.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1470
p-value of test                       :  2.4e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334590
  j =  1                              :        599997060
  j =  2                              :             1470
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1482
p-value of test                       :  8.6e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334602
  j =  1                              :        599997036
  j =  2                              :             1482
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5490
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:58.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:42.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4480
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:58.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:58.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:06.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:06.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:57.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:01.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.44
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.68
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:49.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.9908

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:14.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    3.09
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    4.94
p-value of test                       :  3.1e-3

-----------------------------------------------
CPU time used                    :  00:02:42.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.70
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.86
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.48
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:11.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.61
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.12
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.63
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.38
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.02
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1438.30
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:03.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6931.54
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:43.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.95
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:03.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.07
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  142.56
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:32.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5037.32
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:12.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:59.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45845
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869845
  j =  1                              :        399908314
  j =  2                              :            45837
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45857
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869857
  j =  1                              :        399908288
  j =  2                              :            45853
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:29.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:18.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:45.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:59.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:34.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 9.43e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.34
p-value of test                       :  9.7e-3

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:21.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:33.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:34.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.57
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.48
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.05
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.02
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.95
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:39.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.33
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9918

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.98
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.73
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17445.59
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.85
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.91
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.53
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.97
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.07
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.70
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.78
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.90
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.88
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.50
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.12
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.77
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.66
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.65
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.73
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.74
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.19
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.97
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.84
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.76
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.61
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4992.48
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.61
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.08
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.11
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.54
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4992.11
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.32
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.04
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.50
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:25.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.82
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:24.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   0.076
p-value of test                       :    0.47

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.05e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 4.91e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.88
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.80
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:05.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.84
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:09.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9835.63
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10197.53
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.021
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:42.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    3.46
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4673.63
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:49.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.55
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:50.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4249.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.11
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11597.75
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11890.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:29.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.35
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999939767

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.31
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999851117

Normal statistic for number of bits   :   -1.18
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:52.42
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 10  CollisionOver, t = 14           8.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 186908679.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5471
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:04:00.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:43.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:45.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:59.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7199
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:09.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:09.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:04:02.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:06.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.93
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:49.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.72
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.17
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:02:13.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:44.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.67
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:54.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.16
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.81
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.44
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.99
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.70
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.00
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.56
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.05
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.99
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:47.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.72
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:05.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7021.22
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.58
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.65
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:14.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.6e-3

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.21
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:09.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.54
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  147.55
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:37.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4992.34
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:00.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45919
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869919
  j =  1                              :        399908162
  j =  2                              :            45919
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45723
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869723
  j =  1                              :        399908560
  j =  2                              :            45711
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9968


-----------------------------------------------
CPU time used                    :  00:02:30.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:19.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:47.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:05.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:56.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:36.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 9.68e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.63e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:38.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:39.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.03
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:50.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.35
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.23
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.15
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.93
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.61
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:46.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.86e-3
p-value of test                       :    0.9916

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.35
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:29.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:29.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.00
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  157.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:39.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17469.47
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.48
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.07
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.14
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.64
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.39
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.58
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.59
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.59
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.48
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.34
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.00
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.24
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.38
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.53
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.95
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.51
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.93
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.08
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.61
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.09
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.17
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.78
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5173.47
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.10
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.89
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.99
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.05
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5138.96
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.55
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.79
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.24
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :    1.31
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:24.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.41
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:21.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.47e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.70e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 8.10e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.56
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.76
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.81
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:05.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.30
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:07.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10041.84
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9900.28
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:04:17.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4787.27
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:52.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4795.20
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:53.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.60
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.90
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11874.64
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:30.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11877.51
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:31.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.83
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999975869

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.91
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000080587

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:34.12

 All tests were passed




Server wird beendet - Lösche Semaphor 187924487.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:46.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5482
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:42.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4221
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:37.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:35.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:55.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:02.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7448
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:02.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:55.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:04:01.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    2.26
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     658
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.03
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     270
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    4.46
p-value of test                       :  5.2e-3

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:13.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:33.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.36
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.96
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.24
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.69
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.29
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  200.10
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.31
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:44.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1404.85
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:59.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7064.34
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.17
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.86
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:02.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.11
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.93
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:36.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5157.21
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:15.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:03.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45585
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869585
  j =  1                              :        399908832
  j =  2                              :            45581
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46097
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870097
  j =  1                              :        399907806
  j =  2                              :            46097
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:14.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:29.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:18.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:45.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:01.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:53.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:33.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.19e-6
p-value of test                       :    0.9973

Kolmogorov-Smirnov- statistic = D-    : 2.63e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.15e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.025
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:35.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:38.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.41
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:47.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.14
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   39.64
p-value of test                       :    0.9969

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.92
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:47.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.83
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:52.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.85
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.27
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:36.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.01
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.75
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:33.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:32.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.17
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17487.09
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.81
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.09
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.58
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    7.28
p-value of test                       :    0.9996    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.94
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.25
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.88
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.94
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.68
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.30
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:39.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.16
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.51
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.12
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.96
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.95
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:48.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.96
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.64
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.03
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.46
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.54
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:47.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.62
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.30
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5036.29
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.03
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.14
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.97
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.73
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5054.64
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.53
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.43
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.18
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :    1.57
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:26.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.84
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:13.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.88
p-value of test                       :    0.97

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.94e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.66e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.07
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.70
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.58
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:09.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.72
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:12.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10027.53
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10018.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:04:07.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.11
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:49.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4014.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4140.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11939.95
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12036.09
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:29.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.87
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999935321

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.80
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000069175

Normal statistic for number of bits   :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   0.077
p-value of test                       :    0.47

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.77

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    2.88
p-value of test                       :  2.1e-3

-----------------------------------------------
CPU time used                    :  00:01:29.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.28

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:16:02.86
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 R (L=50, r=0)       0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 168165384.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1252
p-value of test                       :    0.9989

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334372
  j =  1                              :        599997496
  j =  2                              :             1252
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5433
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:43.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:37.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:35.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:02.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:02.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:54.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:04:00.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:47.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:13.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.53
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:40.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.74
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.21
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.21
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.87
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.22
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.00
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   84.72
p-value of test                       :  4.8e-3

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.76
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.08
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  389.17
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:46.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1500.84
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:01.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7076.01
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:47.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    3.42
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.49
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:02.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.67
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.32
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:35.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4963.06
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:04.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45830
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869830
  j =  1                              :        399908343
  j =  2                              :            45824
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45454
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869454
  j =  1                              :        399909094
  j =  2                              :            45450
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:13.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:33.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:19.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:46.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:00.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:15.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.10e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:22.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:31.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:47.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.14
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.16
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.70
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:47.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.38
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.52
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:39.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.07
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.04
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.68
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:01:30.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.79
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17097.64
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.49
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.14
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.48
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.95
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.47
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.95
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.82
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.16
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.16
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.31
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.86
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.20
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.92
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.90
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.80
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:46.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.06
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.11
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.61
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.42
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.27
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.14
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.00
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5144.21
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.15
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.84
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.24
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.26
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.15
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.87
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.81
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.52
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:32.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.78
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:22.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.78e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 6.65e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.13e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.62
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.77
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.19
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:07.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.29
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:09.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9930.18
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9807.26
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:58.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4709.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:48.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5045.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:49.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4277.39
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.96
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11762.63
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12057.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.45
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999975848

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.06
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999917786

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.97
p-value of test                       :    0.02

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:13.25

 All tests were passed




Server wird beendet - Lösche Semaphor 169082888.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5357
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:43.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:37.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:35.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:54.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4215
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:55.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7132
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:03.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:03.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:57.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7147
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:04:01.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.56
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:46.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    2.68
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     566
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:11.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:40.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.43
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.85
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.09
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.24
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:11.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.29
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.19
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.11
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.94
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  471.00
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:51.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.66
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:02.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7013.39
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:52.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   49.87
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.18
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:09.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.45
p-value of test                       :    0.9940


-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   85.65
p-value of test                       :    0.9909


-----------------------------------------------
CPU time used                    :  00:01:36.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5064.57
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:02.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45678
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869678
  j =  1                              :        399908648
  j =  2                              :            45670
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45992
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869992
  j =  1                              :        399908021
  j =  2                              :            45982
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:35.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9952


-----------------------------------------------
CPU time used                    :  00:02:22.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:50.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:04.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:54.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 7.12e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 2.61e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.91
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   17.10
p-value of test                       :    0.9979

-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.97
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.02
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:48.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.73
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.35
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.36
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:29.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.39
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:29.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.60
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:39.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17353.89
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.72
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.14
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.12
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.73
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.03
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.06
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.31
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   45.67
p-value of test                       :  7.0e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.80
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.02
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:38.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.20
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.50
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.83
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.41
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.83
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.21
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.95
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.13
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.65
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.06
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.93
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.68
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.79
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.30
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.16
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.75
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.14
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4856.11
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.27
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.04
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.43
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:29.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.17
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :   -1.23
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:26.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.53
p-value of test                       :    0.06

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 8.94e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.10e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   20.93
p-value of test                       :  7.3e-3

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   20.50
p-value of test                       :  8.6e-3

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.63
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:05.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.57
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:08.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10147.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10020.90
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:11.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:04:28.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4915.91
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:56.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.26
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:56.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4199.88
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3993.47
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11901.91
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:36.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11851.20
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.65
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000081196

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.65
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000147532

Normal statistic for number of bits   :    1.17
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:12:37.92

 All tests were passed




Server wird beendet - Lösche Semaphor 170033160.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:52.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5384
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:49.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4467
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:39.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:38.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:57.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:58.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:08.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:08.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:04.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:04:12.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    2.47
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     543
p-value of test                       :    0.9903

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.15
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:14.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:41.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.68
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.13
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.58
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.90
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:29.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:57.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1360.20
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:08.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7163.29
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:55.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   50.88
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.25
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:16.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.66
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:46.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.03
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5071.66
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:08.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45714
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869714
  j =  1                              :        399908575
  j =  2                              :            45708
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46259
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870259
  j =  1                              :        399907483
  j =  2                              :            46257
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:32.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:20.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:49.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:09.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:56.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:39.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 7.47e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 5.53e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:24.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:24.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:49.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:49.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.61
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.06
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.71
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.77
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:50.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.43
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.90
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.18
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.85
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17281.08
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.53
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.73
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.87
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.77
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.86
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.10
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.79
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.98
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.74
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.59
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.26
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.52
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.45
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.16
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.52
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.95
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.48
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.72
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.76
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.08
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.98
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.51
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.11
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.56
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.96
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.96
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.19
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4934.22
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.18
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.29
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   27.98
p-value of test                       :  5.6e-3


-----------------------------------------------
Normal statistic for number of jumps  :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:24.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.63
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:25.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.56
p-value of test                       :    0.94

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 8.43e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.62
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.13
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.26
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  252.60
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:02:08.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.94
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:08.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10008.52
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9767.18
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.50
p-value of test                       :    0.9937

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:04:33.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4691.68
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:54.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4945.43
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:58.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.52
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.37
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11646.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:35.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11886.85
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:36.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.82
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000082555

Normal statistic for number of bits   :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.57
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000055510

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :  -0.046
p-value of test                       :    0.52

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:15.05

 All tests were passed




Server wird beendet - Lösche Semaphor 171573256.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5344
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:51.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:39.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:38.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:56.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:05.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:04.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7497
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:56.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:01.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:47.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.24
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     330
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:08.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:35.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.16
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.35
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.67
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.08
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.83
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.26
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.15
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.89
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.48
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:43.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1462.06
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:59.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6866.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:43.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.73
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.66
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:02.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.77
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.83
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4960.14
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:58.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45958
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869958
  j =  1                              :        399908087
  j =  2                              :            45952
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46046
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870046
  j =  1                              :        399907913
  j =  2                              :            46036
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:27.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:17.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:45.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:01.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :  2.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.83
p-value of test                       :  3.6e-3

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:32.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.73e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:21.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:33.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.91
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.75
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.70
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.02
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.30
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:42.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.55
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.40
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17475.53
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.85
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.63
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.39
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.81
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.37
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.95
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.83
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.50
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.87
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.12
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.27
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.93
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.40
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.55
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.36
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.94
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.65
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.25
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.40
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.32
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  446.41
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.26
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5025.70
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.47
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.49
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.71
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.04
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4987.08
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.59
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.98
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:36.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.40
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :    3.46
p-value of test                       :  2.7e-4    *****



-----------------------------------------------
CPU time used                    :  00:02:28.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.52
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :   -1.11
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:28.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :  -0.054
p-value of test                       :    0.52

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 6.49e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.15e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 7.64e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.26
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.82
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.94
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:07.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.47
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:06.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9967.97
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9739.57
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:46.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4791.29
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.13
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:51.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.69
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.14
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11681.13
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:29.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11628.92
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:29.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.92
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000052438

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   84.64
p-value of test                       :  4.9e-3


-----------------------------------------------
Total number of bits:  8000098389

Normal statistic for number of bits   :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :  -0.077
p-value of test                       :    0.53

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:03.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0               2.7e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 172916744.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5310
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:50.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:39.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:38.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4223
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:56.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:04.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:04.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7507
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:04:00.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:01.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     853
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:48.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:13.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    2.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:44.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.40
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.70
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.19
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.16
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.97
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.15
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.22
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  197.51
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  480.75
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:44.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1362.70
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:05.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7007.88
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:43.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:02.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.88
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.97
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:35.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5148.43
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:58.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46170
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870170
  j =  1                              :        399907663
  j =  2                              :            46164
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45747
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869747
  j =  1                              :        399908510
  j =  2                              :            45739
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:31.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 5.84e-3
p-value of test                       :    0.9927

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:28.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:17.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:45.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:59.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:32.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.32e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.29e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:21.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:33.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:34.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.17
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.21
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.03
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.73
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.51
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.96
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.20
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.45
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.33
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.21
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.69
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.94
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.67
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17926.32
p-value of test                       :  4.2e-3



-----------------------------------------------
CPU time used                    :  00:00:55.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.57
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.71
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.96
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.26
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.57
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.63
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.77
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.55
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.02
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.35
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.20
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.30
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.90
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.67
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.44
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.06
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.49
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.92
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.33
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.26
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.43
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.61
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4817.92
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.56
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.62
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.52
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.32
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4806.77
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.99
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.29
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.77
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -1.70
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:25.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.41
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:25.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.40e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:46.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.60
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:29.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.25
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.15
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:08.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 9.43e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.79
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:10.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9839.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10051.90
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:50.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.81
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:49.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4934.09
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:51.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4227.90
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4072.91
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11877.56
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:29.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11664.06
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.88
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000011254

Normal statistic for number of bits   :   0.089
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.56
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999933731

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.90
p-value of test                       :    0.03

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:39.36

 All tests were passed




Server wird beendet - Lösche Semaphor 173834248.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5438
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:50.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:39.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:38.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:55.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7459
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:04.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:04.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:55.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:00.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:48.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:15.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:43.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.71
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.05
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.66
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.12
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.22
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.67
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.68
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.98
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.39
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:42.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1379.64
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:58.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7206.25
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:43.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   85.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:00.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.58
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.09
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5101.73
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:06.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46054
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870054
  j =  1                              :        399907896
  j =  2                              :            46046
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46208
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870208
  j =  1                              :        399907589
  j =  2                              :            46198
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:28.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-3
p-value of test                       :    0.9985

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.55
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:17.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:44.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:58.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:55.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:33.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.91e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.65e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.14
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:22.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:33.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.15
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:48.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.88
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.54
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.92
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.19
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.51
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.21
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:41.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.12
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.80
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.35
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.32
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:09.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.06
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17647.69
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   17.78
p-value of test                       :    0.9953


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.76
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.37
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.33
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.86
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.05
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.41
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.27
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.57
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.31
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.66
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.96
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.93
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.27
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.45
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.17
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.57
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.43
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.79
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.39
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.20
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.21
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.83
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.17
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.02
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:36.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.80
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.67
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5083.74
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.64
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.26
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :    1.47
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:26.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.92
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   0.012
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:26.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.46e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 8.08e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.37e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 9.25e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.61
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   40.00
p-value of test                       :  4.5e-3



-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.74
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.47
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:09.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:08.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10062.74
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10142.84
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:50.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.95
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:49.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.84
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:50.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4019.94
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11545.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11845.94
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:30.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.77
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999969410

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.02
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999977798

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :  -0.028
p-value of test                       :    0.51

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:58.25

 All tests were passed




Server wird beendet - Lösche Semaphor 174751752.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:39.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:50.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5486
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:51.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:39.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:58.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:59.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:08.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:08.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:05.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:10.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.08
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    2.71
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     640
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:13.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.84
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    1.83
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:45.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.97
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.43
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.97
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.32
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.82
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.15
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.90
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  471.16
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:54.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1404.38
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:01.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7028.50
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.61
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.34
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.73
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:17.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.14
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:39.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5221.03
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:57.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45961
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869961
  j =  1                              :        399908082
  j =  2                              :            45953
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45827
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869827
  j =  1                              :        399908352
  j =  2                              :            45815
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:32.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:20.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:51.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:08.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:38.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.23e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.71e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 2.93e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.27
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:24.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:46.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:49.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.34
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.09
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.64
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.06
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.91
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.12
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:51.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.00
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.64
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.18
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.18
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17652.37
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.84
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.05
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.40
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.68
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.69
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.98
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.86
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.80
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.12
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.21
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.01
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.30
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.45
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.79
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.66
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.03
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.55
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.97
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.07
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.73
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.83
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.33
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.84
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.77
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.27
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.49
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.62
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5166.79
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.17
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.98
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.43
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:24.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.86
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :    0.51
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:24.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :  -0.082
p-value of test                       :    0.53

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.47e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.88e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.27
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.42
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.18
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:07.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.73
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:08.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9973.05
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10185.78
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:11.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:04:29.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4730.49
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:55.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4773.86
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:59.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3992.15
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11924.43
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:35.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11704.10
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:36.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.45
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000137488

Normal statistic for number of bits   :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.15
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999914105

Normal statistic for number of bits   :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:17.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.19
p-value of test                       :    0.99

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:53.12

 All tests were passed




Server wird beendet - Lösche Semaphor 175702024.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  5.6e-3


-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1484
p-value of test                       :  7.2e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334604
  j =  1                              :        599997032
  j =  2                              :             1484
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5331
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:51.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:39.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:39.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:57.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:05.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:05.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:55.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:04:01.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.43
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    3.67
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     838
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:46.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:13.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.13
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:42.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.04
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.86
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.96
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.40
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.56
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.60
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.80
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  194.99
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.40
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:42.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1410.10
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:00.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7101.86
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:42.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.85
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.63
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:03.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.66
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  155.18
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:35.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5040.92
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:55.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45996
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869996
  j =  1                              :        399908013
  j =  2                              :            45986
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46132
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870132
  j =  1                              :        399907738
  j =  2                              :            46128
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:28.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:18.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 8.56e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:44.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:00.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:54.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:34.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.13e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 9.33e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:21.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:35.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:37.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.62
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.71
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.63
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.17
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.26
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.74
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.06
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:44.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.61
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.42
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.37
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.54
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.94
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17109.91
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.38
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.63
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.55
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.15
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.17
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.01
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.58
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.71
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.56
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.16
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.79
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.22
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.89
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.83
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.63
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.13
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.84
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.72
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.43
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.55
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  450.54
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.28
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.61
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.92
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.93
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.60
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.87
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4861.35
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.06
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.14
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.65
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:24.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.91
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:25.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.33
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.33
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  154.85
p-value of test                       :    0.9922

-----------------------------------------------
CPU time used                    :  00:02:09.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.66
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:07.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10209.89
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10018.56
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.38
p-value of test                       :    0.9913

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:55.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4788.31
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4801.72
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:49.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.80
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4302.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11934.38
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11792.34
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:30.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.61
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000064105

Normal statistic for number of bits   :    0.51
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.43
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999980783

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.95
p-value of test                       :    0.03

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:34.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           7.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 177045512.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:10.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5426
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:51.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:39.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:39.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:57.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:04.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:04.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7135
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:54.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:59.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.97
p-value of test                       :  9.2e-3

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:13.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.41
p-value of test                       :  6.1e-3

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:39.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.59
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.58
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.09
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.29
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.05
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.74
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.38
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.77
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:42.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1423.02
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:00.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7064.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:42.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.87
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.65
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:03.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.86
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  151.46
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:34.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5032.36
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:56.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45827
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869827
  j =  1                              :        399908351
  j =  2                              :            45817
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45869
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869869
  j =  1                              :        399908264
  j =  2                              :            45865
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:27.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:17.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:44.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:59.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:54.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:34.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.53e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 8.98e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:21.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:34.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.095
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:34.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.37
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.54
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.38
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.63
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:48.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.23
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.97
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   47.61
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:42.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9939

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17488.24
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:56.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.94
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.37
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.29
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.75
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.41
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   58.29
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.88
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.03
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.90
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.34
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.38
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.76
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.73
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.09
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.01
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.99
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.87
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.30
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.06
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.05
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.19
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.71
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4930.60
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.55
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.76
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.72
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.97
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4793.77
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.05
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.95
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.54
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :    1.69
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:25.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.35
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:25.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.66e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.30e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 5.99e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.12
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.15
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.49
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:09.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.34
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:09.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10069.85
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9925.96
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:46.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.03
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:47.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.86
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:48.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.39
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4140.39
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11684.19
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11904.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:29.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.08
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000225931

Normal statistic for number of bits   :    1.79
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.25
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000187168

Normal statistic for number of bits   :    1.48
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.72
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.09

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:51.37

 All tests were passed




Server wird beendet - Lösche Semaphor 177995784.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  5.9e-3


-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5560
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:52.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:39.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4209
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4444
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:57.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:05.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:05.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:54.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:04:01.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:46.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     632
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.69
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:14.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.78
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:43.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.07
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.82
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.40
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.28
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.48
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.33
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.12
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.15
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.24
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:43.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1557.83
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:58.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6956.55
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.95
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.79
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:01.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.07
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:34.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5089.53
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:58.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45927
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869927
  j =  1                              :        399908147
  j =  2                              :            45925
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46107
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870107
  j =  1                              :        399907787
  j =  2                              :            46105
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:28.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:18.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:45.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:58.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:17.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 7.76e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.68
p-value of test                       :  3.7e-3

-----------------------------------------------
CPU time used                    :  00:01:35.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:37.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.85
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.12
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.64
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.12
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.89
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.30
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:44.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.15
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.43
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.96
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.63
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:10.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 2.37e-3
p-value of test                       :    0.9976

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   95.39
p-value of test                       :    0.9901

-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17358.40
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.07
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.12
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.20
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.52
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.95
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.63
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.07
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.29
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.20
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.39
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.87
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  105.04
p-value of test                       :    0.9957


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.97
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.12
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.22
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.58
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.15
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.70
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.47
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.17
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:43.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.70
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.97
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.44
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.79
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.19
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.77
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.78
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5093.15
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.45
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.25
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.98
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:25.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.45
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:28.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 6.31e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.58e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.48
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.18
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.23
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:08.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.02
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:09.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10078.52
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10231.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.28
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:03:45.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.35
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:50.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4821.98
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:50.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4040.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.22
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12082.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11739.87
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:29.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   83.90
p-value of test                       :  5.7e-3


-----------------------------------------------
Total number of bits:  7999935918

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.26
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999978176

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.94
p-value of test                       :    0.97

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:42.93

 All tests were passed




Server wird beendet - Lösche Semaphor 179011592.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:40.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5398
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:52.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:40.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7133
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:39.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:56.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:04.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:05.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:54.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:01.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    2.03
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.57
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:14.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    7.33
p-value of test                       :  2.7e-4    *****


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    2.85
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    2.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:42.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.99
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.24
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.16
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.81
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.41
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.92
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:43.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1423.28
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:00.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6948.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.59
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.47
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 5.58e-3
p-value of test                       :    0.9941

Anderson-Darling statistic = A2       :    3.44
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.24
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:03.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.80
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.27
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:35.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5069.74
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:00.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45578
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869578
  j =  1                              :        399908848
  j =  2                              :            45570
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45904
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869904
  j =  1                              :        399908194
  j =  2                              :            45900
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:28.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:18.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:45.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:59.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:15.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:33.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.45e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 9.61e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.48e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:22.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:35.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:36.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.98
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.20
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.87
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.27
p-value of test                       :    0.9958

-----------------------------------------------
CPU time used                    :  00:00:47.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.54
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.06
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.40
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:42.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.58
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.22
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.97
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.55e-3
p-value of test                       :    0.9919

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  158.06
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17496.03
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.88
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.17
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :    8.67
p-value of test                       :    0.9990


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.18
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.77
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.90
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.32
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.31
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.16
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.37
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.63
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.95
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.48
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.42
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.23
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.40
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.27
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  173.07
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.39
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.05
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.07
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.22
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.51
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.97
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.33
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.71
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4957.81
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.53
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.75
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:34.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.28
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:26.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.85
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :   0.012
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:26.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.40

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 2.32e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 8.91e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.46
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.07
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:06.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.83
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:08.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9895.77
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10036.62
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.067
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:43.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4773.73
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:48.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5097.92
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:50.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3965.57
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11704.19
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:28.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11696.93
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:29.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.26
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  7999885170

Normal statistic for number of bits   :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.50
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999951545

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :  -0.041
p-value of test                       :    0.52

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.59
p-value of test                       :    0.06

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:27.13
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs NP, t = 16           2.7e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 179994632.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1484
p-value of test                       :  7.2e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334604
  j =  1                              :        599997032
  j =  2                              :             1484
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5472
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:56.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4250
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:52.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:02.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:11.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:30.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:31.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:12.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:49.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    2.05
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     936
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:46.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.57
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     632
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:14.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:43.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.53
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.28
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.27
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.62
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.89
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.66
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.34
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.45
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.68
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.00
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.08
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:03.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7000.70
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:46.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.37
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:04.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.47
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.50
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:35.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4968.64
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:56.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46425
p-value of test                       :  5.5e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870425
  j =  1                              :        399907153
  j =  2                              :            46419
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46026
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870026
  j =  1                              :        399907953
  j =  2                              :            46016
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:35.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:32.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:03.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:20.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  8.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.46
p-value of test                       :  5.4e-3

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:35.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.75e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 9.45e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:42.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:41.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  101.11
p-value of test                       :  4.5e-3

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.92
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:10.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.31
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.59
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.83
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.23
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.27
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:44.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.71e-3
p-value of test                       :    0.9972

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.55
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.65
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.48
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:29.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.00
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.19
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17666.79
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.63
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.57
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.86
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.50
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.25
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.24
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   58.93
p-value of test                       :  6.9e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.90
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.44
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.90
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.87
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.54
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.79
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.01
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.66
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.14
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.48
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.65
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.30
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.76
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.60
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.65
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.21
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.99
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.91
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.68
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.35
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.37
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.67
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.43
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :    1.58
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:24.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.87
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:23.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.23
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.04e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.23e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.04
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.02
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.89
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:07.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.49
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:08.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.95e-3
p-value of test                       :    0.9926

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10257.28
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9992.55
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.025
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:04:11.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5001.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:50.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4744.93
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:51.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.74
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.53
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11701.22
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11992.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:30.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.04
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999878036

Normal statistic for number of bits   :   -0.96
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.60
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000053122

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:26.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           7.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 181043208.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1470
p-value of test                       :  2.4e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334590
  j =  1                              :        599997060
  j =  2                              :             1470
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5282
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:53.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4212
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:40.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:39.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:04.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:04.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7174
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:55.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:00.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.03
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.79
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:13.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:43.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.31
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.28
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.31
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.03
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.06
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.26
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.56
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  299.31
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  380.71
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:43.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.57
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:01.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7065.21
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:41.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.92
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.5e-3

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.30
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:03.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.14
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.23
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:35.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5036.12
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:13.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:56.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45766
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869766
  j =  1                              :        399908469
  j =  2                              :            45764
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45584
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869584
  j =  1                              :        399908834
  j =  2                              :            45580
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:28.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:17.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:45.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:00.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:54.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:32.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.12e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:36.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:35.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.20
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.79
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.97
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.56
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:43.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.71
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.64
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.95
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:29.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:29.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.40
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17408.98
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.57
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.65
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.03
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.84
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.59
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.78
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.22
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.78
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.26
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.39
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.73
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.36
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.35
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.42
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.88
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.85
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.51
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  571.31
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.20
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.06
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.28
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.17
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4954.99
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.26
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.41
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:37.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.17
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.44
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5177.52
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.06
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  153.55
p-value of test                       :    0.9937


-----------------------------------------------
CPU time used                    :  00:00:36.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   27.75
p-value of test                       :  6.0e-3


-----------------------------------------------
Normal statistic for number of jumps  :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:24.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.98
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :    1.91
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:24.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 4.65e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:46.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.72e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.42
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.26
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.40
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:05.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  245.39
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:07.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10251.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9824.59
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:47.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5019.18
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:48.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.05
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:50.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.46
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.62
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11981.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12025.01
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:29.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.67
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  7999933125

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.94
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999963635

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:41.64

 All tests were passed




Server wird beendet - Lösche Semaphor 182091784.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:50.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5429
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:55.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4195
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:39.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:04.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:03.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:54.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:01.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    3.79
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    2.73
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     261
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:15.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:43.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.81
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.53
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.93
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.43
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.18
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.48
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.98
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.07
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.28
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:43.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1371.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:01.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7252.67
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:41.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.24
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.81
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   36.13
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:03:03.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.93
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.47
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:34.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5254.51
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:00.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45868
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869868
  j =  1                              :        399908266
  j =  2                              :            45864
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46045
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870045
  j =  1                              :        399907912
  j =  2                              :            46041
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:28.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:18.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:45.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:59.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  8.5e-3

Kolmogorov-Smirnov- statistic = D-    : 8.88e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.06
p-value of test                       :  8.3e-3

-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:32.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.38e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.67e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.06
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.059
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:39.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.19
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:38.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.90
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.64
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.07
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.89
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.01
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.78
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:40.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.06
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.13
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.91
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.09
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:37.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17279.31
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   65.67
p-value of test                       :  1.8e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.95
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.52
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.09
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.12
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.40
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.66
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.00
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.03
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.09
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.12
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.91
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.88
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.06
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.57
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.88
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.54
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.46
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.28
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.54
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.04
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.99
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5199.75
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.84
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.23
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.85
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.25
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5268.62
p-value of test                       :  4.1e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.57
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.46
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.95
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:25.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.90
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:24.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.09e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.36
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.84
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.1e-3

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  242.61
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:06.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:09.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9954.49
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10075.89
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:47.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4964.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5009.54
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:49.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4025.36
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.78
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11926.54
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11871.53
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:29.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.00
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999947729

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.61
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000034720

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :  -0.042
p-value of test                       :    0.52

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:21.95

 All tests were passed




Server wird beendet - Lösche Semaphor 183042056.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1467
p-value of test                       :  3.1e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334587
  j =  1                              :        599997066
  j =  2                              :             1467
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5511
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:56.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:39.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:57.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:05.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:05.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7137
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:55.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7447
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:04:01.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:47.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:14.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9949

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:42.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.07
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.54
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.14
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.93
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.02
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  276.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:16.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.45
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:43.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1513.66
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:01.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7108.98
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:41.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.68
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   85.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:02.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.28
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   84.11
p-value of test                       :    0.9935


-----------------------------------------------
CPU time used                    :  00:01:34.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4925.66
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:59.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45879
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869879
  j =  1                              :        399908246
  j =  2                              :            45871
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45894
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869894
  j =  1                              :        399908216
  j =  2                              :            45886
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:28.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:18.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.8e-3

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:45.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:00.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:55.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:33.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 8.84e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:36.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:37.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.75
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.77
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:48.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.57
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.97
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.51
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:41.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.68
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.14
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.51
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.21
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  8.0e-3

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17758.02
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.90
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.10
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.98
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.67
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.14
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.83
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.89
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.02
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.29
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.15
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.42
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.73
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.68
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.86
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.67
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.01
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.57
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.04
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.22
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.18
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.08
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.23
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.42
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.44
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  321.52
p-value of test                       :    0.9910


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.01
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4895.98
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.63
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.78
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.58
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:24.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.31
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :   -1.63
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:25.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :  -0.011
p-value of test                       :    0.50

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 6.63e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.67e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 6.80e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.95
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.78
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.17
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:04.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.25
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:07.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9974.70
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9946

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.84
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.097
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:44.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.91
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5007.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:50.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4240.23
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4203.17
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11741.30
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11899.98
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:29.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.25
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  7999946157

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.05
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999898085

Normal statistic for number of bits   :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :  -0.034
p-value of test                       :    0.51

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    2.66
p-value of test                       :  4.5e-3

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.76
p-value of test                       :    0.96

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:54.45

 All tests were passed




Server wird beendet - Lösche Semaphor 183992328.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5369
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:57.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:42.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4434
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:56.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4475
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:57.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:06.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:05.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:55.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:00.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.11
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    2.58
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.87
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:14.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.84
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:46.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.95
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.20
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.35
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.57
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.41
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.86
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.99
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:44.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1414.04
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:01.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6867.15
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.45
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:03.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.70
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.62
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:35.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4975.81
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:00.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45634
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869634
  j =  1                              :        399908736
  j =  2                              :            45626
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45953
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869953
  j =  1                              :        399908097
  j =  2                              :            45947
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:28.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:19.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:00.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:33.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 8.90e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 8.38e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:40.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.076
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:41.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.61
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.71
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.18
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.92
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.31
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.13
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.92
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:44.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.11
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.03
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.79
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17526.36
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.24
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.60
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.29
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.94
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.78
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.70
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.08
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.03
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.61
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.17
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.30
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.27
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.68
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.87
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.69
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.34
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.86
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.01
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.98
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.60
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.38
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5090.21
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.57
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.68
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.39
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.11
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.27
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.82
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.05
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.94
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :    0.57
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:25.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.07
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :    1.47
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:25.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 9.19e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 9.79e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.48
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.26
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:05.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.49
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:07.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9916.56
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10062.36
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.080
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:43.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.36
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.50
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:50.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.25
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4188.24
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11804.06
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:29.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11939.88
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:30.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.09
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000025585

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.63
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000046105

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :  -0.074
p-value of test                       :    0.53

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:01.90

 All tests were passed




Server wird beendet - Lösche Semaphor 185040904.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5267
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:59.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:42.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:58.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7085
p-value of test                       :    0.9969


-----------------------------------------------
CPU time used                    :  00:03:06.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:06.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:55.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:04:00.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.74
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:13.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.34
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:43.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.41
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.52
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.99
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.69
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.06
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.18
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.51
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.73
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.83
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:45.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1503.05
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:01.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7033.86
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.93
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.54
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:03.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.03
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.26
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4954.01
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:02.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45892
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869892
  j =  1                              :        399908221
  j =  2                              :            45882
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45837
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869837
  j =  1                              :        399908330
  j =  2                              :            45829
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:28.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 5.61e-3
p-value of test                       :    0.9934

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:18.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:45.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:00.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:54.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:32.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 3.05e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:35.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:35.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.63
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:49.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.96
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.80
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.96
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.29
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.34
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:43.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.98
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.38
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.73
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.92
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.75
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17457.70
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.27
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.78
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.68
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.96
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.48
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.62
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.61
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.62
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.09
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.59
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.14
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.28
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  428.74
p-value of test                       :    0.9906


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.71
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.91
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.35
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.19
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.84
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.36
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.47
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.22
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.84
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4892.48
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.86
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.60
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.41
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.09
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.20
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.07
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.28
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.41
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:23.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.99
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:24.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 8.23e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.69
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.69
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.30
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:05.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.87
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:07.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10180.80
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10069.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:43.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4852.17
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.66
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:49.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4279.30
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4049.78
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11612.30
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11788.93
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.90
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999904448

Normal statistic for number of bits   :   -0.76
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.54
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999986804

Normal statistic for number of bits   :   -0.10
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.19
p-value of test                       :    0.12

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.34
p-value of test                       :  9.7e-3

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:51.95

 All tests were passed




Server wird beendet - Lösche Semaphor 186089480.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1462
p-value of test                       :  4.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334582
  j =  1                              :        599997076
  j =  2                              :             1462
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5499
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:56.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:41.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:57.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:57.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:05.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:06.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:55.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:00.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    4.21
p-value of test                       :  6.9e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    2.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9949


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.77
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     331
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:13.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.78
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    2.01
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:41.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.73
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.61
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.15
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.41
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.85
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.65
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  190.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.95
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:44.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1498.31
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:02.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7157.60
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.78
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:04.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   19.71
p-value of test                       :  1.4e-3


-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  143.88
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:35.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4951.92
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:58.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45775
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869775
  j =  1                              :        399908452
  j =  2                              :            45771
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45988
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869988
  j =  1                              :        399908025
  j =  2                              :            45986
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :  3.9e-3

Anderson-Darling statistic = A2       :    3.16
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:28.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:18.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:45.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:01.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:55.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:33.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.34e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.14e-5
p-value of test                       :    0.9948

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.62e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:37.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:36.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.08
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.31
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.09
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.22
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.14
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:45.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.01
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.55
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.18
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.90
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.91
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17330.50
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.08
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.59
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.57
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.34
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.84
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.32
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.35
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.35
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.25
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.08
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.50
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.53
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.40
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.23
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.21
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.43
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.97
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  439.27
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.52
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.22
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.01
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.44
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5205.83
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.53
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.18
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.74
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  329.53
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.54
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.52
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.01
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.86
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.83
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    1.18
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:26.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 6.32e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 6.29e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.38
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.51
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.88
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:07.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.40
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:08.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9940.47
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10081.63
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:41.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4868.10
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:48.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5087.42
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:50.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.09
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4207.34
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11843.31
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:28.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11972.86
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:30.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.40
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000037798

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.33
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999851336

Normal statistic for number of bits   :   -1.18
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.17
p-value of test                       :    0.02

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:10.40

 All tests were passed




Server wird beendet - Lösche Semaphor 187105288.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:39.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5559
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:58.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:41.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:41.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:57.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:58.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:06.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:06.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7479
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:56.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:04:00.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.75
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    2.67
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    5.33
p-value of test                       :  2.0e-3

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.69
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:13.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:46.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.32
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.56
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.47
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.71
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.62
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  268.84
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  490.78
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1422.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:01.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7170.84
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:41.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.31
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.10
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:04.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.26
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.22
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5172.60
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:04.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45801
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869801
  j =  1                              :        399908403
  j =  2                              :            45791
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45781
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869781
  j =  1                              :        399908442
  j =  2                              :            45773
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:28.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 6.46e-3
p-value of test                       :    0.9922

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:18.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:45.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9960


-----------------------------------------------
CPU time used                    :  00:02:00.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:33.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.43e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 4.45e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.78e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.57e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:22.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:33.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:34.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.95
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.04
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:51.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.56
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.75
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.74
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.21
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.65
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.24
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.99
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.74
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16986.17
p-value of test                       :    0.9917



-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.61
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.59
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.35
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.72
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.08
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.99
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.09
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.49
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.68
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.01
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.35
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.31
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.21
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.32
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.86
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.65
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.42
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.49
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.15
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.52
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.94
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.91
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4802.81
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.66
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.58
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  469.05
p-value of test                       :  1.9e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.13
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.41
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.28
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.78
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:36.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.24
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:21.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.82
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:24.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.17e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 8.96e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 5.76e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.43
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:30.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.63
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.25
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:05.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.00
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:06.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10098.39
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10266.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.018
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.077
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:39.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4844.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4943.18
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:49.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.97
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4040.89
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12013.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11568.99
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:29.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.44
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000014356

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.74
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000036094

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         : 1.80e-4
p-value of test                       :    0.50

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:33.22

 All tests were passed




Server wird beendet - Lösche Semaphor 188153864.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:47.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5400
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:43.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:37.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:36.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:54.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4462
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:03.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:04.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:58.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:03.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     859
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:50.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.76
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:08.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.94
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    2.00
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:42.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.59
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.64
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.68
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.16
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.58
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.17
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.18
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.33
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1397.76
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:06.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6732.52
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:01:52.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.00
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9916

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.68
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:16.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.79
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:47.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.15
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:41.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5162.25
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:30.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:23.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45749
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869749
  j =  1                              :        399908505
  j =  2                              :            45743
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46083
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870083
  j =  1                              :        399907838
  j =  2                              :            46075
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:30.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:18.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:44.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:59.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:54.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:36.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 7.95e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.057
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:51.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:50.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.55
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:50.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.10
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.51
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.24
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:51.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.46
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:50.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.63e-3
p-value of test                       :    0.9918

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.77
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.94
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.62
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:35.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.25
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:29.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17520.55
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:50.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.63
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.92
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.42
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.45
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.33
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.42
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.11
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.39
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.76
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.03
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.67
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.52
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.51
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.63
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.49
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.86
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.48
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.22
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.06
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.89
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.77
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.79
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4852.74
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  293.39
p-value of test                       :    0.9995    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.87
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.27
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.55
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5089.90
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.84
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.67
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:36.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.74
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :   -2.90
p-value of test                       :    0.9982



-----------------------------------------------
CPU time used                    :  00:02:26.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.82
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:28.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.93

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.53e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 7.19e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 5.48e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:47.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.02
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:29.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.87
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:07.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:08.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10124.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.24e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10143.14
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:11.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.075
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:04:23.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4889.19
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:53.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4913.31
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:55.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.28
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.25
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:29.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11836.98
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:36.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11690.45
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:35.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.89
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999980633

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.83
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  7999922514

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.61
p-value of test                       :    0.05

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:20:22.22
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 R (L=10000, r=0)    0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 168198153.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:46.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5322
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:49.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:39.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:38.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:55.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:03.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:04.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:55.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:04:00.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     560
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:16.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.53
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.86
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:17.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9920

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:48.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.26
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.66
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.61
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.96
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.26
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.12
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:47.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1528.03
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:01.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7043.01
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:43.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.01
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:05.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.78
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.94
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:36.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5038.75
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:04.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46015
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870015
  j =  1                              :        399907973
  j =  2                              :            46009
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45965
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869965
  j =  1                              :        399908077
  j =  2                              :            45951
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:27.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:17.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:44.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:59.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:54.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:33.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.38e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:21.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:33.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:31.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.19
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.25
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.40
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.05
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.98
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.84
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.41
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.40
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.64
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17630.64
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.40
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.55
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.66
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.96
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.19
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.44
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.97
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.00
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.03
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.08
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:38.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.38
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.06
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.52
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.23
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.87
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.92
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.13
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.34
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.88
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.36
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.21
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.71
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.91
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.68
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  241.29
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.14
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.17
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5034.47
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.53
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.61
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.32
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:25.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.59
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   -1.43
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:27.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:11.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.86e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:48.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 4.16e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:46.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   21.09
p-value of test                       :  6.9e-3

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.50
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.34
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:08.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.15
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:10.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9917.16
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.3e-3

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10295.65
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:49.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4969.90
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:49.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4964.90
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:52.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4071.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.95
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11926.99
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:32.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11938.22
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:33.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.22
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000016108

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.59
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999929840

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :  -0.084
p-value of test                       :    0.53

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:38.00

 All tests were passed




Server wird beendet - Lösche Semaphor 169869321.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:46.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1470
p-value of test                       :  2.4e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334590
  j =  1                              :        599997060
  j =  2                              :             1470
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5353
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:49.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:38.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:38.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:56.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:03.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:03.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:53.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:00.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    2.42
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.70
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:15.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:44.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.36
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.36
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.16
p-value of test                       :    0.9946

-----------------------------------------------
CPU time used                    :  00:01:09.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.48
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.67
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.16
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.17
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:44.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.32
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:58.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6934.03
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:39.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.94
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:12.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.20
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:03.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.92
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.97
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4817.30
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:15.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45632
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869632
  j =  1                              :        399908741
  j =  2                              :            45622
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45663
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869663
  j =  1                              :        399908676
  j =  2                              :            45659
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:28.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:17.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:44.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:59.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:54.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:15.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:33.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.97
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:22.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:34.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:35.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.16
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:47.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.87
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.62
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.94
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:47.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.34
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.14
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.36
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:42.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.23
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:28.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.77
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17505.15
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:55.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.10
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.62
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.87
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.43
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.08
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.07
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.95
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.71
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.52
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.04
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.72
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.71
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.69
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.57
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.62
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.72
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.20
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.77
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.84
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.40
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.79
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.91
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4928.82
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.47
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  244.24
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.69
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.28
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.20
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.15
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.23
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.97
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :    0.86
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:25.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.67
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :   -1.43
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:26.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.96
p-value of test                       :    0.02

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.97e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 6.27e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.93
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.10
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:06.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.89
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:09.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10119.28
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10003.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.096
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:56.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:43.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4804.93
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:48.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.97
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:50.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4234.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4078.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11746.98
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11931.30
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:30.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   89.84
p-value of test                       :  1.6e-3


-----------------------------------------------
Total number of bits:  7999966482

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.56
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999885455

Normal statistic for number of bits   :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:55.57

 All tests were passed




Server wird beendet - Lösche Semaphor 170819593.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:51.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5299
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:49.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:39.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:37.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:55.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4205
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:03.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:03.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:54.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:00.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     867
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:46.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    3.84
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    2.57
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.04
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:15.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:47.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.14
p-value of test                       :    0.9922

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.62
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.43
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.67
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.07
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.21
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.02
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  200.38
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.37
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:43.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1392.99
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:59.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6891.25
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.08
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.03
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:03.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.11
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  143.39
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:35.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4973.47
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:58.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45764
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869764
  j =  1                              :        399908475
  j =  2                              :            45758
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45739
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869739
  j =  1                              :        399908524
  j =  2                              :            45735
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:30.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:18.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:45.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:00.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:54.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:31.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.74e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.39e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:33.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:33.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.40
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:48.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.10
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.77
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.37
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:47.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.61
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.79
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:40.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.09
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.47
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.06
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.64
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17494.68
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:55.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.51
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.25
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.94
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.90
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.12
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.26
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.45
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.92
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.88
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.08
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.27
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.19
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.63
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.25
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.84
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.69
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.64
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.28
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.36
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.36
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.02
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5118.46
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.25
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.70
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.26
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.59
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4832.94
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.45
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.34
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.31
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :   -0.14
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:25.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.75
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :   0.066
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:27.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   0.087
p-value of test                       :    0.47

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.28e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:46.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.33
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.49
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.40
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:07.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.75
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:08.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.23e-3
p-value of test                       :    0.9934

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10285.58
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10034.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.052
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:50.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.46e-3
p-value of test                       :    0.9964

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5139.84
p-value of test                       :  6.4e-3

-----------------------------------------------
CPU time used                    :  00:01:49.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4772.93
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:50.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.23
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4188.42
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11730.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:29.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11950.15
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:30.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.78
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999927209

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.15
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000021664

Normal statistic for number of bits   :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.38

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   0.038
p-value of test                       :    0.48

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:28.76

 All tests were passed




Server wird beendet - Lösche Semaphor 171540489.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1474
p-value of test                       :  1.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334594
  j =  1                              :        599997052
  j =  2                              :             1474
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5415
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:46.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:36.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7191
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:35.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:55.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:55.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:02.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7145
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:02.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:53.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7189
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:59.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:45.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9948


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.57
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     266
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:13.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    2.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:40.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.62
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.47
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.33
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.27
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.28
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.11
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  268.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.43
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:43.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1385.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:00.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6991.82
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:44.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.44
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.74
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:01.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.86
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.58
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:34.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5055.07
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:01.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45777
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869777
  j =  1                              :        399908450
  j =  2                              :            45769
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45923
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869923
  j =  1                              :        399908158
  j =  2                              :            45915
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:29.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:18.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:44.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:58.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.40e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:34.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.77
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:33.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.34
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:47.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.07
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.56
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:48.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.19
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.04
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.63
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.27
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.03
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.99
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   99.75
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17484.97
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.39
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.68
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.46
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.47
p-value of test                       :    0.9923


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.98
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.83
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.47
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.33
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.91
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.85
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.52
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.76
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.82
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.87
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.99
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.20
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.83
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.83
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.28
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.11
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.13
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.74
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4903.76
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.63
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.38
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.24
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.81
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.93
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  436.79
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:36.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.67
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :   -1.41
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:25.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.91
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :   -1.12
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:24.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.011
p-value of test                       :    0.50

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.75e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.49
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.11
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.01e-3
p-value of test                       :    0.9948

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  248.57
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:05.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.74
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:08.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9834.88
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10060.52
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.078
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.076
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:48.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:50.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.3e-3

Anderson-Darling statistic = A2       :    3.66
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5034.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:50.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4260.51
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.51
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11918.07
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:28.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12082.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:30.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.20
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000022258

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.94
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000055279

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    3.85
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.35
p-value of test                       :    0.9907

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:02.98

 All tests were passed




Server wird beendet - Lösche Semaphor 172392457.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5438
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:53.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:38.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:55.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:55.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:02.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:02.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:53.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:58.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.60
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.24
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    2.97
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     665
p-value of test                       :  4.7e-3

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:13.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:41.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.39
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.92
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.73
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.84
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.26
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.05
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:43.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.95
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6930.85
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:43.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.38
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.50
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   86.57
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:03:03.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.00
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.88
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:35.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4940.31
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:00.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45529
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869529
  j =  1                              :        399908945
  j =  2                              :            45523
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46314
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870314
  j =  1                              :        399907373
  j =  2                              :            46312
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:29.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:18.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:44.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:59.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:56.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 5.90e-4
p-value of test                       :    0.9994    *****

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:36.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 9.85e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.015
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:35.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.44
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:48.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   40.24
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.78
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:48.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.38
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.20
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.83
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    4.98
p-value of test                       :  3.1e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.09
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.24
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.71
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  171.21
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17357.62
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.98
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.44
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.79
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.14
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.69
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.43
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.21
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.09
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.95
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.70
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.04
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.62
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.01
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.51
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.32
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.90
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.02
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.71
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.26
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.52
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.85
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4967.70
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.50
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.31
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.92
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.79
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4879.61
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.01
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.83
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.46
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:24.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.91
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :   -0.48
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:23.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 8.54e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 9.52e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.53
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.68
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:06.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.73
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:07.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10185.00
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9924.14
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:04:00.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4777.42
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:50.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 8.32e-5
p-value of test                       : 1 -  8.3e-5    *****

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4688.56
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:51.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.29
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4278.65
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11819.65
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11958.27
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:30.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.17
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999845483

Normal statistic for number of bits   :   -1.22
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.42
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999874520

Normal statistic for number of bits   :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.20

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:46.42

 All tests were passed




Server wird beendet - Lösche Semaphor 173309961.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:48.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5359
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:57.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7168
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4427
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:57.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:04.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:03.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:52.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:59.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     936
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    5.05
p-value of test                       :  2.7e-3

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.23
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    2.11
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:14.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:44.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.04
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.52
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.91
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.30
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.03
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.33
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.67
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.05
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.78
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.98
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:43.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1441.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:00.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7072.63
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:41.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.08
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:02.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.17
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.02
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:34.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5099.59
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:02.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45657
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869657
  j =  1                              :        399908688
  j =  2                              :            45653
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45647
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869647
  j =  1                              :        399908711
  j =  2                              :            45637
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:29.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:17.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:43.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:58.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:56.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:36.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 3.34e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:21.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:33.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:34.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.07
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.52
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.31
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.71
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:48.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.74
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.25
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.46
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:38.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.46
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.69
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.51
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17477.89
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.24
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.87
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.39
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.33
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.95
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.02
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.71
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.96
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.43
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.74
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.43
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.86
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.27
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.20
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.68
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.33
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.37
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.97
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.98
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.52
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.19
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.75
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.46
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.92
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.34
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.36
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.04
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.29
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  434.55
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.07
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:34.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.26
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :   -1.27
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:23.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.05
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :   0.057
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:23.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.51
p-value of test                       :    0.07

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 6.78e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.54e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.08
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.74
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.35
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:04.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 3.53e-3
p-value of test                       :    0.9964

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.73
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:06.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10212.85
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9929.82
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:49.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4805.96
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:50.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4978.36
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:52.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.44
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.65
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11472.32
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:29.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11679.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:30.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.94
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999974357

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   31.54
p-value of test                       :    0.9937


-----------------------------------------------
Total number of bits:  8000000004

Normal statistic for number of bits   : 3.16e-5
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    0.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.86
p-value of test                       :    0.03

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:10.30

 All tests were passed




Server wird beendet - Lösche Semaphor 174358537.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:50.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1467
p-value of test                       :  3.1e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334587
  j =  1                              :        599997066
  j =  2                              :             1467
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.08

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5456
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:58.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:42.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:43.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:57.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:58.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7499
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:03.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:03.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:53.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:58.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.57
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.18
p-value of test                       :    0.9955

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     336
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.83
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:11.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:43.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.54
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.12
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.64
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.39
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.45
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.93
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  453.85
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:44.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1531.06
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:00.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7212.19
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.51
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:02.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.05
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.21
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:34.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5128.79
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:55.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46044
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870044
  j =  1                              :        399907917
  j =  2                              :            46034
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45654
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869654
  j =  1                              :        399908694
  j =  2                              :            45650
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:27.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:18.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:44.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:58.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:35.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.53e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.68e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 4.99e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:33.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:34.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.32
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.68
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.78
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.64
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.25
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:38.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.17
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.58
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.05
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:16.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  158.56
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17311.57
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.97
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.42
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.56
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.82
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.89
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.35
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.10
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   46.59
p-value of test                       :  5.5e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.14
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.80
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.20
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.61
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.05
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  175.23
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.79
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.08
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.95
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.16
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.88
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.41
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.25
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.25
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4881.48
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.56
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.64
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.83
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.08
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4915.47
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.32
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.47
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.44
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :  -0.010
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:23.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.02
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:23.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.02
p-value of test                       :    0.98

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.94e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 5.12e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.55
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.80
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.40
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:06.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.45
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10120.96
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10006.69
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:49.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.90
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:49.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4842.79
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:51.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4147.73
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.88
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11793.39
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11914.05
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.73
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999927677

Normal statistic for number of bits   :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.20
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000163750

Normal statistic for number of bits   :    1.29
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:15.87

 All tests were passed




Server wird beendet - Lösche Semaphor 175374345.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1516
p-value of test                       :  2.8e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334636
  j =  1                              :        599996968
  j =  2                              :             1516
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5436
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:02.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:44.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7444
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:45.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:01.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:01.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:10.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:08.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:04:04.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:03.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.80
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    2.18
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:51.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:17.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.53
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    2.61
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:44.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.59
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.86
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.59
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.68
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.37
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.81
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.23
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  185.03
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:29.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:52.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1363.31
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:09.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7011.09
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.04
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.37
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:02.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.72
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.65
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:33.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5067.65
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:55.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45874
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869874
  j =  1                              :        399908259
  j =  2                              :            45860
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45574
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869574
  j =  1                              :        399908858
  j =  2                              :            45562
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:28.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:22.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:49.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:05.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:57.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:38.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.75e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:24.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.062
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:37.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:37.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.68
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.14
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.47
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.62
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.21
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.70
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:50.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.61
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.76
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.15
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  158.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17251.77
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:52.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.93
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.59
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.11
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.32
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.41
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.07
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.42
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.04
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.16
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:37.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.21
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.79
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.12
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.20
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.63
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.34
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.59
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.96
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.03
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.42
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.08
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.59
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.40
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.17
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.55
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.79
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4903.64
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.99
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.30
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.24
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :    0.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:23.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.56
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :    1.38
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:24.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 7.69e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.49e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.09
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.02
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.98
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:08.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.35
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:07.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10117.80
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9878.03
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.051
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:46.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4940.07
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:52.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4946.95
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:51.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4159.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3969.74
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11770.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:30.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11957.40
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:31.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.16
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000041437

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.81
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999781343

Normal statistic for number of bits   :   -1.73
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   0.018
p-value of test                       :    0.49

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:06.96
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           2.8e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 176357385.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5397
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:04:03.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:44.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:45.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:00.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:06.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7096
p-value of test                       :    0.9954


-----------------------------------------------
CPU time used                    :  00:03:04.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:55.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:59.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.98
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.16
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     866
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:51.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.72
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:16.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.16
p-value of test                       :    0.9974

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:46.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.96
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.92
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.61
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.21
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.30
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.60
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.33
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  266.03
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.75
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:44.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1386.54
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:01.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7241.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:42.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.27
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-3
p-value of test                       :    0.9984

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.97
p-value of test                       :  3.1e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :  105.62
p-value of test                       :  2.5e-4    *****

-----------------------------------------------
CPU time used                    :  00:03:04.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.68
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.77
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:33.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5297.61
p-value of test                       :  5.5e-3


-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:59.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46009
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870009
  j =  1                              :        399907989
  j =  2                              :            45995
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45791
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869791
  j =  1                              :        399908421
  j =  2                              :            45785
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 9.01e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:27.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:17.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:59.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:36.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.64e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:41.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:40.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.98
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.57
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.79
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.85
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.26
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.28
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:37.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.68
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.19
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.05
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.01
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17421.12
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.87
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.19
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.26
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.91
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.68
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:37.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.93
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.48
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.63
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.75
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.66
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:36.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.93
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.61
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.19
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.68
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.41
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.27
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.43
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.47
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.47
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.31
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.83
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.44
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5025.95
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.77
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.49
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.19
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.84
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4895.57
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.96
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.56
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:34.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.70
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:22.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.13
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:23.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.48e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 8.61e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.57
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.54
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:05.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.20
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:04.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10235.98
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10055.65
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:45.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5026.52
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4990.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:51.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.37
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4224.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11689.24
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:30.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11743.73
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.22
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  8000059446

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.99
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000148570

Normal statistic for number of bits   :    1.17
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:27.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 39  Run, r = 15                     2.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 177373193.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:49.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5575
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:04:03.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4214
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:43.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:47.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:00.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:02.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:13.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:11.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:52.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:58.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     865
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:53.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:17.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.60
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:46.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.62
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:55.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.11
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.54
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.21
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.77
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  483.37
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:55.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.33
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:01.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7262.26
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:06.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.35
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.37
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:02.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.56
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5086.05
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:57.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46260
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870260
  j =  1                              :        399907482
  j =  2                              :            46256
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45967
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869967
  j =  1                              :        399908068
  j =  2                              :            45963
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:28.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:17.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 2.86e-3
p-value of test                       :    0.9970

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:44.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:55.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9979

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:35.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 7.71e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 6.39e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:33.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:34.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.32
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.06
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.09
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.20
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.95
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   63.12
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.04
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.30
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  174.87
p-value of test                       :  5.3e-3

-----------------------------------------------
CPU time used                    :  00:00:50.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17393.22
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.96
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.61
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.69
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.09
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.23
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.36
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.76
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.37
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.21
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.74
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.38
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.58
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.42
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.11
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.91
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.65
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.46
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.92
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.66
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.66
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.65
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.50
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4807.17
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.59
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.81
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.54
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.52
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5110.43
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.74
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.61
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.39
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :   -1.29
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.20
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:22.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 9.20e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.06e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.26
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.88
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.51
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:11.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-3
p-value of test                       :    0.9979

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  241.60
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:13.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9858.60
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9963.17
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:42.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4913.55
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:48.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4971.62
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:50.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4038.71
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4173.56
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11742.60
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:29.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11628.08
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.80
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999967610

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.89
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000077275

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :  -0.037
p-value of test                       :    0.51

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:43.94

 All tests were passed




Server wird beendet - Lösche Semaphor 178421769.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1274
p-value of test                       :    0.9929

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334394
  j =  1                              :        599997452
  j =  2                              :             1274
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5355
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:02.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:44.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:58.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:00.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:09.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:09.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:56.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:59.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:52.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     564
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:19.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.48
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:44.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.56
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.39
p-value of test                       :    0.9997    *****

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.14
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:55.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.99
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   82.20
p-value of test                       :  8.0e-3

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.92
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.43
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.00
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.34
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.54
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:44.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1433.81
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:01.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7071.78
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:43.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.96
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.61
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:04.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.99
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.95
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5158.33
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:53.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46046
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870046
  j =  1                              :        399907915
  j =  2                              :            46032
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45915
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869915
  j =  1                              :        399908172
  j =  2                              :            45911
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:27.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:17.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:45.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:58.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:17.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  1.0e-2

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    4.02
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:01:36.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 5.65e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:37.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.77
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.28
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.16
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.39
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.70
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.55
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.51
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.06
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.87
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.89
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.87
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.85
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17230.86
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.68
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.34
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.67
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.54
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.53
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.33
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.82
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.85
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.33
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.94
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.18
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.49
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.96
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.88
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.77
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.68
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.66
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  592.84
p-value of test                       :  2.6e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.60
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.94
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.77
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.23
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5099.71
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.18
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.28
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.08
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.48
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.02
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.28
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.81
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.46
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :   -0.63
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:22.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.82
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:22.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.67
p-value of test                       :    0.05

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.74e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 9.33e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.72e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 8.37e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.89
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.94
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.90
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:04.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.17
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:05.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10088.31
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10156.33
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:42.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4996.76
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:49.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4778.75
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:50.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.88
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4008.13
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11861.06
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11897.11
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:29.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.73
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999959648

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.17
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000042052

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.7e-3

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.92
p-value of test                       :    0.03

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:34.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 27  SimpPoker, r = 27               0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 179437577.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5308
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:01.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:43.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:46.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4427
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:59.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:01.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:09.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:07.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:57.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:00.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:55.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    2.08
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:18.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:47.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.90
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.45
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.56
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.21
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.73
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.48
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.06
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  478.71
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:44.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1471.98
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:01.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6849.90
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:43.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.24
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:04.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.62
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.86
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:34.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5103.42
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:54.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46024
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870024
  j =  1                              :        399907955
  j =  2                              :            46018
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46054
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870054
  j =  1                              :        399907893
  j =  2                              :            46052
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:27.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:17.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:45.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:59.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:55.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:16.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:36.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 7.91e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.38e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.022
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:38.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.35
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.58
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.96
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.65
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.85
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.00
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.73
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.26
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.23
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17392.66
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.29
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.16
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.88
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.90
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.67
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.81
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.01
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.17
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.16
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   36.64
p-value of test                       :  3.8e-3


-----------------------------------------------
CPU time used                    :  00:00:36.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.30
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.72
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.80
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.98
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.01
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.67
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.38
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.32
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.58
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.90
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.63
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  459.06
p-value of test                       :  5.0e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4957.03
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  324.47
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.08
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.97
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.23
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4991.40
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.05
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.97
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:35.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.20
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:22.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.58
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :    0.14
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:22.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 5.65e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.72e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 7.39e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.39
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.83
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.50
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:05.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.78
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:05.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10118.79
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9925.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:41.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4701.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:49.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4978.59
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:50.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4169.40
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4237.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11885.17
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:28.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11692.22
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:29.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.20
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999898496

Normal statistic for number of bits   :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.92
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999993266

Normal statistic for number of bits   :  -0.053
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :  -0.100
p-value of test                       :    0.54

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:40.92

 All tests were passed




Server wird beendet - Lösche Semaphor 180486153.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9948


-----------------------------------------------
CPU time used                    :  00:01:12.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5457
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:59.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:43.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:45.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:02.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:11.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:11.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:58.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:01.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.40
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.90
p-value of test                       :  9.9e-3

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    2.48
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.05
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.54
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:18.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:45.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.07
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.79
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.44
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.90
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.54
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.88
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.00
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:43.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1368.23
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:02.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7079.38
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:42.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.47
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.31
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:03.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.04
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.42
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:34.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4999.06
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:54.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45827
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869827
  j =  1                              :        399908350
  j =  2                              :            45819
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45913
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869913
  j =  1                              :        399908176
  j =  2                              :            45909
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:28.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:19.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:01.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.68e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 9.69e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:21.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.046
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:38.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:38.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.29
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.58
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.81
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.92
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.98
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.04
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.51
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:45.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9928

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.78
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.89
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   14.49
p-value of test                       :  2.3e-3

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.07
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.50
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.00
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17346.92
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:52.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.62
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.77
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.79
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.56
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.60
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.55
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.98
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.39
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.36
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.23
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.99
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.63
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.83
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.40
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.40
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.12
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.54
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.44
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.71
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.48
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.19
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.93
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4986.95
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.50
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.14
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.95
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.70
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.92
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.82
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.00
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.10
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -1.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:21.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.52
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:21.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 4.84e-3
p-value of test                       :    0.9949

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -2.15
p-value of test                       :    0.98

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.82e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 4.31e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.57
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.70
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.91
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:05.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.00
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:05.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10154.61
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9826.12
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:40.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.76
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:49.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.03
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:50.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.93
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4021.38
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11673.35
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:29.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11711.67
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.25
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000112342

Normal statistic for number of bits   :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.98
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999911123

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.12

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   0.088
p-value of test                       :    0.47

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:55.63

 All tests were passed




Server wird beendet - Lösche Semaphor 181534729.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:50.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5423
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:04:00.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4475
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:44.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:46.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:02.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:03.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:15.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7133
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:15.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7459
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:12.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:13.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:53.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.00
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.07
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:18.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:48.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.22
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.47
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.44
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.43
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:11.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.09
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.11
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.10
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  266.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.64
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:51.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.09
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:05.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7123.62
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:56.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.90
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.99
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:15.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.07
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.57
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:39.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4917.57
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:00.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45852
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869852
  j =  1                              :        399908299
  j =  2                              :            45846
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45829
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869829
  j =  1                              :        399908344
  j =  2                              :            45825
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:32.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:20.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:49.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:04.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:38.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.04e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:24.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.059
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:42.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.58
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.89
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.18
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.49
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.51
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.59
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.29
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:51.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.86
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.47
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   12.28
p-value of test                       :  6.5e-3

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.21
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:40.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17233.81
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.31
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.19
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.75
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.18
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.28
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.55
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.76
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.95
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.88
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.15
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.52
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.00
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  433.74
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.27
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.87
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.46
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.43
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.54
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.83
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.35
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  451.30
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.20
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4918.69
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.68
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.70
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.25
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.56
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.37
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.41
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.52
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.88
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:22.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.73
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :    1.13
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:23.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    0.13
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :  -0.027
p-value of test                       :    0.51

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.62e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 2.65e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   21.80
p-value of test                       :  5.3e-3

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.98
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:05.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.37
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:06.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9916.18
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9908.28
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:10.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:04:26.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5034.14
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:59.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4954.02
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:00.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3942.22
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4188.41
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11941.69
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:38.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11971.47
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:37.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.48
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999902120

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.95
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999892367

Normal statistic for number of bits   :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.94
p-value of test                       :    0.03

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:12.90

 All tests were passed




Server wird beendet - Lösche Semaphor 182583305.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5399
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:58.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:43.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:44.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4455
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:00.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:00.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:09.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:06.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:55.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:01.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     939
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    3.95
p-value of test                       :  9.2e-3

-----------------------------------------------
CPU time used                    :  00:01:50.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.38
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     562
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.21
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:15.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    2.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:40.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.97
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.44
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.68
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.22
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.32
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.71
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.21
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  485.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:44.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1458.55
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6915.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:42.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.66
p-value of test                       :  5.9e-3

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.11
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.70
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:03.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.76
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.38
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:34.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4911.73
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:55.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46015
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870015
  j =  1                              :        399907975
  j =  2                              :            46005
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45795
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869795
  j =  1                              :        399908415
  j =  2                              :            45785
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:27.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:17.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:45.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:00.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:36.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.46e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 2.92e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.84e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:34.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.25
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.65
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:48.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.85
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.67
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.21
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:38.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.72
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.59
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17209.80
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.20
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.85
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.01
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    8.95
p-value of test                       :    0.9977


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.90
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.10
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.20
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.60
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.55
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.55
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.08
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.40
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.09
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.72
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.10
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.48
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.24
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.27
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.44
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.18
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.87
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.99
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.34
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.53
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.39
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.00
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5083.18
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.57
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.96
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.04
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:22.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.83
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :   -0.40
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:23.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    2.01
p-value of test                       :    0.02

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.95e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 7.34e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.05
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.61
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.51
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:04.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:05.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10037.35
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9965.64
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:38.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.31
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:48.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4920.43
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:50.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3923.93
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4319.42
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11653.68
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12119.63
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:29.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.13
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999986195

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.02
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000022360

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9939

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :  -0.047
p-value of test                       :    0.52

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    2.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:59.89

 All tests were passed




Server wird beendet - Lösche Semaphor 183664649.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1463
p-value of test                       :  4.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334583
  j =  1                              :        599997074
  j =  2                              :             1463
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5425
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:59.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:43.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:45.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4428
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:00.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:07.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:06.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:56.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:04:01.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     550
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:13.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.9904


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    4.87
p-value of test                       :  3.3e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    3.64
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:41.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.24
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.50
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.37
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.89
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.30
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.75
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.89
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  272.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.40
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:44.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1494.42
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:03.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7202.49
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.22
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.81
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:03.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.02
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:48.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.38
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:33.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4999.37
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:56.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45873
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869873
  j =  1                              :        399908256
  j =  2                              :            45869
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45477
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869477
  j =  1                              :        399909048
  j =  2                              :            45473
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:27.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:18.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:45.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:00.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:36.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.08e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:34.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:34.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.52
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.63
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.87
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.46
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.84
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.27
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.49
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:38.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.59
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.68
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   12.39
p-value of test                       :  6.2e-3

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.51
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.62
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.99
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:39.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17324.09
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.64
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.60
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.53
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   43.89
p-value of test                       :  7.9e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.57
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.81
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.86
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.09
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.64
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.19
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:37.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.38
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.24
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.62
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  173.31
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.01
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.19
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.19
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.63
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.29
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.49
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.88
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5060.71
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.10
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.24
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.46
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.36
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.81
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.15
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.90
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.70
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:23.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.66
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:23.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   0.098
p-value of test                       :    0.46

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 3.83e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.57e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 6.14e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.68
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.84
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.50
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:06.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.38
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:06.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10017.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10028.10
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:43.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4760.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:48.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5056.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:50.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4201.72
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.38
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11680.39
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.58
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:30.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.44
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999944003

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.48
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000088819

Normal statistic for number of bits   :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.78

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.85
p-value of test                       :    0.03

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.76
p-value of test                       :    0.96

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:11.11

 All tests were passed




Server wird beendet - Lösche Semaphor 184713225.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5452
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:01.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:44.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:47.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:03.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4241
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:02.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:12.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:09.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:05.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:04:08.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    4.80
p-value of test                       :  3.6e-3

-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.75
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     644
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.72
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     325
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:16.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:43.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.52
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.77
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.15
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.19
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.07
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.34
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.07
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.21
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:46.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1390.19
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:04.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7071.20
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.64
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:10.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.38
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.35
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:36.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5092.52
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:11.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:57.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45777
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869777
  j =  1                              :        399908448
  j =  2                              :            45773
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45860
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869860
  j =  1                              :        399908285
  j =  2                              :            45850
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  9.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:28.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:17.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:45.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :  2.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    3.75
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:02.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:36.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.96e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.94e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 7.98e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:40.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.25
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.51
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.83
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.09
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.77
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.29
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:10.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.04e-3
p-value of test                       :    0.9914

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 2.47e-3
p-value of test                       :    0.9975

Anderson-Darling statistic = A2       :    3.64
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   20.24
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.25
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.59
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.91
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17549.76
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.29
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.08
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.07
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.76
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.91
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:38.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.71
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.21
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.58
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.10
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.39
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.84
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.93
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.83
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.84
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.70
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.09
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.14
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.38
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.04
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.92
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.48
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.55
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.03
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.08
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.89
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:36.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.83
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.73
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4862.50
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.31
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.05
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.74
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:22.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.09
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :  -0.078
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:22.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.35e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 7.63e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9973

-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.94e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.36
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.11
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.67
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:05.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.42
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:06.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10175.47
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10152.48
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:04:15.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.20
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:52.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4962.66
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:53.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.89
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3987.62
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12001.62
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11592.80
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.95
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999924386

Normal statistic for number of bits   :   -0.60
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.24
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  7999992633

Normal statistic for number of bits   :  -0.058
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.50
p-value of test                       :    0.93

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:10.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:13.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:54.06

 All tests were passed




Server wird beendet - Lösche Semaphor 185761801.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9970


-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5400
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:01.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:43.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:59.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:01.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:08.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:07.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:57.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:01.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.24
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:14.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.18
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:41.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.42
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.06
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.41
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.49
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.81
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:10.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.96
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.34
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   86.45
p-value of test                       :  3.3e-3

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  261.90
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.83
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:43.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1460.89
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:00.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7101.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:42.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.86
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.88
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:03.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.91
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.57
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:32.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5025.96
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:57.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46278
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870278
  j =  1                              :        399907447
  j =  2                              :            46272
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45473
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869473
  j =  1                              :        399909060
  j =  2                              :            45461
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:27.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 3.00e-3
p-value of test                       :    0.9967

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:18.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:45.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:58.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:56.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:35.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:35.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:34.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.38
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:49.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.27
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.16
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.49
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:48.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.04
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:50.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.56
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.29
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.61
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17630.25
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.88
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.50
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.03
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.15
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.86
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.48
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.17
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.83
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.21
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.54
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.41
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.21
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.74
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.48
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.54
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.71
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.93
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.40
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.56
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.67
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.31
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.97
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5099.62
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.38
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.66
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.95
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.04
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4984.52
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.03
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.23
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.95
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :   -1.79
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:22.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.98
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :    1.17
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    1.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.95e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.00e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.61
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.58
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.15
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:05.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.90
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:08.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10017.46
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10119.28
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:41.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.76
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:49.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4834.89
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4192.12
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.90
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11842.49
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:28.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11840.36
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:29.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.52
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999957965

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.40
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000024913

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    2.60
p-value of test                       :  5.3e-3

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:19.93

 All tests were passed




Server wird beendet - Lösche Semaphor 186843145.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5497
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:03.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:45.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:45.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:01.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:03.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7163
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:15.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:12.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:06.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7198
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:06.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:49.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:16.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.40
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.77
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    2.43
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:46.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.69
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.04
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.63
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.40
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.10
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.04
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.88
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.31
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.76
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:48.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1401.96
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:04.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6940.78
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.23
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 4.33e-3
p-value of test                       :    0.9955

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   37.70
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:03:07.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.35
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.12
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:36.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5107.23
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:11.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:58.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46081
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870081
  j =  1                              :        399907841
  j =  2                              :            46075
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46023
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870023
  j =  1                              :        399907959
  j =  2                              :            46013
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :  5.5e-3

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:30.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:18.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:47.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:04.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:56.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.70e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:37.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.64e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:40.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:40.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.95
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.91
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.48
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.59
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:47.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.57
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.90
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.12
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:39.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17238.62
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.68
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.05
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.32
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.69
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.24
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.66
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.12
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.69
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.42
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.48
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.95
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.07
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.64
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  100.61
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.32
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.87
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.05
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.43
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.39
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.57
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.52
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.64
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.81
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.17
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.19
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.56
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.52
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.46
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.89
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.95
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:22.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.07
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :    1.25
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:22.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.09

Sample variance                       :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 9.74e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 8.75e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.48
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.04
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.51
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:05.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.68e-3
p-value of test                       :    0.9962

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.40
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  257.14
p-value of test                       :  4.0e-3

-----------------------------------------------
CPU time used                    :  00:02:07.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9784.66
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10044.33
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:04:21.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4915.78
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:53.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.57
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:54.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.49
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.97
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11953.24
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:31.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11765.33
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:32.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.42
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999936923

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.92
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  7999999353

Normal statistic for number of bits   : -5.11e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   0.033
p-value of test                       :    0.49

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:16.98

 All tests were passed




Server wird beendet - Lösche Semaphor 187858953.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:47.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5532
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:43.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:36.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7452
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:35.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:55.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7469
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:02.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:02.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:54.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:59.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    2.81
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     848
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:51.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     566
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:12.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.94
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:35.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.13
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.79
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.27
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.69
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.47
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.36
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.68
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.05
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.03
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1441.52
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:01.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7015.50
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:02.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.06
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.82
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4936.02
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9959


-----------------------------------------------
CPU time used                    :  00:03:13.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45722
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869722
  j =  1                              :        399908559
  j =  2                              :            45716
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45789
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869789
  j =  1                              :        399908424
  j =  2                              :            45785
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:30.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:19.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :  1.9e-3

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    3.85
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:46.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:00.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  9.5e-3

Anderson-Darling statistic = A2       :    3.66
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:52.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.17e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 2.42e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:22.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:36.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:38.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.51
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.23
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.81
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.56
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.06
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.90
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:43.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.90
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.65
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.90
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:33.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:32.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17175.82
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.78
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.05
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.99
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.29
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.30
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.85
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.47
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.41
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.10
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.07
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.61
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.51
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.97
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.85
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:48.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.75
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.65
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.76
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.06
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.10
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:48.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.82
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.06
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5029.06
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.58
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.11
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.37
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.74
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5148.48
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  325.04
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.67
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.54
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:21.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.63
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:13.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 9.50e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.69e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 9.85e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.28
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:29.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.12
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:11.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.34
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:12.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10207.68
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10009.29
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -3.06
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:03:50.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.95
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:48.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4967.97
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:50.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.05
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4159.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11916.87
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:28.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11755.29
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.49
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000120820

Normal statistic for number of bits   :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.27
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000140302

Normal statistic for number of bits   :    1.11
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.38

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:29.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:16:45.63

 All tests were passed




Server wird beendet - Lösche Semaphor 168230922.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5538
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:43.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:37.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7493
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:36.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:54.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:56.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:03.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:03.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:57.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:01.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.36
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9948

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     645
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.96
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.98
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:11.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:38.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.98
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.70
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.71
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.31
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.37
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.44
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.69
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  202.13
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.84
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:50.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1427.31
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:05.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6874.14
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:55.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.19
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   85.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:14.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.52
p-value of test                       :    0.9912


-----------------------------------------------
CPU time used                    :  00:00:47.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.63
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:40.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5179.89
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:22.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45619
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869619
  j =  1                              :        399908767
  j =  2                              :            45609
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45821
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869821
  j =  1                              :        399908361
  j =  2                              :            45815
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:32.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:19.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:48.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:02.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:54.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.90e-4
p-value of test                       :    0.9991    *****

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:36.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:24.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:38.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:39.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.97
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.86
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.52
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:50.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.96
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.38
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:48.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.72
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.59e-4
p-value of test                       :    0.9992    *****

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.15
p-value of test                       :  7.7e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   74.28
p-value of test                       :  8.0e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:32.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.07
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17210.67
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.79
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.35
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.63
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.31
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.02
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.49
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.27
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.36
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.42
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.96
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:38.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.35
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.83
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.74
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.55
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.90
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.65
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.24
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.35
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.70
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.42
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.33
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.26
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4961.33
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.60
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.22
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.24
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.69
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5130.33
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.45
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.61
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.44
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :   -1.93
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:25.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.88
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:26.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 9.24e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:47.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.48e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:46.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.92
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:30.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.17
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.16
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:09.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.84
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:09.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10268.31
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9799.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.26
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:10.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:04:26.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4740.22
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:55.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.87
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:57.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3987.52
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.98
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11952.08
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:34.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11843.91
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.40
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000010906

Normal statistic for number of bits   :   0.086
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.69
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000034558

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:11.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:14:29.59
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 67  MatrixRank, L=30, r=26          8.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 169148426.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1257
p-value of test                       :    0.9983

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334377
  j =  1                              :        599997486
  j =  2                              :             1257
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5464
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:51.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4418
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:38.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4441
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4437
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:58.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:06.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:07.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:59.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:10.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     861
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    2.69
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:49.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     635
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.91
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:17.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.38
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    2.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:48.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.16
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.11
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.45
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:10.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.74
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.88
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.98
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  506.07
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:01:52.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1461.94
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:58.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7206.61
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:50.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.20
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:19.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.97
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.23
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:54.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5163.39
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:33.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:24.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46304
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870304
  j =  1                              :        399907397
  j =  2                              :            46294
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46038
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870038
  j =  1                              :        399907926
  j =  2                              :            46034
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:28.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 2.53e-3
p-value of test                       :    0.9973

Anderson-Darling statistic = A2       :    3.87
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9966


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:16.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:46.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:03.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.09e-3
p-value of test                       :    0.9989

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:56.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:37.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.41e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 4.28e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:24.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:42.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.32
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.20
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.17
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.43
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.16
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.63
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:51.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.50
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-3
p-value of test                       :    0.9987

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   65.67
p-value of test                       :  6.4e-3

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.34
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:30.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  151.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:43.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17538.36
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.18
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.06
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.69
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.68
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.52
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.75
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.87
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.00
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.54
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.23
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.37
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.49
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.47
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.33
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.48
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.44
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.62
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.82
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.02
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.42
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.23
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.67
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  431.53
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.43
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.05
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.16
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4925.08
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.82
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.90
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.03
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :    0.14
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:27.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.39
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:28.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 8.91e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:46.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.96e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.60
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.15
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.51
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:06.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.67
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  158.87
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:07.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10129.97
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9965.42
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:04:31.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.45
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:56.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.10
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:59.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.12
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4217.04
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:28.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11685.53
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:35.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11939.63
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:35.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.29
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000046102

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.75
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000113320

Normal statistic for number of bits   :    0.90
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.74
p-value of test                       :    0.96

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:10.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:37.73

 All tests were passed




Server wird beendet - Lösche Semaphor 170852362.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5432
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:51.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:39.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:39.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4211
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7133
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:05.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:07.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:04:02.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:07.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.99
p-value of test                       :  3.0e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.63
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:16.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:45.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.22
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.55
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.61
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.10
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.22
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  261.17
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.57
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:52.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1403.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7022.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:54.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.70
p-value of test                       :  2.9e-3

Anderson-Darling statistic = A2       :    3.30
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.51
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.97e-3
p-value of test                       :    0.9926

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   84.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:16.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.57
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.78
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:37.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5113.53
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:57.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45943
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869943
  j =  1                              :        399908117
  j =  2                              :            45937
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46378
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870378
  j =  1                              :        399907248
  j =  2                              :            46370
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:29.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:18.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:03.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:36.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.23e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.01
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:43.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.47
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.61
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.27
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.81
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:50.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.66
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.19
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.26
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.68
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.48
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 2.91e-3
p-value of test                       :    0.9970

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17054.66
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.56
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.72
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.48
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.13
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.86
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.67
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.43
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.02
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.81
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.75
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  193.32
p-value of test                       :  5.3e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.97
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.36
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.49
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.63
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.65
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.12
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.18
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.59
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.42
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.82
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.13
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4881.08
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.15
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.99
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.27
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.28
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.92
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.73
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.85
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.76
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:25.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.44
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:26.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.96e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 8.32e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 4.88e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.96
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.13
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:06.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.02
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:07.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9787.34
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9742.61
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:10.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:04:25.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4987.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:56.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:59.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4003.75
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.39
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11710.94
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:31.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11773.65
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:31.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.35
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999994718

Normal statistic for number of bits   :  -0.042
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.86
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000058342

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :  -0.075
p-value of test                       :    0.53

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:51.73

 All tests were passed




Server wird beendet - Lösche Semaphor 171999242.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  5.1e-3


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:55.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5395
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:50.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:40.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:41.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:59.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:00.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:10.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7462
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:11.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:04:09.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:13.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.42
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:49.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.54
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.01
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.69
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:15.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.51
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.67
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:45.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.97
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.02
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.00
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.68
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.17
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.52
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.72
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.07
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:54.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1531.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:01.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6979.49
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:55.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.62
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.78
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:16.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.51
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.98
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:39.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5098.56
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:58.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45600
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869600
  j =  1                              :        399908800
  j =  2                              :            45600
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46107
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870107
  j =  1                              :        399907791
  j =  2                              :            46097
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:31.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:17.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:07.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:56.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.09e-3
p-value of test                       :    0.9956

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.18
p-value of test                       :  7.3e-3

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:38.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 3.13e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:24.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:53.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:50.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.52
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:50.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.76
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.26
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.52
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.61
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.85
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:50.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.91
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.31
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:29.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:29.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.46
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17469.90
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.57
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.31
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.01
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.32
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.94
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.40
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.91
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.64
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.29
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.53
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.25
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.46
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.70
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.39
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.08
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.34
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.06
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.98
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.75
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.77
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.84
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.91
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5112.83
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.64
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:37.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.36
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.31
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4900.90
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.73
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.95
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.71
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:26.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.78
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :   0.052
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:26.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  8.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.73
p-value of test                       :    0.96

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.88
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.89
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:07.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.37
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:07.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9835.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10178.86
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:11.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:04:26.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5037.69
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4983.39
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:58.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.98
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3949.53
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11734.31
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:33.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11851.73
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:32.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.20
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999975386

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.60
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000107542

Normal statistic for number of bits   :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   0.072
p-value of test                       :    0.47

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    0.17
p-value of test                       :    0.9971

-----------------------------------------------
CPU time used                    :  00:01:11.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:52.25

 All tests were passed




Server wird beendet - Lösche Semaphor 173047818.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5326
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:53.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4198
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:40.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:58.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:06.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:06.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:55.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:00.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    2.41
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     950
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    3.08
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:15.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.9901


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:43.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.24
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.90
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.80
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.51
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.32
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.08
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.38
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.05
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1402.17
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:00.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7049.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.58
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.51
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:01.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.36
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.18
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:34.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4992.23
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:00.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45762
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869762
  j =  1                              :        399908482
  j =  2                              :            45750
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46118
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870118
  j =  1                              :        399907767
  j =  2                              :            46112
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:28.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:18.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:44.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :  5.1e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    5.16
p-value of test                       :  2.4e-3

-----------------------------------------------
CPU time used                    :  00:01:54.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:36.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 9.68e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.34e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.69
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.80
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.68
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.08
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.76
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.44
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.75
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:44.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.73
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.37
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.40
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  159.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 2.75e-3
p-value of test                       :    0.9972

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17773.68
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:54.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.54
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.53
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.94
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.92
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.78
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.10
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.47
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.48
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.84
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.48
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:38.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.48
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.58
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.82
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.39
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.27
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.17
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.81
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.38
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.04
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.12
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.78
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.04
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.44
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.16
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.79
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.54
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.18
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4987.62
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.82
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.63
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.35
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :    1.05
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:27.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.33
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:27.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.14e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:46.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.26e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 9.23e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.63
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.19
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.82
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:08.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.07
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:09.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10209.80
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10103.59
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:55.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.91
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.40
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:49.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4288.56
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4157.71
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11971.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11625.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.60
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999952166

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.34
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999997121

Normal statistic for number of bits   :  -0.023
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.71

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:59.86

 All tests were passed




Server wird beendet - Lösche Semaphor 174161930.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5354
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:56.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:42.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:59.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:00.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:08.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7450
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:09.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:02.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:07.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:49.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    3.87
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     348
p-value of test                       :  3.6e-3

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:17.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.93
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.13
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:44.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.35
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.99
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.10
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.45
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.28
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.46
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.01
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.80
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.87
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:51.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1375.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:58.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6925.11
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:50.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.13
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.55
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:08.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.86
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.51
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:36.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5077.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:03.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45601
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869601
  j =  1                              :        399908803
  j =  2                              :            45591
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45929
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869929
  j =  1                              :        399908148
  j =  2                              :            45917
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:30.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:19.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:47.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:06.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:36.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.46e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 9.57e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:50.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.43
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.85
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.47
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.42
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.39
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:47.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.54
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.88
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.84
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.57
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.65
p-value of test                       :  5.2e-5    *****

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    7.44
p-value of test                       :  2.3e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16811.53
p-value of test                       :    0.9996    *****



-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.90
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.33
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.77
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.00
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.53
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.87
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.44
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   43.20
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.05
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.21
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.79
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.25
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.18
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.20
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  100.13
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.45
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.45
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.31
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.29
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.06
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.16
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.80
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4948.23
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.12
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.59
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:36.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.90
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.04
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4919.94
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.65
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  162.59
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.35
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :   -1.11
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:26.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.52
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :    2.11
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:26.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.17
p-value of test                       :    0.99

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.45e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 9.55e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.04e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.99
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.13
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:09.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.32
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:08.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10006.66
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10126.11
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.032
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:04:17.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.63
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:52.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4726.32
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:53.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4136.02
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.33
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11957.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:29.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11908.09
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.19
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000084202

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.33
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000060886

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    3.69
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.21
p-value of test                       :    0.99

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:58.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 73  GCD                             0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 175144970.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:39.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5402
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:54.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4218
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:41.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4427
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:57.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:05.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:06.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:55.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:04:00.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.73
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:16.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:43.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.96
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.78
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.89
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.21
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.93
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.01
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.97
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.54
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:43.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1552.29
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:00.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7180.09
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:44.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.12
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:03.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.45
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.98
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:32.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5113.96
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:00.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45539
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869539
  j =  1                              :        399908923
  j =  2                              :            45537
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45984
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869984
  j =  1                              :        399908035
  j =  2                              :            45978
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:27.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :  3.1e-3

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:18.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:46.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:00.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:55.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:01:35.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.82e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 3.92e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:38.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:34.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.77
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.76
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.93
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.34
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.93
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.56
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:43.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.22
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:29.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.98
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17481.19
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.42
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.91
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.66
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.49
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.08
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.32
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   15.80
p-value of test                       :    0.9978


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.24
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.56
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.35
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.54
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.08
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.08
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.98
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.94
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.93
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.39
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.07
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.63
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.58
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.01
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.45
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5186.23
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.38
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.18
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.29
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.14
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5068.41
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.36
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.85
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.38
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:26.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.49
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :    0.72
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:25.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 8.89e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:46.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.22
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.45
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  241.93
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:07.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:08.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9941.46
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9778.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.011
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:45.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4747.89
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4949.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:49.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4306.92
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4070.52
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11825.68
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11786.90
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.33
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999971933

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.60
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999952298

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.50
p-value of test                       :    0.07

Sample variance                       :    2.31
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:23.46

 All tests were passed




Server wird beendet - Lösche Semaphor 176226314.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5493
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:53.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:40.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7178
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:39.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:57.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:05.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:05.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:55.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:01.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.56
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.12
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.16
p-value of test                       :    0.9976

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.82
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    3.37
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     331
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:14.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.51
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:45.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.81
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.37
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.75
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.37
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.14
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.03
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  268.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.64
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:43.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1476.97
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:00.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6928.52
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:44.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.83
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.01
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:02.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.60
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.19
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:32.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4980.16
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:56.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45618
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869618
  j =  1                              :        399908765
  j =  2                              :            45616
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45978
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869978
  j =  1                              :        399908049
  j =  2                              :            45968
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:27.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:18.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:45.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:58.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:55.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:34.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:38.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:38.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.85
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.92
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.98
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.84
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.21
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.30
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.55
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:44.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.48
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.87
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.23
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.51
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   11.50
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.43
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17555.78
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.31
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.63
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.22
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.90
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.90
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.91
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.95
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.22
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.79
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.38
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.88
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.77
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.68
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.15
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.03
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.95
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.01
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.60
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.67
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.47
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.95
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.29
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4934.25
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  425.85
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.04
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.91
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.51
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.82
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.40
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.48
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    2.51
p-value of test                       :    0.9981


-----------------------------------------------
Normal statistic for number of jumps  :  -0.046
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:26.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.79
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :    0.72
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:25.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.83e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 9.88e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:46.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.01e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.91
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.85
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.50
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:07.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.95
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:08.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9902.46
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.50
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:49.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4982.20
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.79
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:49.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4036.64
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.73
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11628.78
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11677.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.88
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000006229

Normal statistic for number of bits   :   0.049
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.11
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000112303

Normal statistic for number of bits   :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:30.54

 All tests were passed




Server wird beendet - Lösche Semaphor 177209354.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:41.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5407
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:53.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:40.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4221
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:58.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:05.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7176
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:05.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:55.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:04:00.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.85
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:49.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.13
p-value of test                       :  7.9e-3

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:16.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    2.52
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:42.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.43
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.40
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.13
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.78
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.96
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.36
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:44.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1420.21
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:00.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7056.66
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:03.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.26
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:33.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4931.97
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:56.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45677
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869677
  j =  1                              :        399908651
  j =  2                              :            45667
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45669
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869669
  j =  1                              :        399908664
  j =  2                              :            45665
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:27.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:16.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:44.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:57.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:55.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:34.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.96e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 6.05e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.035
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.20
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:34.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.022
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:35.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:48.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.11
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.18
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.34
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.88
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.41
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:44.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.57
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.97
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.64
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.79
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17109.07
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.54
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.79
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.67
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.41
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.24
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.48
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.86
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.10
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.05
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.99
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.61
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.68
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.52
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.21
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.27
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:46.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.24
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.38
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.17
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.81
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.86
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.13
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4933.72
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.61
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.53
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.75
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.93
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.18
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.49
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.14
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:36.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.46
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:28.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.96
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :   -1.33
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:30.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.23

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.73e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:46.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 4.59e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.78
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.67
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.33
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:07.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.27
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:07.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9824.52
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9865.01
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:46.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5003.84
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4773.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4232.50
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.58
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11816.79
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11583.81
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.54
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999824756

Normal statistic for number of bits   :   -1.39
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.35
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000028357

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   0.061
p-value of test                       :    0.48

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:28.47

 All tests were passed




Server wird beendet - Lösche Semaphor 178225162.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5370
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:54.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4235
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:04.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:05.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:55.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:04:00.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:50.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.87
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    2.49
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     554
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    2.24
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:18.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:49.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.35
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.54
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.88
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.63
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.09
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.29
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.45
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  205.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.91
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1375.68
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:59.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7127.37
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:44.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.40
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.54
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:00.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.87
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.87
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:33.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5087.90
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:57.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45460
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869460
  j =  1                              :        399909084
  j =  2                              :            45452
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45847
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869847
  j =  1                              :        399908309
  j =  2                              :            45841
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:27.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:17.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:44.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:59.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:55.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:35.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.55e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:21.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:36.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:34.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.04
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.83
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.70
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:49.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.05
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.81
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:45.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.92
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.02
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.13
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:29.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.28
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:29.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  2.8e-3

Anderson-Darling statistic = A2       :    3.64
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  169.21
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17428.83
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.47
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.12
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.58
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.64
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.69
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.63
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.23
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.25
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.65
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.18
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.75
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.85
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  557.12
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.58
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  102.14
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.98
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.47
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.78
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.75
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.35
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.29
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.07
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.06
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.77
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  154.52
p-value of test                       :    0.9927


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.86
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.42
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.80
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.42
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.51
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.40
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :    1.73
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:27.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.14
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :   -1.52
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:28.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.54e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 5.02e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.70
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.95
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.67
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:06.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:06.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10079.79
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10170.06
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.082
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:45.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:48.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.51
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:50.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.64
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.19
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11818.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11884.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:29.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.77
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000208921

Normal statistic for number of bits   :    1.65
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.73
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000068305

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   0.032
p-value of test                       :    0.49

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.43
p-value of test                       :    0.9924

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :  -0.064
p-value of test                       :    0.53

Sample variance                       :    1.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:30.32

 All tests were passed




Server wird beendet - Lösche Semaphor 179240970.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5532
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:52.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:40.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4251
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:57.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:04.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7145
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:04.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:55.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7162
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:04:01.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.33
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:48.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.60
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:15.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:43.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.18
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.73
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.92
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.17
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.81
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.65
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.01
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.32
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.86
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:43.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1409.84
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:00.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7081.43
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:44.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    3.27
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   59.26
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:02.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   13.63
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.59
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:35.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4993.83
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:02.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45584
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869584
  j =  1                              :        399908837
  j =  2                              :            45574
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45901
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869901
  j =  1                              :        399908201
  j =  2                              :            45895
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:28.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:18.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:45.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:55.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:35.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.65e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.45e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:39.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:35.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.11
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.37
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.50
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.64
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.03
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:44.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.74
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.99
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.23
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.08
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17342.79
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.41
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.92
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.03
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.85
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   33.51
p-value of test                       :  9.7e-3


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.95
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.78
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.15
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.88
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.76
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.53
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.28
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.59
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.07
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.06
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.49
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.99
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.09
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.33
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.33
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.01
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.93
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.15
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.26
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.73
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.15
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.45
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4984.45
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.23
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.47
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.85
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:24.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.86
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :    2.01
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:27.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.9e-3

Anderson-Darling statistic = A2       :    4.26
p-value of test                       :  6.8e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.68
p-value of test                       :  3.6e-3

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.06e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:47.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 5.91e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.76
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.15
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.72
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:07.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.16
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:08.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10112.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9907.79
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.047
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:49.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.86
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:49.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.09
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.30
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4061.88
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11758.29
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11972.75
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.62
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000080875

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.98
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000167368

Normal statistic for number of bits   :    1.32
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.11

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.92
p-value of test                       :    0.97

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:34.19

 All tests were passed




Server wird beendet - Lösche Semaphor 180256778.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:52.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5477
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:51.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:39.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:40.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:04.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:04.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:56.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:01.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.12
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.86
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    2.05
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:14.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.50
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    6.78
p-value of test                       :  4.3e-4    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     117
p-value of test                       :    0.9970

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:47.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.17
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.18
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.93
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.95
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.44
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.21
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.70
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.45
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:42.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1460.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:00.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7067.49
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:42.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.72
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   91.34
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:03:03.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.14
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.06
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:33.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5064.82
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:56.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45543
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869543
  j =  1                              :        399908919
  j =  2                              :            45533
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46058
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870058
  j =  1                              :        399907886
  j =  2                              :            46054
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:27.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:17.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:45.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:00.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:55.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:35.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.23e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.99e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.79
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.36
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.17
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.29
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:49.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.51
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.48
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.01
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.11
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.14
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:29.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.43
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:31.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.75
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17324.44
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.57
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.34
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.64
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.24
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.47
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.20
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.78
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.22
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.26
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.89
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.99
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.95
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.27
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.83
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.33
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.90
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.61
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.75
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.69
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.32
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.00
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.75
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4824.98
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.87
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.51
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.23
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.26
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.56
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.76
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.67
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.15
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :  -0.073
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:25.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.02
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :   -2.18
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:02:26.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    2.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 6.94e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.93e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 6.25e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.53
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.81
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.96
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:07.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.25
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:07.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.7e-3

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10231.18
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10071.86
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:41.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5054.36
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.23
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:50.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.94
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4328.25
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11826.36
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11925.14
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.35
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000089407

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.05
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999948467

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:51.36
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs mNP1, t = 16         4.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 181239818.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:52.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5391
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:51.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:40.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:40.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:05.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:04.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:55.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:04:01.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    3.92
p-value of test                       :  9.6e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     840
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.75
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.47
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:14.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    2.26
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:44.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.89
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.11
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.48
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.65
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.72
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:10.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.55
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.86
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.81
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.58
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.53
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:42.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1485.24
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:02.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6875.79
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.17
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.29
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:27.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.22
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   85.82
p-value of test                       :    0.9905


-----------------------------------------------
CPU time used                    :  00:01:35.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4927.49
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:58.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45954
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869954
  j =  1                              :        399908095
  j =  2                              :            45948
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46156
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870156
  j =  1                              :        399907694
  j =  2                              :            46144
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:28.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:18.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:01.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:54.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:35.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:24.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.29
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:22.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:37.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:36.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.84
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.62
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.79
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.44
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:43.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.45
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:29.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.58
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.60
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17470.20
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.02
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.41
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.44
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.31
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.73
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.23
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.33
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.81
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.97
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.42
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:37.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.87
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.11
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.09
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.49
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.82
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.55
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.72
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.87
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.06
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.71
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.39
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.75
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.97
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.09
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.08
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.39
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.04
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4889.06
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.30
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.47
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.40
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   -1.28
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:25.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.16
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:23.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.77

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 5.04e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.47e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.24
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.62
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.62
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:07.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.25
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:07.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10066.82
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10195.64
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.36
p-value of test                       :    0.9910

-----------------------------------------------
CPU time used                    :  00:03:43.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.03
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9931

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.73
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:50.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.71
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4116.61
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11810.03
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11814.30
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.62
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999904175

Normal statistic for number of bits   :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   30.44
p-value of test                       :    0.9960


-----------------------------------------------
Total number of bits:  7999899372

Normal statistic for number of bits   :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9980

Tests on the sum of all N observations
Standardized normal statistic         :  -0.035
p-value of test                       :    0.51

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:55.15

 All tests were passed




Server wird beendet - Lösche Semaphor 182255626.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:39.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:50.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5391
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:57.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:42.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:00.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:00.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:11.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:12.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:10.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:04:14.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.17
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.00
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     866
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:49.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.84
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    2.34
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:15.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     130
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:43.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.19
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.11
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.00
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.48
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.03
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:58.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:58.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.37
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:57.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.55
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:34.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.23
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:59.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1373.58
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:06.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6918.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:53.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 9.78e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.91
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.47
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:46.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.43
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.55
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5097.35
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:00.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45642
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869642
  j =  1                              :        399908721
  j =  2                              :            45633
  j =  3                              :                3
  j =  4                              :                1
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45937
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869937
  j =  1                              :        399908129
  j =  2                              :            45931
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 6.21e-3
p-value of test                       :    0.9921

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:31.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9993    *****


-----------------------------------------------
CPU time used                    :  00:02:21.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:54.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:09.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:56.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:37.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.53e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 3.47e-4
p-value of test                       :  8.1e-3

Anderson-Darling statistic = A2       :    3.43
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:24.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:54.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:54.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.15
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:51.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.45
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.20
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:50.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.70
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.89
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.35
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:52.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9966

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.91
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.90
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.66
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.50
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17558.52
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:55.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.63
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.54
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.88
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.50
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.08
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.16
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.68
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.57
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.71
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.33
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.87
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.20
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.21
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.12
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.00
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.26
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.18
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.23
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.11
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.97
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5181.05
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.47
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.58
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.56
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.40
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.27
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.16
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.05
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.91
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:24.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.59
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :    1.15
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:25.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.93
p-value of test                       :    0.97

Sample variance                       :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.19e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.83e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.73
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.82
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.42
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:05.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.42
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:07.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10057.52
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10081.06
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:04:37.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5038.30
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:52.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5055.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:55.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4300.87
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.10
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11674.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:34.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11692.70
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:36.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.52
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999968054

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.45
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000094948

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    2.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:04.60
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 47  MaxOft AD, t = 16               0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 183173130.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5508
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:54.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:41.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4415
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:57.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:59.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:09.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:10.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:04:03.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:04:05.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:49.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    2.89
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     273
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:16.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    2.17
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:42.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.12
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.67
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.83
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.81
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.00
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.85
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.85
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.05
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:51.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1322.42
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:01.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6955.97
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:49.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.71
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:13.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.18
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:08.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.76
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.85
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:36.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5040.36
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:02.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45744
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869744
  j =  1                              :        399908517
  j =  2                              :            45734
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46162
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870162
  j =  1                              :        399907677
  j =  2                              :            46160
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:30.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:19.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:06.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.93e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 3.22e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:24.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:47.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.11
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.30
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.15
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.25
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.49
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.19
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   14.79
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:46.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.68
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:28.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.34
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17626.87
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.47
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.61
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.89
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.17
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.90
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.85
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.25
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.51
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.62
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.42
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:38.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.15
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.99
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.98
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.32
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.48
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.25
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.58
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.15
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.82
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.46
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.07
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  463.01
p-value of test                       :  3.5e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5173.42
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.31
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.34
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.90
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.38
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.75
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  331.21
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.17
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.48
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:24.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.39
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:25.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.63e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 8.72e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.39e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.96
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.55
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.21e-3
p-value of test                       :    0.9967

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  243.60
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:07.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:07.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9795.87
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10144.99
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:04:09.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4796.93
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:52.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.59
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:53.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.25
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4090.32
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12059.05
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:30.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11421.18
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:01:31.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.43
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000067984

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.36
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999909284

Normal statistic for number of bits   :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:27.03

 All tests were passed




Server wird beendet - Lösche Semaphor 184451082.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1479
p-value of test                       :  1.1e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334599
  j =  1                              :        599997042
  j =  2                              :             1479
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5400
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:56.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:41.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4169
p-value of test                       :    0.9947


-----------------------------------------------
CPU time used                    :  00:01:57.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:58.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:06.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:06.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:56.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:04:01.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    2.16
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     855
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.05
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.80
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:15.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:47.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.69
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.46
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.99
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.38
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.90
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.68
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.64
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:42.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1411.07
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:00.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7011.49
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:40.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.81
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:15.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.36
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:02.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.93
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.28
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:33.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5166.03
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:58.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46058
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870058
  j =  1                              :        399907891
  j =  2                              :            46044
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46019
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870019
  j =  1                              :        399907969
  j =  2                              :            46005
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:29.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:18.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:44.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:59.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:36.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.44e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 5.50e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:22.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.060
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:40.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:38.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.13
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.48
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.49
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.06
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.50
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   14.61
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:38.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.32
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.30
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.95
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.47
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.49
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17559.34
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.29
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.80
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.30
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.01
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.24
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.14
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.03
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.40
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.19
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.85
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.24
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.00
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.54
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.77
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.58
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.62
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.23
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.39
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.27
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.16
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.64
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.01
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5128.74
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  446.01
p-value of test                       :  9.1e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.36
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.06
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.18
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4883.59
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.56
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.13
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.13
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:25.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.02
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:24.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 4.83e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.97e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 7.93e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.57
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.44
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.68
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:06.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.84
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:08.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9910.29
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10164.94
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:41.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5009.67
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:47.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.73
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4244.25
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4035.91
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11698.71
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11858.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:28.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   90.10
p-value of test                       :  1.5e-3


-----------------------------------------------
Total number of bits:  8000065662

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.43
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999957020

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:23.14

 All tests were passed




Server wird beendet - Lösche Semaphor 185434122.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5357
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:55.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:58.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:05.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:05.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:56.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7166
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:04:01.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     945
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    2.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:15.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.67
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:42.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.63
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.45
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.59
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.93
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.33
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.73
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.14
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.44
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.90
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1551.39
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:01.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7208.56
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.88
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:03.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.14
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.38
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:33.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5082.83
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:59.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45499
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869499
  j =  1                              :        399909005
  j =  2                              :            45493
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45649
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869649
  j =  1                              :        399908705
  j =  2                              :            45643
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:29.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:18.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:44.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:59.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:34.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.83e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 5.31e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 8.71e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:22.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.64
p-value of test                       :  4.1e-3

-----------------------------------------------
CPU time used                    :  00:01:40.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:38.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.92
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.06
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.43
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.71
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.07
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.99
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:42.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.60
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.77
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  159.24
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17178.74
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.33
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.13
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.48
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.48
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.24
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.24
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.26
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.79
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.12
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.46
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.16
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.64
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.99
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.75
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.39
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.32
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  110.42
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  578.65
p-value of test                       :  8.5e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.20
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.52
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.58
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.68
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.82
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.59
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  154.82
p-value of test                       :    0.9923


-----------------------------------------------
CPU time used                    :  00:00:36.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.47
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.68
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5073.15
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.49
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.22
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :   -2.13
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:26.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.39
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:24.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 6.40e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 4.58e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.10
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.58
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.99
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:07.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:06.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.88
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9882.26
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:45.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4964.81
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:47.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.63
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:49.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.37
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.34
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12129.96
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11700.96
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:28.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.44
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000044893

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.55
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999954959

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.062
p-value of test                       :    0.52

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:49.19

 All tests were passed




Server wird beendet - Lösche Semaphor 186482698.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:49.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5343
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:56.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:44.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:59.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:59.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:08.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:07.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:04:01.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:06.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.14
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:15.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:46.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.91
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.56
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   34.88
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.75
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.24
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.46
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.40
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.87
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  394.86
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:51.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.25
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:04.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7013.94
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:51.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.68
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.90
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:11.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.65
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.88
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:37.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5112.82
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:59.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45999
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869999
  j =  1                              :        399908002
  j =  2                              :            45999
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46107
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870107
  j =  1                              :        399907792
  j =  2                              :            46095
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:33.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:23.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:07.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:37.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.96e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.71e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.56e-4
p-value of test                       :  2.4e-4    *****

Kolmogorov-Smirnov- statistic = D-    : 4.13e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    7.38
p-value of test                       :  2.3e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.095
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:47.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:48.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.85
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.27
p-value of test                       :    0.9922

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.24
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.39
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:49.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.78
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.88
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:47.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.95
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.82
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.32
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.57
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17630.03
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.46
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.47
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.43
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.41
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.07
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.39
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.83
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.84
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.26
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.66
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.55
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.07
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.87
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.44
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.90
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.42
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.96
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.13
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.93
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.20
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.50
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.74
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5061.52
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.15
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.57
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.78
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.77
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5037.69
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.82
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  245.44
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.51
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :  -0.015
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:26.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.52
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:28.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.5e-3

Kolmogorov-Smirnov- statistic = D-    : 8.86e-3
p-value of test                       :    0.9904

Anderson-Darling statistic = A2       :    6.06
p-value of test                       :  9.9e-4    *****

Tests on the sum of all N observations
Standardized normal statistic         :   -3.34
p-value of test                       :    0.9996    *****

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 4.37e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.23e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.62
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.88
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.97
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:07.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.48
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:07.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.97e-3
p-value of test                       :    0.9937

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10236.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9981.43
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:04:18.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4964.73
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:53.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4735.65
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:53.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.51
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4005.26
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11706.59
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:30.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11574.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:31.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.05
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999929072

Normal statistic for number of bits   :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.23
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999965714

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.16e-3
p-value of test                       :    0.9957

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    2.12
p-value of test                       :    0.02

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:11.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:50.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 54  SampleMean, r = 10              2.3e-4
 82  LempelZiv, r = 0                0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 187465738.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5454
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:55.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:40.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:56.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4241
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:57.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:05.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:06.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:57.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:04:02.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     866
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:49.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:15.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.90
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.35
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:16.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:44.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.52
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.18
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.19
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.17
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.98
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.98
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.13
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.46
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.03
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:44.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.23
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:01.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7068.33
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:40.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.03
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.67
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:03.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.82
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.60
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:32.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5116.07
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:58.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45943
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869943
  j =  1                              :        399908117
  j =  2                              :            45937
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46027
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870027
  j =  1                              :        399907951
  j =  2                              :            46017
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:29.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9905

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:18.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:45.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:59.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:33.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:21.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:34.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:33.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.06
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.29
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.71
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.07
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:48.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.97
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.73
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.34
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:38.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.18
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.7e-3

Anderson-Darling statistic = A2       :    3.58
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.79
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   13.01
p-value of test                       :  1.5e-3

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.28
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17257.72
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.03
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.51
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.78
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.22
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.06
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.29
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.40
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.79
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.04
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.38
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.09
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.42
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.35
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.47
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.50
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.75
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.89
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.12
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.35
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.38
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.44
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.94
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.40
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.16
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.42
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.46
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.45
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.85
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.13
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.71
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.42
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :    0.72
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:18.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.54
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:14.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.56e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 8.15e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   23.50
p-value of test                       :  2.8e-3

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.59
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.59
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:54.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.97
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:55.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9907.47
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.00
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:48.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:22.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.62
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4761.02
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3852.86
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:01:12.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4071.71
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11964.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12028.91
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.17
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000048529

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.49
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999952154

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.1e-3

Anderson-Darling statistic = A2       :    4.48
p-value of test                       :  5.4e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.62
p-value of test                       :  4.4e-3

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   0.051
p-value of test                       :    0.48

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   02:57:34.32

 All tests were passed




Server wird beendet - Lösche Semaphor 188547082.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:47.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5442
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:43.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:36.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7150
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:35.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4454
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:55.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:55.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:02.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:02.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:54.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:04:00.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     941
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:52.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.84
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     568
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.74
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:11.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:33.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.72
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.88
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.00
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.39
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.30
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.64
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.81
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:48.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.62
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:00.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7198.77
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.50
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.94
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:02.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.58
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.99
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:37.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4977.53
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:19.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45658
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869658
  j =  1                              :        399908691
  j =  2                              :            45644
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46050
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870050
  j =  1                              :        399907904
  j =  2                              :            46042
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:29.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:18.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:45.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:00.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:52.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:33.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.51e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 3.33e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:22.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.95e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 6.58e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.020
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:37.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:38.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:47.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.86
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.28
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.23
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:48.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.38
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.04
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.50
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:43.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.46
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.15
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.87
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:32.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.21
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:30.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.02
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17301.09
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.94
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.87
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.84
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.88
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.51
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:40.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   17.39
p-value of test                       :    0.9962


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.76
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.05
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.30
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.16
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:41.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.09
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.89
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.42
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.73
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.75
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.48
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.98
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.89
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.86
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.20
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:47.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.81
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.99
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4936.50
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.07
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.62
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.92
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.81
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5123.90
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.48
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.10
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.25
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :    0.40
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:16.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.10
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -1.47
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:13.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :  -0.033
p-value of test                       :    0.51

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:11.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.74e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 9.68e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:46.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 7.23e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.35
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.90
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.58
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:10.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.38
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:11.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9913.90
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10029.29
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:59.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.85
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:49.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4772.84
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3915.96
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4184.14
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11753.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11783.04
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:30.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.77
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000105862

Normal statistic for number of bits   :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.78
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999985562

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.74
p-value of test                       :    0.96

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.83

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:30.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:17:10.85

 All tests were passed




Server wird beendet - Lösche Semaphor 168263691.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5412
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:44.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:37.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7157
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:36.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4499
p-value of test                       :  7.3e-3


-----------------------------------------------
CPU time used                    :  00:01:54.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4230
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:02.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:02.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:53.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7136
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:59.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:48.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    2.11
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.20
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.92
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:12.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:33.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.77
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.05
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.81
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:11.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.14
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.25
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.15
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.55
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.06
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:43.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.13
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:00.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7242.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:41.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.17
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.98
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:02.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.88
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.35
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:35.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5045.92
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:01.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45308
p-value of test                       :    0.9962


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869308
  j =  1                              :        399909388
  j =  2                              :            45300
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45920
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869920
  j =  1                              :        399908163
  j =  2                              :            45914
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:13.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:31.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:18.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:45.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:00.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:53.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:32.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.79e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 3.13e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.38e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 8.53e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.13
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.050
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:34.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:35.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.96
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:48.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.93
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.68
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.62
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.27
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.25
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:39.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.88
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.39e-3
p-value of test                       :    0.9932

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   63.00
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.35
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.26
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.96
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17666.84
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.26
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.87
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.80
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.87
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.20
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.62
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.66
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.18
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.60
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.57
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:40.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.21
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.33
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.76
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.08
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.03
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:48.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  105.06
p-value of test                       :    0.9957


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.60
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.96
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.11
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.16
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:46.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.10
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.98
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5121.07
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.95
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.41
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.91
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.27
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.63
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.68
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.43
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.34
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:21.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.66
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:17.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9960

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:46.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.84e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 8.13e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.99
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.70
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  243.64
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:07.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.41
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:11.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9882.70
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9982.79
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:04:06.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4961.13
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4998.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:50.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4130.05
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4150.95
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11707.25
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11853.48
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:29.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.77
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000065572

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.70
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999934997

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    2.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:29.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:55.09

 All tests were passed




Server wird beendet - Lösche Semaphor 169443339.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5458
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:45.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:37.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:37.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:55.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:56.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:04.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:05.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:59.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:04:03.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.56
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.86
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:13.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:43.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.17
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.19
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.79
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:10.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.77
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.57
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.64
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.16
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.88
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:53.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1500.09
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:03.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7025.32
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:53.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.63
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.35
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:13.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.96
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.34
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:38.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4988.11
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:07.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45471
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869471
  j =  1                              :        399909062
  j =  2                              :            45463
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45566
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869566
  j =  1                              :        399908870
  j =  2                              :            45562
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:34.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:21.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:50.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:03.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:54.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:38.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.70e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.033
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:40.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:41.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.02
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.54
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   96.51
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.31
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.26
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.58
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.59
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:50.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.49
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.59
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.055
p-value of test                       :    0.9966

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  102.29
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9935

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17398.50
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:55.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.81
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.22
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.54
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.46
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.97
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:39.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.75
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.18
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.68
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.11
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.59
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.85
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.73
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.33
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.10
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.11
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.43
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.84
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.88
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.87
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.33
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.35
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4919.72
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.97
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  252.30
p-value of test                       :  7.2e-3


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.24
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.22
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.99
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.60
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.28
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.94
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :   -1.06
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:25.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.49
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:27.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   0.092
p-value of test                       :    0.46

Sample variance                       :    1.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         : -5.43e-3
p-value of test                       :    0.50

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:46.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 2.59e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.40
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.04
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.04
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:08.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.98
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:09.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9817.07
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10099.62
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:12.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:04:29.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4902.37
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:54.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4824.14
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:58.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.52
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4070.58
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11862.45
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:34.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11866.71
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:35.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.97
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999958601

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.52
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  8000045859

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.82
p-value of test                       :    0.97

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:27.60

 All tests were passed




Server wird beendet - Lösche Semaphor 170360843.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5567
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:49.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:38.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:37.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:55.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:03.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7499
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:03.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:54.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:00.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     848
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:13.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.14
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:42.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:54.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.20
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.11
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.67
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.47
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:10.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.59
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.77
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.51
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  276.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.97
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:44.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1390.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:01.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7147.97
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.92
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.61
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:03.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.09
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   86.23
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4982.89
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:59.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45767
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869767
  j =  1                              :        399908472
  j =  2                              :            45755
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45848
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869848
  j =  1                              :        399908307
  j =  2                              :            45842
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:29.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 3.37e-3
p-value of test                       :    0.9963

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9956


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9959


-----------------------------------------------
CPU time used                    :  00:02:18.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9986


-----------------------------------------------
CPU time used                    :  00:02:02.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:54.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:32.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 8.66e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:22.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:34.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:34.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.47
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:48.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.50
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.46
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.42
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:49.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.02
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.17
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.06
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:39.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.95
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.57
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.59
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:29.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.92
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.16
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17313.05
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.06
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.19
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.33
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.09
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.79
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.83
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.53
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.79
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.19
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.43
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.72
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.22
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.53
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.15
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.03
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.46
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.26
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.18
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.08
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.43
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.41
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.10
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.28
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.07
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.18
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.92
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.56
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5103.04
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.76
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.07
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.57
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :    1.01
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:26.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.98
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:26.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.21e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 8.71e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.85e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.77
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:28.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.26
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.90
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:07.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.13
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:08.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10033.50
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10158.31
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:52.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5032.03
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:49.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5035.60
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:51.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.99
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.19
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12212.85
p-value of test                       :  6.2e-3

-----------------------------------------------
CPU time used                    :  00:01:28.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11951.22
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:30.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.90
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999969353

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.35
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999921851

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.88
p-value of test                       :    0.03

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:13.47

 All tests were passed




Server wird beendet - Lösche Semaphor 171671563.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5378
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:47.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:38.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:37.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:04.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:04.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:58.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:02.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.12
p-value of test                       :  2.6e-3

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:48.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:14.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    2.32
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:42.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.51
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.71
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.82
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.11
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.76
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.02
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.31
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.47
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.33
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:51.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1349.27
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:04.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7069.15
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:51.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.85
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.05
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:11.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.81
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.19
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:37.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4990.67
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:03.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45825
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869825
  j =  1                              :        399908352
  j =  2                              :            45821
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45820
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869820
  j =  1                              :        399908362
  j =  2                              :            45816
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:31.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:20.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:48.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:04.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.29e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 5.29e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.39
p-value of test                       :    0.9916

-----------------------------------------------
CPU time used                    :  00:00:22.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:40.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:41.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.20
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.21
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:50.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.45
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.09
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.82
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.31
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.15
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.86
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:39.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17239.01
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.18
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.78
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.13
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.78
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.99
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.67
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.18
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.46
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.73
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.58
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.34
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.78
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.54
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.39
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.65
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.83
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.48
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.46
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.59
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.22
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.74
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.95
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.62
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.80
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.31
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.51
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.05
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5093.45
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.43
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.60
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.89
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :    1.26
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:26.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.32
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:24.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    1.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 4.31e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.27e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.15
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.35
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  241.91
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:06.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:09.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10101.12
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9915.24
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:04:28.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5009.56
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:54.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:56.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.04
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.59
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11692.76
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:35.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12097.90
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.88
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999928076

Normal statistic for number of bits   :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.83
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000035185

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   0.095
p-value of test                       :    0.46

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    4.55
p-value of test                       :  5.0e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.26
p-value of test                       :    0.99

Sample variance                       :    2.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:50.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 53  SampleMean, r = 0               0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 172490763.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5391
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:49.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:38.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:37.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:54.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:04.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:04.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:55.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:00.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:48.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     325
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:13.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:43.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.71
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.68
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.83
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.07
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.74
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  270.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.21
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:46.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1487.40
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:59.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6937.53
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:47.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.58
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.94
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:06.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.00
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.86
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:36.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4985.88
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:55.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45689
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869689
  j =  1                              :        399908625
  j =  2                              :            45683
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45916
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869916
  j =  1                              :        399908170
  j =  2                              :            45912
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:29.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  6.5e-3

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:16.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:44.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:00.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:55.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.83e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:22.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:37.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:37.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.38
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:48.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.64
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.82
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.70
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.09
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.74
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:44.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.41
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.97
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.02
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:28.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.05
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17655.48
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.00
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.90
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.60
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.32
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.04
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.90
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.28
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.69
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.75
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.75
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.70
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.84
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.56
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  101.49
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.54
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.26
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.35
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.16
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.22
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.44
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.86
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.91
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.20
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.35
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.39
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.19
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.46
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4853.82
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.92
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.52
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.85
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :   -0.86
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:25.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.71
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:26.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.08

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.79e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:47.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 7.19e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:46.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.13
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.93
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.03
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:06.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.20
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:08.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9938.87
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10013.50
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.086
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:04:11.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4756.86
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:51.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.48
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:53.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4040.15
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11860.71
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:30.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12107.67
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:29.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.92
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000024229

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.50
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000017380

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:10.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:06.52

 All tests were passed




Server wird beendet - Lösche Semaphor 173801483.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1264
p-value of test                       :    0.9968

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334384
  j =  1                              :        599997472
  j =  2                              :             1264
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5539
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:51.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:39.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:39.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:55.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:04.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:05.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7158
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:55.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:04:01.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     861
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:48.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:14.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:44.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.79
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.74
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.54
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.24
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:10.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.86
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.84
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.87
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.80
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:44.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1456.67
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:58.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7007.24
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:44.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:01.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.18
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.40
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:34.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5061.86
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:01.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45818
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869818
  j =  1                              :        399908369
  j =  2                              :            45808
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45804
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869804
  j =  1                              :        399908400
  j =  2                              :            45788
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:28.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 9.52e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:18.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:44.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:59.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:34.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.11e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:35.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.82
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.11
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.25
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.00
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:49.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.02
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.52
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.66
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:44.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.63
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   65.39
p-value of test                       :  6.8e-3

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.62
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.11
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   10.13
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.29
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.40
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17598.34
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:54.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.20
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.67
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.25
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.85
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.32
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.13
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.03
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.08
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.28
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.98
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  191.57
p-value of test                       :  6.8e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.87
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.89
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.49
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.40
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.05
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.87
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.72
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.72
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.53
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.19
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.24
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5052.38
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.51
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.80
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.93
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.59
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5100.97
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  320.82
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.33
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.91
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:23.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.93
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :   0.057
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:23.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.45e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 5.67e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9968

-----------------------------------------------
CPU time used                    :  00:00:47.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.91e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.72
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.08
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.71e-3
p-value of test                       :    0.9917

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  239.55
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:08.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:07.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9984.91
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10002.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:04:06.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.67
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:49.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5035.30
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:51.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.75
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.46
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11788.39
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12060.11
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.95
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000155764

Normal statistic for number of bits   :    1.23
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   86.42
p-value of test                       :  3.3e-3


-----------------------------------------------
Total number of bits:  7999922442

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :  -0.031
p-value of test                       :    0.51

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:02.61

 All tests were passed




Server wird beendet - Lösche Semaphor 174817291.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:50.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5493
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:49.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:39.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7463
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:38.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4217
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:56.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:04.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:04.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:55.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:04:01.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.93
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:46.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.42
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    3.31
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     333
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:11.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.80
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    3.59
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:40.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.83
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.45
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.13
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.50
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.96
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.74
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.24
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.28
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.28
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:43.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1363.72
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:59.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7258.35
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:41.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.75
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.09
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:02.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.73
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.96
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:34.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5244.14
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:55.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46132
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870132
  j =  1                              :        399907741
  j =  2                              :            46122
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46099
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870099
  j =  1                              :        399907807
  j =  2                              :            46089
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:29.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:18.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:00.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:55.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:34.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 3.20e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:24.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.70e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:21.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:32.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:32.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  107.72
p-value of test                       :  1.2e-3

-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.07
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.40
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.59
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:48.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.59
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.12
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.04
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.61
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.97
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.33
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17417.69
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.25
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.97
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.84
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.00
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.43
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.91
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.14
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.39
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.17
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.52
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.97
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.32
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.67
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.64
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  105.44
p-value of test                       :  9.6e-3


-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.41
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.10
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.14
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.41
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.83
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.44
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.20
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.60
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.77
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  162.56
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.21
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.95
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4897.77
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.85
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.91
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:36.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.13
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:26.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.52
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :   -1.77
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:25.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.18e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:46.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.22e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 8.71e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.39
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.90
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.79
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:05.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.34
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:06.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10062.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9854.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:49.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4976.14
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.74
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4194.44
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4039.30
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11613.81
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11872.76
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.52
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000091114

Normal statistic for number of bits   :    0.72
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.03
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000027013

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    1.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:07.10

 All tests were passed




Server wird beendet - Lösche Semaphor 175800331.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:49.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5342
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:51.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4233
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:39.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:39.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4456
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:03.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:03.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7106
p-value of test                       :    0.9936


-----------------------------------------------
CPU time used                    :  00:03:55.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:04:00.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    2.74
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.14
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.64
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    2.02
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:14.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.21
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.34
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.28
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.50
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.22
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.68
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   30.00
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.96
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.53
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:42.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1455.78
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:00.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7216.26
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:40.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.03
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.65
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:02.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.86
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  157.04
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:33.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5122.16
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:56.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46379
p-value of test                       :  1.0e-2


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870379
  j =  1                              :        399907242
  j =  2                              :            46379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45867
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869867
  j =  1                              :        399908273
  j =  2                              :            45853
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:29.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:17.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:44.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:58.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:34.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.77e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.49
p-value of test                       :  6.5e-3

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:34.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.00
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.40
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.91
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.31
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:38.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.25
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.94
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  8.3e-3

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  161.32
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17231.21
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.28
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.06
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.35
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.81
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.24
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.65
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.63
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.02
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.74
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.48
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.18
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.09
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.05
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.49
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.73
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.72
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.08
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.09
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.58
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.43
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.08
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.01
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4766.16
p-value of test                       :    0.9911


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  450.81
p-value of test                       :  5.9e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.80
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.81
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.70
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5026.38
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.46
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.58
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.43
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :    0.79
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:25.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.96
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:27.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 9.93e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.58
p-value of test                       :    0.94

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 3.60e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:46.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 8.85e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.08
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.60
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.71
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:07.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.24
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:07.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10056.80
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9916.32
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:55.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.89
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.57
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:50.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.65
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11752.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11763.29
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:29.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.59
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999828545

Normal statistic for number of bits   :   -1.36
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.49
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000050554

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    1.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:14.25

 All tests were passed




Server wird beendet - Lösche Semaphor 176717835.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5493
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:53.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4235
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:39.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:03.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:03.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:54.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:00.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:47.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     549
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    3.28
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:09.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:34.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.86
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.05
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.43
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.56
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.78
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.68
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.72
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.04
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.89
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  488.55
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:44.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1394.00
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:01.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7108.57
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:44.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.53
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.58
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:03.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.31
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.94
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:35.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4839.06
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:57.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45712
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869712
  j =  1                              :        399908579
  j =  2                              :            45706
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45706
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869706
  j =  1                              :        399908589
  j =  2                              :            45704
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 5.32e-3
p-value of test                       :    0.9935

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:28.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:17.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:44.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:59.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:33.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.87e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:34.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:34.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.49
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:48.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.39
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.11
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.70
p-value of test                       :  8.3e-3

-----------------------------------------------
CPU time used                    :  00:00:48.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.37
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.66
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.18
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:38.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.95
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.56
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.48
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17501.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.47
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.95
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.94
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.69
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.54
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.98
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.73
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.81
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    9.87
p-value of test                       :    0.9951


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.93
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.37
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.55
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.24
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.85
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.08
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.74
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.02
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.21
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.90
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.49
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.56
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.72
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4855.37
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.92
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.03
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.33
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.37
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4932.31
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.26
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.12
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:34.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.04
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :   -1.99
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:23.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.56
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :   -0.90
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:26.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  3.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    4.10
p-value of test                       :  8.2e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.53
p-value of test                       :    0.9942

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.59e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:46.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.32e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.56
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.59
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.79
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:10.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.94
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:08.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10040.57
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9994    *****

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.80
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:04:11.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5091.52
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:50.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4830.84
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:51.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.10
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4005.84
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11933.59
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11621.09
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:29.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.12
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000108997

Normal statistic for number of bits   :    0.86
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.63
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999864284

Normal statistic for number of bits   :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :  -0.012
p-value of test                       :    0.50

Sample variance                       :    2.39
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:42.69

 All tests were passed




Server wird beendet - Lösche Semaphor 177700875.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5425
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:53.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:39.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:39.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:55.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:02.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:03.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:53.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:00.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.48
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:13.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.70
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:40.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.49
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.87
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.77
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.63
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.63
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.66
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.91
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.12
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.93
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.55
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:43.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1489.66
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:58.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6913.20
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.03
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   85.39
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:01.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.04
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.41
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:33.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5073.91
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:00.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46123
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870123
  j =  1                              :        399907758
  j =  2                              :            46115
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46000
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870000
  j =  1                              :        399908001
  j =  2                              :            45998
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:29.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:17.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:44.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:58.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.76e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:21.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:32.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:33.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.07
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.12
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.50
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.44
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.78
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.28
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.40
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:38.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   20.65
p-value of test                       :    0.9951

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.64
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.46
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.89
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17415.70
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.66
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.85
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.77
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.29
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.17
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.62
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.01
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.19
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.81
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.91
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.75
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.43
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.47
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.25
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.03
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.22
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.02
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.82
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.58
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.83
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.21
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  453.44
p-value of test                       :  8.4e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5109.68
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.27
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.91
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.38
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.86
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5074.30
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.90
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.68
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.48
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:23.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.86
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :  -0.095
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:25.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.14
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 7.71e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.57e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.99
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.48
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.55
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:08.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.24
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:07.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9845.97
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10135.49
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:50.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.29
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:50.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4945.67
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:51.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3936.75
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.35
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11787.16
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12067.22
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:30.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.18
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999965003

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.36
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000006313

Normal statistic for number of bits   :   0.050
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.63
p-value of test                       :    0.95

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    0.72
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:29.44

 All tests were passed




Server wird beendet - Lösche Semaphor 178651147.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5477
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:53.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:40.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:39.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:02.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:03.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7193
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:54.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:59.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.88
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.96
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:47.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:12.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:42.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.83
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.58
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.38
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.36
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.83
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.36
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.85
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.08
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.11
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:45.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1493.19
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:00.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7093.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.65
p-value of test                       :  7.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.48
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   14.16
p-value of test                       :    0.9937

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.20
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:01.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.07
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:33.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5019.17
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:55.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45774
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869774
  j =  1                              :        399908456
  j =  2                              :            45766
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45670
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869670
  j =  1                              :        399908665
  j =  2                              :            45660
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:28.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:17.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:44.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :  3.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    4.22
p-value of test                       :  7.0e-3


-----------------------------------------------
CPU time used                    :  00:01:58.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:35.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.19e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:22.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 9.88e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:21.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:34.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.82
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.87
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.77
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:48.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.01
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.54
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.77
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:38.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.96
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.55
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.48
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.90
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17402.56
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.73
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.77
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.20
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.98
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.76
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.45
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.56
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.66
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.74
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.64
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.62
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.05
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.27
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.46
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.24
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.47
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.22
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.83
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.28
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.63
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.73
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4938.20
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.84
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  151.12
p-value of test                       :    0.9959


-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.44
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.63
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5160.21
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.56
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.45
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.36
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :   -1.20
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:24.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.42
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :    1.53
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:25.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.83e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 6.64e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:46.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.62e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 7.94e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.84
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.36
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  158.15
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:05.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.20
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:06.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10016.06
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.91
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9630.80
p-value of test                       :    0.9958

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:46.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4765.67
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:49.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4962.25
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:51.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4035.01
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.28
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11645.00
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11720.52
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:29.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.95
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000117733

Normal statistic for number of bits   :    0.93
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.37
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  7999997937

Normal statistic for number of bits   :  -0.016
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.97
p-value of test                       :    0.02

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:05.80

 All tests were passed




Server wird beendet - Lösche Semaphor 179699723.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:49.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5452
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:55.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:41.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4552
p-value of test                       :  6.1e-4    *****


-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:03.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:03.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:54.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:59.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9914

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:13.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:41.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.70
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.40
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.68
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.14
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.05
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.90
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.17
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.15
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.62
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:43.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1475.79
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:01.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6927.79
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:41.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.77
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.58
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:03.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.45
p-value of test                       :    0.9938


-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   82.97
p-value of test                       :    0.9951


-----------------------------------------------
CPU time used                    :  00:01:33.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4970.79
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:55.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46077
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870077
  j =  1                              :        399907848
  j =  2                              :            46073
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45601
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869601
  j =  1                              :        399908799
  j =  2                              :            45599
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:28.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:17.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:44.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:58.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:35.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.17e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:33.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:34.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.67
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:49.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.68
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.48
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:48.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.62
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.32
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.86
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:39.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.34
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.60
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.15
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.28
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17348.82
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.76
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.22
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.11
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.11
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.09
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.16
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.45
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.25
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.69
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.34
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.47
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.41
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.88
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.43
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.34
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.38
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.11
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.28
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.18
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.85
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.79
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.12
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4876.57
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  446.04
p-value of test                       :  9.0e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.42
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  440.89
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.64
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4873.64
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.03
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.34
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.83
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:24.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.21
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:24.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.54e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 6.56e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.27
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.37
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.09
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:06.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.32
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:06.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10145.72
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9964

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9975.01
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.039
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:44.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.82
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:49.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4796.04
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:50.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4005.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.26
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11951.42
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11829.15
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.78
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000116416

Normal statistic for number of bits   :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.22
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000029263

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.39
p-value of test                       :    0.9915

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:09.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 17  BirthdaySpacings, t = 7         6.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 180682763.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5420
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:54.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:41.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7145
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:41.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:56.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:04.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:05.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:54.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:59.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:47.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     653
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:13.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.05
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:45.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.93
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.68
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.27
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.73
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.34
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.07
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  262.76
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.84
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:43.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1544.79
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:01.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6992.60
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.19
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:04.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.75
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.80
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:33.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5013.37
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:59.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46098
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870098
  j =  1                              :        399907806
  j =  2                              :            46094
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45842
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869842
  j =  1                              :        399908320
  j =  2                              :            45834
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 3.86e-3
p-value of test                       :    0.9955

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:28.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:17.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:58.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:56.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:36.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:21.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:35.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.07
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.26
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.94
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.03
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:48.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.09
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.74
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.38
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.15
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.67
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.095
p-value of test                       :    0.9924

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17404.17
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.18
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.21
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.69
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.98
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.47
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.42
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.88
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.31
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.25
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.68
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.35
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.27
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.02
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.82
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  108.01
p-value of test                       :  6.1e-3


-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.28
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.43
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.46
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.16
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.46
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.40
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.73
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4923.63
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.16
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.97
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.14
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.48
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5108.60
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.94
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.21
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.35
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :    1.67
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:23.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.82
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :   -1.12
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:23.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.62e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 7.76e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.79
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.71
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 4.20e-3
p-value of test                       :    0.9956

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:07.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.56
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:09.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10196.28
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9819.83
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.19
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:03:48.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4818.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:48.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4798.85
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:50.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4207.49
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.72
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12031.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11958.54
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:30.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.42
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000014002

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.46
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000041437

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         : -3.44e-3
p-value of test                       :    0.50

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    2.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:08.48

 All tests were passed




Server wird beendet - Lösche Semaphor 181665803.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:57.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5380
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:58.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4244
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:42.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7141
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:43.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:57.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:57.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:07.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7112
p-value of test                       :    0.9922


-----------------------------------------------
CPU time used                    :  00:03:07.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7180
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:00.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:01.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.94
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.87
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     952
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.82
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    2.99
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:14.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.25
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:39.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.19
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.88
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.98
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.53
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.86
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.85
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.00
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.01
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:48.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1406.75
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:03.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7138.56
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:50.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.07
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.44
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:09.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.69
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.95
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5172.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:59.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45923
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869923
  j =  1                              :        399908157
  j =  2                              :            45917
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45686
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869686
  j =  1                              :        399908630
  j =  2                              :            45682
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:31.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:19.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:07.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:36.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.70e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-5
p-value of test                       :    0.9906

Kolmogorov-Smirnov- statistic = D-    : 3.44e-4
p-value of test                       :  8.7e-3

Anderson-Darling statistic = A2       :    3.29
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.088
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:38.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.27
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:39.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.98
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.18
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.03
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:55.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.75
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:50.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.05
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.68
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:46.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    3.48
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.20
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.76
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.53
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:38.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17436.88
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.94
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.08
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.18
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.75
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.76
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.01
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.12
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.88
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.33
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.37
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.04
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.33
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.83
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.61
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.49
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.91
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.86
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.39
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.54
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.86
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.25
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.67
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5053.96
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.24
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.92
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.44
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.25
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5171.56
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.23
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  244.63
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.83
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:23.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.54
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :    1.26
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:22.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.89
p-value of test                       :    0.97

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 6.92e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.48e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 6.59e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.10
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.37
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.78
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:07.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.10
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:07.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10002.49
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9940.52
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:04:26.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.26
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:53.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5009.40
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4233.66
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.77
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11793.65
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11594.26
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:31.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.82
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000014164

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.68
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000027712

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   0.066
p-value of test                       :    0.47

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.27

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:53.35

 All tests were passed




Server wird beendet - Lösche Semaphor 182714379.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5524
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:54.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:40.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7183
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:41.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:57.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4229
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:57.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:07.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:03.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7467
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:55.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:00.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.67
p-value of test                       :  4.2e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.75
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:50.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:17.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.25
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    2.04
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:44.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.07
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.77
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.05
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.36
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.15
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.34
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.88
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:45.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.78
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:01.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6949.65
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.69
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.15
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:04.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.25
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  151.35
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:33.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5125.24
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:59.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45318
p-value of test                       :    0.9956


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869318
  j =  1                              :        399909365
  j =  2                              :            45316
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45598
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869598
  j =  1                              :        399908806
  j =  2                              :            45594
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:28.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:17.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 3.06e-3
p-value of test                       :    0.9968

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :  3.0e-3

Anderson-Darling statistic = A2       :    5.49
p-value of test                       :  1.8e-3


-----------------------------------------------
CPU time used                    :  00:01:44.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:59.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:33.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.89e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.56e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.99e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.78e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:34.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:34.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.18
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.26
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.05
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.67
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.59
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:39.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.48
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.24
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.91
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.23
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17466.75
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.42
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.92
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.84
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.54
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.24
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.80
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.45
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.19
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.18
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:38.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.68
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.84
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.89
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.57
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.08
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.87
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.97
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.27
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.00
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.71
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.62
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.00
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4911.25
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.21
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.55
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.53
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.19
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4869.54
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  438.55
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.33
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.72
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :    1.27
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:24.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.78
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :    0.37
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:24.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.12

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.83

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 5.70e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.49
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.01
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.79
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:07.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.95
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:06.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9944.49
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9905.07
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:51.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4998.75
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:48.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4740.94
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:50.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4241.59
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4133.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12041.78
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:28.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11838.31
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.52
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999881471

Normal statistic for number of bits   :   -0.94
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.70
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000092023

Normal statistic for number of bits   :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.84
p-value of test                       :    0.03

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:08.14

 All tests were passed




Server wird beendet - Lösche Semaphor 183828491.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1468
p-value of test                       :  2.8e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334588
  j =  1                              :        599997064
  j =  2                              :             1468
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5361
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:57.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:41.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:57.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:58.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:06.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:05.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:55.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:04:00.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:51.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    2.60
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     659
p-value of test                       :  9.2e-3

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    4.42
p-value of test                       :  5.4e-3

-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    2.41
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:16.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.9904


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.98
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:49.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.68
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.63
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.29
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.16
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.78
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.01
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.14
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:43.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1410.13
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:01.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7184.43
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:42.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.12
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.41
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:05.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.64
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   89.90
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:32.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5094.67
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:08.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46027
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870027
  j =  1                              :        399907947
  j =  2                              :            46025
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45875
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869875
  j =  1                              :        399908254
  j =  2                              :            45867
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:29.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:18.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:44.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:58.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:55.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 9.78e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:36.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:35.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.35
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:48.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.78
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.83
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.42
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.34
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:41.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.05
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.86
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.10
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.29
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17433.58
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.89
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.71
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.63
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.10
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.30
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.25
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.82
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.00
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.55
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.84
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.85
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.09
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.87
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.65
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.16
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.48
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.30
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  418.02
p-value of test                       :    0.9968


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.54
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.07
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  454.84
p-value of test                       :  7.4e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.16
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4841.60
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.90
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.87
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.31
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.26
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.14
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.34
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.51
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.41
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : 2.98e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:24.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.32
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :    1.10
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:25.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.57e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.19e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 9.49e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.27
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.00
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.65
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:06.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.47
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:06.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10041.13
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10246.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:43.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4786.21
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4999.16
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:50.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.11
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4332.73
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11949.21
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11574.23
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.16
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000109510

Normal statistic for number of bits   :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.08
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000079702

Normal statistic for number of bits   :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    2.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:25.62

 All tests were passed




Server wird beendet - Lösche Semaphor 184811531.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5393
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:00.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:43.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:45.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:00.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:01.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:10.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7165
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:08.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7159
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:04:02.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:04.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:49.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    2.21
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:18.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:47.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.43
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:55.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.74
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.60
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.58
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.81
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.24
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.81
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.05
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.96
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:48.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1407.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7039.86
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:07.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.43
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.43
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:37.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4941.83
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:57.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46298
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870298
  j =  1                              :        399907408
  j =  2                              :            46290
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45800
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869800
  j =  1                              :        399908402
  j =  2                              :            45796
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:30.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:19.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:47.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:03.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:56.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:36.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 8.17e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.12e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.09e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:43.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:44.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.97
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.93
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.93
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   59.10
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.29
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.43
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.39
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:45.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.57
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.30
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.04
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.64
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.40
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17389.61
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.61
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.79
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.28
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.79
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   34.62
p-value of test                       :  7.0e-3


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.14
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.16
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.42
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.14
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.94
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.89
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.59
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.42
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.52
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.81
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.08
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.18
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.25
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  193.21
p-value of test                       :  9.2e-4    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.53
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.55
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.61
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4870.44
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.67
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.28
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.38
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.19
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5071.43
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.75
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.30
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.04
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :   -1.21
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:24.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.72
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:23.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    0.23
p-value of test                       :    0.9909

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.72e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.98e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.56
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.20
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.21
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:05.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.34
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:05.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9851.88
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9989.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:04:22.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4948.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:52.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5037.12
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:54.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.06
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.18
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11687.53
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:31.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11764.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:31.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.92
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000023920

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.08
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000010129

Normal statistic for number of bits   :   0.080
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9955

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.86
p-value of test                       :    0.97

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:15.77
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 77  RandomWalk1 R (L=1000, r=20)    9.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 185827339.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:50.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5418
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:58.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:41.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4461
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:56.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:58.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:06.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:06.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:56.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:02.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    4.89
p-value of test                       :  3.3e-3

-----------------------------------------------
CPU time used                    :  00:01:51.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    2.28
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     661
p-value of test                       :  7.4e-3

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    2.19
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.17
p-value of test                       :    0.9968

-----------------------------------------------
CPU time used                    :  00:02:18.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:49.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.71
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.94
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:10.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.57
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.13
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  357.89
p-value of test                       :    0.9968

-----------------------------------------------
CPU time used                    :  00:01:45.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1421.10
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:01.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7064.76
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.42
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.99
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:03.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.92
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.93
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:34.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5010.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:01.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45438
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869438
  j =  1                              :        399909128
  j =  2                              :            45430
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45975
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869975
  j =  1                              :        399908053
  j =  2                              :            45969
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:28.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:18.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:45.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:59.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:54.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9970

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:33.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.93e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.40e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:36.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:37.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.71
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.74
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.40
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.95
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.00
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:43.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.20
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.39
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.36
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:29.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:29.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.89
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17195.44
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.80
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.31
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.24
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.57
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.95
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.05
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.35
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.99
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.78
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.85
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.23
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.11
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.78
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.52
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.78
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.09
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.21
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.83
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.76
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.04
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4957.53
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.25
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.61
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:36.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.70
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.13
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5086.39
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.75
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.04
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.83
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:22.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.00
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :  -0.019
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:22.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.94
p-value of test                       :    0.97

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.69e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 8.27e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 5.74e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.78
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.92
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.96
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:04.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:06.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10202.68
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10141.78
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.083
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:44.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 6.16e-3
p-value of test                       :    0.9935

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4729.79
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4943.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:50.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.55
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4188.02
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12086.10
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11712.70
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:30.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.99
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999934496

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.10
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000029428

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.38

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:14.26

 All tests were passed




Server wird beendet - Lösche Semaphor 187039755.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5378
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:00.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:43.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:45.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4250
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:00.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:01.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:12.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:12.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:04:09.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7181
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:10.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:51.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    2.37
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:17.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.64
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:47.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.67
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.20
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.30
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.19
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:10.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.29
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.61
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.34
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.96
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.06
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.26
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:53.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1492.54
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:06.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7006.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.78
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:17.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.68
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   85.11
p-value of test                       :    0.9919


-----------------------------------------------
CPU time used                    :  00:01:39.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5179.05
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:01.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45978
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869978
  j =  1                              :        399908051
  j =  2                              :            45964
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46033
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870033
  j =  1                              :        399907937
  j =  2                              :            46027
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 4.51e-3
p-value of test                       :    0.9946

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:33.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:20.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:49.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:07.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:01:37.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 8.13e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:24.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.07
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:24.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:24.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:52.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:54.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.95
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.69
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.82
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.12
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.10
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.38
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:50.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.24
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.60
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.04
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17273.91
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.26
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.92
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.91
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.81
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.35
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.42
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.43
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.18
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.15
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.29
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.72
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.72
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.94
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.35
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.80
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.41
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.63
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.32
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.72
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.60
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.33
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.48
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.57
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.03
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.91
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.16
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.95
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.24
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.59
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.67
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:34.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.22
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :   -1.71
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:21.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.28
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:22.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.73e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 5.70e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.31
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.26
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.05
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:06.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.53
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:06.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10176.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9919.74
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.029
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:04:25.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:55.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5010.54
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:57.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.85
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4209.69
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11626.90
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:33.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11806.82
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.04
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000126343

Normal statistic for number of bits   :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.91
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000032536

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.77
p-value of test                       :    0.04

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.03
p-value of test                       :    0.98

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:00.59

 All tests were passed




Server wird beendet - Lösche Semaphor 188055563.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:48.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5531
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:42.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:36.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:35.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:54.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:55.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:02.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:02.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:55.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:00.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    2.80
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     835
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    3.21
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:52.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.66
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.17
p-value of test                       :    0.9962

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.90
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.60
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    2.92
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:11.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:34.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.48
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.33
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.75
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.07
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.02
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.91
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  338.92
p-value of test                       :    0.9997    *****

-----------------------------------------------
CPU time used                    :  00:01:51.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1460.77
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:00.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7090.87
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:50.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.66
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.70
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:03.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.65
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.17
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:36.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5050.36
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:17.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45886
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869886
  j =  1                              :        399908233
  j =  2                              :            45876
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45721
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869721
  j =  1                              :        399908566
  j =  2                              :            45705
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:14.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:28.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:18.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:45.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9967


-----------------------------------------------
CPU time used                    :  00:01:59.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:52.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:33.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.02e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 9.43e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:37.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:38.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.54
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:47.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.73
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.29
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.78
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.03
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.62
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:43.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.92
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.87
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:32.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.70
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:31.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.08
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17346.79
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.03
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.95
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.16
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.80
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.28
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:40.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.93
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.88
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   43.64
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.02
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.03
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.12
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.06
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.41
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.81
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.26
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:49.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.92
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.19
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.67
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.53
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.92
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:47.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.00
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.01
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4948.37
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.90
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.94
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:37.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.05
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.99
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.35
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.72
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  240.45
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.99
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :   -1.57
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:16.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.22
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:12.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 8.15e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.41
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.81
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.98
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:11.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.28
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:12.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10099.99
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10091.59
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:51.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.64
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:48.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.70
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:50.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4434.79
p-value of test                       :  3.1e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4162.12
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11697.65
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12001.33
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:30.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.05
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999951119

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.99
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000043516

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :  -0.044
p-value of test                       :    0.52

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   0.056
p-value of test                       :    0.48

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:30.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.22
p-value of test                       :    0.99

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:17:05.97
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 35  Gap, r = 25                     0.9997 
 97  HammingIndep, L=300, r=0        3.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 168296460.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5268
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:43.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:36.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:36.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4457
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:03.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:02.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:53.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:04:00.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.15
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.42
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    4.32
p-value of test                       :  6.1e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.81
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.99
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:14.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:40.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.64
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.76
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.83
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.99
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.06
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.50
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  453.58
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1446.33
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:59.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7117.17
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:43.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.39
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   37.16
p-value of test                       :    0.9910

-----------------------------------------------
CPU time used                    :  00:03:03.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.09
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.42
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:35.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5023.06
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:04.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45671
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869671
  j =  1                              :        399908661
  j =  2                              :            45665
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45290
p-value of test                       :    0.9971


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869290
  j =  1                              :        399909423
  j =  2                              :            45284
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:14.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:32.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:19.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:45.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:00.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:54.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:33.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:34.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.01
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:35.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.10
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:48.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.65
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.84
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:47.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.13
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.93
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   49.08
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:37.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.90
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.4e-3

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:30.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.88
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.78
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17232.71
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.07
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.35
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.27
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.06
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.37
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:39.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.01
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.12
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.53
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.55
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.48
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.30
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.73
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.87
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.39
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  106.30
p-value of test                       :  8.3e-3


-----------------------------------------------
CPU time used                    :  00:00:48.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.33
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.12
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.28
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.64
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.96
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:47.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.79
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.49
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4792.46
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.06
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.40
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.79
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5099.50
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.07
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.14
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.51
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:25.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.87
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:18.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.00e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 9.80e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.64
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:29.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.27
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:08.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:10.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10011.05
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10114.97
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:04:00.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5042.15
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4748.71
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:50.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.83
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.40
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11570.55
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11840.08
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:29.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.57
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999982304

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.69
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999903719

Normal statistic for number of bits   :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :  -0.085
p-value of test                       :    0.53

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:55.42

 All tests were passed




Server wird beendet - Lösche Semaphor 169312268.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5402
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:43.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4503
p-value of test                       :  6.2e-3


-----------------------------------------------
CPU time used                    :  00:01:37.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7169
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:36.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:54.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4429
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:55.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:02.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:02.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:53.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:59.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.01
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.77
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:46.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:12.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:41.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.60
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.00
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.84
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   84.44
p-value of test                       :  5.1e-3

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.63
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.02
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.24
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.59
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.00
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:58.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7048.16
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:41.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.09
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:15.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:58.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.71
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.16
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:33.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4996.71
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:02.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46202
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870202
  j =  1                              :        399907599
  j =  2                              :            46196
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45590
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869590
  j =  1                              :        399908822
  j =  2                              :            45586
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:32.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:19.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:46.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:00.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:54.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:33.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 9.89e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 9.39e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:22.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:33.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.34
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.78
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.10
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.68
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:47.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.71
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.18
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:38.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.62
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  8.3e-3

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.03
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.70
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.72
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.92
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9924

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17361.29
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   62.66
p-value of test                       :  3.9e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.07
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.10
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.44
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.18
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.89
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.64
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.99
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.08
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.44
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.97
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.92
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.61
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.20
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.06
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.13
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.52
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.84
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.27
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.94
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.70
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.64
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.90
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.21
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.03
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  448.29
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  457.38
p-value of test                       :  5.9e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4773.19
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.53
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.98
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:26.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.50
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:23.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :  -0.082
p-value of test                       :    0.53

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.62e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.96
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.33
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.28
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:06.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.33
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:08.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9882.89
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9697.47
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:50.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4967.63
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:50.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.86
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:51.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4010.93
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.32
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11740.52
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11807.33
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:30.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.29
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000122632

Normal statistic for number of bits   :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.06
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999862073

Normal statistic for number of bits   :   -1.09
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.69e-3
p-value of test                       :    0.9962

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.39
p-value of test                       :  8.4e-3

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:28.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:29.23

 All tests were passed




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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:49.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5349
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:44.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:37.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:34.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:54.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:54.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:01.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:02.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:53.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:59.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:46.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:10.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.10
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:39.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.72
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.56
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.94
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.97
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.70
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.74
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.84
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  500.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1409.66
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:00.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7004.14
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:41.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.80
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.30
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:04.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.24
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.05
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:32.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5084.02
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:59.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45957
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869957
  j =  1                              :        399908091
  j =  2                              :            45947
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45910
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869910
  j =  1                              :        399908181
  j =  2                              :            45908
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:30.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:18.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:45.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:00.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:57.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  6.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.74
p-value of test                       :  3.9e-3

-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.21e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:33.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.21
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:48.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.60
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.78
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:48.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.15
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.99
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.68
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:36.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.21
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.39
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.19
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.97
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.89
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 7.15e-3
p-value of test                       :    0.9924

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17734.58
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.19
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.78
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.02
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.36
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.75
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.09
p-value of test                       :    0.9944


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.03
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.20
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.84
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   35.29
p-value of test                       :  5.7e-3


-----------------------------------------------
CPU time used                    :  00:00:37.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.48
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.70
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.89
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.90
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.15
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.88
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.13
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.68
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.15
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.39
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.54
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.25
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4905.29
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.51
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.09
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.31
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.16
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5134.56
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.23
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.71
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    2.85
p-value of test                       :    0.9965


-----------------------------------------------
Normal statistic for number of jumps  :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:22.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.51
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :   -1.22
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:23.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.46e-3
p-value of test                       :    0.9909

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.1e-3

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.41
p-value of test                       :  8.0e-3

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.70e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 9.96e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.10
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.97
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.52
p-value of test                       :  5.1e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  148.94
p-value of test                       :    0.9972

-----------------------------------------------
CPU time used                    :  00:02:08.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.53
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:06.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10196.32
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.61
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:52.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4772.44
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:49.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4798.64
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:51.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.84
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11903.71
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11807.37
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:30.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.08
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999909062

Normal statistic for number of bits   :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.85
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999957509

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.19
p-value of test                       :    0.12

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:02.19

 All tests were passed




Server wird beendet - Lösche Semaphor 171114508.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:56.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:41.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:06.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:05.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:04:03.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:09.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    2.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:45.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     640
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.28
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:11.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:41.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.89
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.91
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.60
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.81
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.47
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.11
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  469.67
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:58.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1458.94
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:06.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7049.30
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:58.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.61
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.48
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.25
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:18.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.46
p-value of test                       :    0.9934


-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.90
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4947.07
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:00.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45740
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869740
  j =  1                              :        399908522
  j =  2                              :            45736
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45818
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869818
  j =  1                              :        399908370
  j =  2                              :            45806
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:31.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:22.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:53.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:08.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  7.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:57.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:37.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 5.95e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:24.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.31
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:24.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:24.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:43.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:44.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.99
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.68
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.72
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.78
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.60
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.68
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:52.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.70
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.36
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.47
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.95
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17350.97
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.03
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.44
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.45
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.53
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.80
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.65
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.57
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.25
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.15
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.05
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.88
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.15
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.47
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.46
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.11
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.45
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.24
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  571.02
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.45
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.34
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.53
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.44
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.11
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.44
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.49
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.48
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.70
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5100.23
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.78
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.49
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.33
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :   -1.49
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:23.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.07
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -1.83
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:23.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.44e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.23e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.19
p-value of test                       :    0.9967

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.39
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:07.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.51
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:07.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9821.17
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10069.46
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:13.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:04:36.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4804.01
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:52.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5010.02
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4179.56
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.76
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11920.26
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:33.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11800.75
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:35.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.24
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000016237

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.84
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000114208

Normal statistic for number of bits   :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.14

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:25.48

 All tests were passed




Server wird beendet - Lösche Semaphor 172097548.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:50.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5405
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:50.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:38.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:37.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4433
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:55.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:02.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:02.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:54.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:04:00.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.33
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.18
p-value of test                       :    0.9942

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:40.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.84
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:05.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:34.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.43
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.71
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:10.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.55
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.14
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.08
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:10.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.58
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.42
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.12
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.18
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.27
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1488.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:01.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6938.05
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:40.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.68
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.02
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:03.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.93
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.86
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:33.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4844.64
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:56.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46060
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870060
  j =  1                              :        399907883
  j =  2                              :            46054
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45560
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869560
  j =  1                              :        399908884
  j =  2                              :            45552
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:27.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:17.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:44.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:00.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:56.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:33.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.32e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 3.52e-4
p-value of test                       :  7.0e-3

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 6.95e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:21.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:21.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:32.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:33.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:47.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.84
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.58
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.44
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:47.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.99
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.33
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:37.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.75
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.33
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:28.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.29e-3
p-value of test                       :    0.9933

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  168.33
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17353.30
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.29
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.03
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.76
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.41
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.98
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.37
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.44
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.40
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.03
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.45
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.67
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.46
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   96.28
p-value of test                       :    0.9960


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.51
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.91
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.72
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.02
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.52
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.56
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.42
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.60
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5129.02
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.49
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.34
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.50
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.65
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4814.68
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.10
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.05
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.00
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:25.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.18
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :   0.043
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:24.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.57e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 9.79e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:46.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 7.57e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.02
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.41
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.83
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:08.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.19
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:08.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9894.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10087.59
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.35
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:48.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5019.37
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:49.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.82
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:51.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4183.00
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.86
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12083.35
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11784.38
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.10
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999942746

Normal statistic for number of bits   :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.41
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999776018

Normal statistic for number of bits   :   -1.77
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    1.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:29.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   0.076
p-value of test                       :    0.47

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:19.31

 All tests were passed




Server wird beendet - Lösche Semaphor 173539340.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5402
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:55.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:39.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:39.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:55.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:02.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:01.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:53.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:58.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.89
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.97
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    2.34
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:14.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.23
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:43.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.90
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.07
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.28
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.74
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.57
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.86
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.00
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.78
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.28
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  378.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:45.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:00.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7037.24
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:46.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 9.16e-3
p-value of test                       :    0.9905

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.56
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:02.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.79
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.61
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5086.95
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:01.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45777
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869777
  j =  1                              :        399908453
  j =  2                              :            45763
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45952
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869952
  j =  1                              :        399908101
  j =  2                              :            45942
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:29.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:17.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:01.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:01.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:41.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 8.86e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.87e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:34.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:35.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.37
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  101.46
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.85
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.62
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.09
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.78
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.76
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:44.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.73
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.97
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.21
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17290.93
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.27
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.14
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.38
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.49
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.61
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.73
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.25
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.48
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.89
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.56
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.87
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.63
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.36
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.30
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.77
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.55
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.00
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.72
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.12
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.20
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.03
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.48
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4872.20
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.96
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.35
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.50
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.14
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4984.64
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.62
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.41
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.23
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:22.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.69
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :   -1.94
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:23.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.97e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 5.43e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:46.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 5.06e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.76
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.97
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.41
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:08.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.04
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:06.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10187.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10143.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:04:12.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.76
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4661.44
p-value of test                       :    0.9904

-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4825.83
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:51.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3994.70
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.23
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11985.94
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:29.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11556.13
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:30.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.40
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999910796

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   32.91
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  7999984197

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9973

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:09.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    2.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:09.19

 All tests were passed




Server wird beendet - Lösche Semaphor 174555148.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5476
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:53.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:40.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:38.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:55.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:57.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:04.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:04.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7507
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:56.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:00.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.81
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:14.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.90
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    2.14
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:41.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.27
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.04
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.44
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.32
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.75
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.12
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.42
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.90
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:48.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1385.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:01.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6969.89
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:49.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.80
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.51
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:09.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.90
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  146.13
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:37.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5235.36
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:55.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46055
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870055
  j =  1                              :        399907890
  j =  2                              :            46055
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46021
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870021
  j =  1                              :        399907962
  j =  2                              :            46013
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9939

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:30.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:19.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:50.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:08.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:56.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:36.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:38.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:38.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.12
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:50.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.79
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.91
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.70
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.40
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.92
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.22
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:46.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.74
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.18
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.98
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.92
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:39.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17239.48
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.98
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.74
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.30
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.43
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.00
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.89
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.44
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.03
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.61
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.43
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.83
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.03
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.13
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.44
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.10
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.80
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.30
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.11
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.23
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.25
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  448.40
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.22
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5071.88
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.59
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.88
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.61
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.04
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4800.12
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.48
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.23
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.41
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:22.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.82
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :    1.63
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:23.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.63e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.99
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   43.00
p-value of test                       :  5.7e-4    *****



-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.70
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.12
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:07.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.60
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:08.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10116.34
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10116.26
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.015
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -3.74
p-value of test                       : 1 -  9.3e-5    *****

-----------------------------------------------
CPU time used                    :  00:04:24.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.31
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:55.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4974.50
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4034.71
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11632.43
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:31.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11585.70
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:31.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.03
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999986153

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.95
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000032296

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:15.76
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 86  LongestHeadRun, r = 0           5.7e-4
 94  HammingCorr, L = 1200          1 -  9.3e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 175603724.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:39.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5481
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:54.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:40.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:58.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:59.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:08.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:07.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:04:03.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:04:07.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.24
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.71
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     857
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    3.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.51
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    6.17
p-value of test                       :  8.2e-4    *****

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:13.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:40.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.17
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:11.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.52
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:11.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.86
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.22
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  189.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  453.01
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:55.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1368.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:02.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6958.26
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:55.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.95
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.62
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:17.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.61
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.64
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5119.28
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:03.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46178
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870178
  j =  1                              :        399907648
  j =  2                              :            46170
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45778
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869778
  j =  1                              :        399908447
  j =  2                              :            45772
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  8.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:32.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:20.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:52.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:08.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:37.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.68e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -3.02
p-value of test                       :    0.9988

-----------------------------------------------
CPU time used                    :  00:00:24.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.048
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:45.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:49.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.55
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:50.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.58
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.08
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.89
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.77
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.40
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:50.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.52
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:18.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.48
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  170.70
p-value of test                       :  9.6e-3

-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17640.29
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.67
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.50
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.31
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.18
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.72
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.94
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.10
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.18
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.02
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.99
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.39
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.89
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.28
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.60
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.66
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.45
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.70
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.67
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.09
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.43
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.63
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4892.44
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.26
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.48
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.39
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.27
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4925.66
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.72
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.76
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.68
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :   -1.42
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:25.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.20
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:27.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.49
p-value of test                       :  5.3e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.74
p-value of test                       :    0.9969

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 5.54e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.38e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 9.39e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.75
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.11
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.71
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:06.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.58
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:08.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 5.41e-3
p-value of test                       :    0.9943

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9680.14
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10110.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:12.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:04:34.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5014.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.36
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:59.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4157.60
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.74
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:28.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11781.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:35.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11746.54
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:37.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.41
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  8000019927

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.51
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000048484

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:35.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP2, t = 9          8.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 176619532.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5391
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:50.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:39.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:38.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:55.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:57.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:05.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:04.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7453
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:55.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7198
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:01.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.15
p-value of test                       :    0.9984

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    4.22
p-value of test                       :  6.8e-3

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    2.96
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:13.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    2.44
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     130
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:45.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.97
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.66
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.09
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.33
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.30
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.86
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.05
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.04
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  472.85
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:42.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1479.67
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:00.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7129.34
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:41.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.22
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.67
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:03.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.12
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.36
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:34.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5081.43
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:04.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46024
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870024
  j =  1                              :        399907956
  j =  2                              :            46016
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46362
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870362
  j =  1                              :        399907277
  j =  2                              :            46360
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:27.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:17.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:45.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:59.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:54.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:34.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.33e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.29e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:21.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:21.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:48.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.23
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.04
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.70
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.70
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.78
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.07
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.31
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:29.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.05
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17374.51
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.40
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.21
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.24
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.27
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.32
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.07
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.16
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.03
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.41
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.36
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.37
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.23
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.90
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.02
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.04
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:46.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.37
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.40
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.67
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.92
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.48
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.34
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.29
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.06
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.49
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.86
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.01
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.44
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5140.95
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.72
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.87
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.43
p-value of test                       :    0.9917


-----------------------------------------------
Normal statistic for number of jumps  :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:28.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.70
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :    1.69
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:27.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9913

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.90e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.18e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.41
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.96
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.46
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  259.43
p-value of test                       :  3.0e-3

-----------------------------------------------
CPU time used                    :  00:02:09.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.72
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:10.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9707.31
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9848.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:45.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4849.39
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4813.95
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:50.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4137.29
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.06
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11972.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11761.47
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:29.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.63
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000157183

Normal statistic for number of bits   :    1.24
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.83
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000150955

Normal statistic for number of bits   :    1.19
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:28.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.60
p-value of test                       :    0.06

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:23.73

 All tests were passed




Server wird beendet - Lösche Semaphor 177930252.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:52.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5281
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:52.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:39.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:56.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:57.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:06.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7476
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:07.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:59.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:04:04.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     636
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:13.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.24
p-value of test                       :  7.3e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:43.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.92
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.34
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.68
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:10.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.39
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.60
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.23
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:49.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1389.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:58.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7096.61
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.02
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.95
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:10.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.87
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.00
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4959.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:03.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46005
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870005
  j =  1                              :        399907994
  j =  2                              :            45997
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45911
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869911
  j =  1                              :        399908184
  j =  2                              :            45899
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:30.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:18.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:46.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:03.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:36.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:44.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.76
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.14
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.12
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.50
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.38
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.96
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:46.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.70
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:29.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.92
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:30.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  159.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17274.06
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.28
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.11
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.16
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.52
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.85
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.14
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.32
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.78
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.83
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.82
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.68
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.94
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.29
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.51
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.39
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.14
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.48
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.98
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.47
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.31
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.08
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.65
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4901.57
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  332.57
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.42
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.08
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.78
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5050.26
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.47
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.37
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.11
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :   -1.45
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:23.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.03
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:24.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.83

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.59e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 5.84e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 7.12e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:46.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.55
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.62
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.45
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:07.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  1.7e-3

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    4.12
p-value of test                       :  8.0e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  154.46
p-value of test                       :    0.9927

-----------------------------------------------
CPU time used                    :  00:02:07.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10263.30
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.96e-3
p-value of test                       :    0.9937

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.11
p-value of test                       :  8.0e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10404.90
p-value of test                       :  2.3e-3

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:04:24.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.73
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:54.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4820.11
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:54.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.08
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4201.45
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11897.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:32.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11688.22
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:31.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.44
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000145933

Normal statistic for number of bits   :    1.15
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.56
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000048442

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    0.18
p-value of test                       :    0.9958

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.32

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.50
p-value of test                       :    0.07

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:59.43

 All tests were passed




Server wird beendet - Lösche Semaphor 178946060.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:54.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5519
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:52.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:39.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:39.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:57.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:03.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:05.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7447
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:55.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:04:01.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.01
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:16.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:47.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.85
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.32
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.10
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.01
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.90
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.02
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.09
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.93
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.68
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.13
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:43.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.89
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:00.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6818.48
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:43.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.03
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:03.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.03
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.16
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:35.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5025.28
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:03.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45762
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869762
  j =  1                              :        399908480
  j =  2                              :            45754
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45599
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869599
  j =  1                              :        399908808
  j =  2                              :            45587
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:28.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:18.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:44.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9964


-----------------------------------------------
CPU time used                    :  00:02:00.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:54.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:33.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 8.71e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:38.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:40.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.85
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:48.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.92
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:54.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.85
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.38
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.81
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:43.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.77
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.54
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.58
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17407.36
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.08
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.59
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.54
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.09
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.11
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.06
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.41
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.83
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.96
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.51
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.50
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.31
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.54
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.01
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.29
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.35
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.60
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.99
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.26
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.17
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.72
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.08
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.43
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.74
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.26
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.33
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.97
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4908.67
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.03
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.28
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.62
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:25.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.48
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   -1.27
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:26.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 8.86e-3
p-value of test                       :    0.9904

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.71
p-value of test                       :    0.96

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.68e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 9.48e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:46.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.48e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.78
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.54
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.16e-3
p-value of test                       :    0.9901

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:06.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.78
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:07.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10097.85
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10316.18
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:47.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.20
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:49.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 3.02e-3
p-value of test                       :    0.9969

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4706.54
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:51.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4028.04
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4009.46
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11953.99
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11899.52
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:29.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.15
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000098068

Normal statistic for number of bits   :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.41
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000035713

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    1.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.61
p-value of test                       :    0.95

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:15.79

 All tests were passed




Server wird beendet - Lösche Semaphor 180191244.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:53.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4438
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:39.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7467
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:39.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:57.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:04.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:04.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:56.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:01.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.90
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:15.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:45.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.69
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.88
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   38.74
p-value of test                       :  3.1e-3

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.30
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.88
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.11
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.11
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:43.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.36
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:59.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6995.10
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:44.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.89
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:01.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.89
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   93.16
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:35.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5022.75
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:58.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45675
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869675
  j =  1                              :        399908652
  j =  2                              :            45671
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46135
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870135
  j =  1                              :        399907734
  j =  2                              :            46127
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:27.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:17.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:00.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:55.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 7.22e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:35.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.057
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:37.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.21
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:47.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.94
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.62
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.64
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.44
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.76
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.84
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:44.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.42
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.31
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.21
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17396.82
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:52.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.10
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.97
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.40
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.76
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.37
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.07
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.54
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.15
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.19
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.19
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.54
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.97
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.30
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.16
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.74
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.43
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.68
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.74
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.75
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.20
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.14
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.04
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.97
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.61
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.65
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.33
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.90
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.44
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.79
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.10
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  :    1.47
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:26.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.48
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :  -0.042
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:27.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.86e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 9.97e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.20e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 4.51e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.61
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.29
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:07.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.26
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:06.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10166.06
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9832.24
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:49.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4838.05
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:49.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.17
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:50.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4325.59
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3995.14
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12194.08
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:01:29.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11748.03
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:29.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.12
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000024250

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.99
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  7999985688

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 1.55e-3
p-value of test                       :    0.9984

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -2.19
p-value of test                       :    0.99

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    1.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:07.11

 All tests were passed




Server wird beendet - Lösche Semaphor 181207052.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997101
  j =  2                              :             1448
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5426
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:51.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4472
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:39.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:39.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4458
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7489
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:06.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:07.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:58.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:05.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9907

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:52.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.86
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:15.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:44.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.26
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:55.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.96
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.86
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.81
p-value of test                       :    0.9916

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.53
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.26
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.57
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.53
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.47
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  519.46
p-value of test                       :  3.0e-3

-----------------------------------------------
CPU time used                    :  00:01:48.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1505.42
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:03.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7232.86
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.18
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.31
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:08.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.70
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.65
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:36.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5087.72
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:59.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46081
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870081
  j =  1                              :        399907843
  j =  2                              :            46071
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45537
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869537
  j =  1                              :        399908928
  j =  2                              :            45533
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:29.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.37
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  9.9e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:17.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:44.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:00.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:36.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 5.61e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 3.07e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.094
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:42.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.41
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.39
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.81
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.76
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.18
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.50
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.78
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:44.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.45
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.16
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.89
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.91
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:39.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17532.96
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:55.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.99
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.05
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.76
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.22
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.17
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.49
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.73
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.91
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   47.92
p-value of test                       :  2.6e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.42
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:37.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.03
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.33
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.01
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.34
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.59
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.85
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.49
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.63
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.27
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.06
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.26
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5078.91
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.88
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.02
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.74
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.64
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.18
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.55
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.34
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.48
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :    2.02
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:24.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.43
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :   -0.82
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:26.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.73e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:46.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.96e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.01
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.06
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.73
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:08.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.39
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:07.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10037.75
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9950.80
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:04:14.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4911.20
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:52.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4740.42
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:53.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.97
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4183.99
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12290.15
p-value of test                       :  1.4e-3

-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11844.87
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:30.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.72
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000065443

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.11
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000041413

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.46
p-value of test                       :  6.9e-3

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:33.02

 All tests were passed




Server wird beendet - Lösche Semaphor 182222860.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5296
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:52.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:40.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:39.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:57.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:04.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:05.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:55.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7175
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:02.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.84
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    2.08
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     938
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.61
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:14.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:42.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.33
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.97
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.98
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.18
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.07
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   82.63
p-value of test                       :  7.3e-3

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.85
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.81
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.97
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  392.02
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:44.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1403.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:01.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7218.41
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.41
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.65
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:02.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.83
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.13
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:34.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5242.28
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:02.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45850
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869850
  j =  1                              :        399908303
  j =  2                              :            45844
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46014
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870014
  j =  1                              :        399907975
  j =  2                              :            46008
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:28.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:18.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:59.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:55.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 8.20e-3
p-value of test                       :    0.9904

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:35.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.04e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.36
p-value of test                       :    0.9908

-----------------------------------------------
CPU time used                    :  00:01:37.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:38.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.07
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.37
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.50
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.71
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:48.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.16
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.10
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:45.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.58
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.09
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.01
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.87
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17498.47
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.32
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.46
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.02
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.06
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.85
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.12
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.33
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.07
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.42
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.10
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.15
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  108.71
p-value of test                       :    0.9909


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.20
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.22
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.74
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  196.38
p-value of test                       :  3.4e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.34
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.96
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.95
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.66
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.36
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.55
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5019.19
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  435.37
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.54
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.64
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.06
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.39
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.15
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.67
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.85
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :   -1.18
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:26.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.95
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :   -0.37
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:28.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 6.75e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.48e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 9.36e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.69
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.04
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:07.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.25
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:06.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9905.87
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9867.11
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:41.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.00
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:48.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4794.21
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:50.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4207.73
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.21
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11551.98
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11612.95
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.37
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000041335

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.68
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999919433

Normal statistic for number of bits   :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:26.18

 All tests were passed




Server wird beendet - Lösche Semaphor 183271436.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5381
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:55.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4415
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:42.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4222
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:59.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:00.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:10.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:10.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:07.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7191
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:04:11.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.83
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     559
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.39
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:15.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    2.46
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:41.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.41
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.72
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.43
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.18
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.02
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.07
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.55
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:29.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  389.93
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:56.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:02.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6868.94
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.02
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.77
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:18.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.33
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.81
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4950.51
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:02.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45858
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869858
  j =  1                              :        399908287
  j =  2                              :            45852
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45710
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869710
  j =  1                              :        399908583
  j =  2                              :            45704
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:32.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:21.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:53.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:08.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:56.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:38.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.61e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 5.36e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.69
p-value of test                       :  3.6e-3

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.072
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:47.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:47.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.26
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.53
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.67
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.97
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.46
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:51.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.47
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.50
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.50
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.78
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17455.15
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.30
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.53
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.75
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.46
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.70
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.47
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.88
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.41
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.77
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.09
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.19
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.34
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.96
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.21
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.88
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :   98.71
p-value of test                       :    0.9990    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.58
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.60
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.56
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.93
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.98
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.34
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4901.77
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.78
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.70
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.61
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.91
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4988.63
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.05
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.61
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.20
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:23.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.61
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:24.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.092
p-value of test                       :    0.54

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 5.20e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.18
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.79
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.16
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:06.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.14
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:07.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10101.46
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10131.25
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:10.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:04:28.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:56.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4694.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:59.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3976.44
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.12
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11902.46
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:35.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11995.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:36.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.97
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999931397

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.18
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000030670

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.83
p-value of test                       :    0.03

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:05.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 77  RandomWalk1 H (L=1000, r=20)    0.9990 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 184254476.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:48.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1467
p-value of test                       :  3.1e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334587
  j =  1                              :        599997066
  j =  2                              :             1467
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1465
p-value of test                       :  3.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334585
  j =  1                              :        599997070
  j =  2                              :             1465
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5346
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:55.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:40.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4447
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:57.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:05.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7116
p-value of test                       :    0.9911


-----------------------------------------------
CPU time used                    :  00:03:05.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:56.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:00.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:47.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.23
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.68
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:13.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:44.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   18.35
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:54.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.96
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.14
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.73
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.83
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.57
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.90
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.99
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:44.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.30
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:00.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6954.38
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:43.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.64
p-value of test                       :  7.5e-3

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.09
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.50
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:03.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.26
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:46.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.98
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:34.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5127.91
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:55.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45722
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869722
  j =  1                              :        399908561
  j =  2                              :            45712
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45694
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869694
  j =  1                              :        399908618
  j =  2                              :            45682
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:28.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:19.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:44.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:59.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:37.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 5.29e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.16e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:41.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:38.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.27
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:49.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.92
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.21
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.50
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.69
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.07
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:45.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.27
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.43
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.09
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.52
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17321.16
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.18
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.15
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.66
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.31
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.09
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.60
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.45
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.75
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.96
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.76
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.54
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.64
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.67
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.07
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.76
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.89
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.39
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.34
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.23
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.33
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.89
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.54
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5138.94
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.44
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.08
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.91
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.00
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5113.66
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.57
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.88
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.15
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :   -1.91
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:22.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.26
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:24.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.06
p-value of test                       :    0.02

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 3.28e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 3.26e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.38
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.06
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.54
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:07.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.46
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:07.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9871.23
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9981.05
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:57.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.97
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:48.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4794.39
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.08
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.86
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11673.48
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11773.73
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:29.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.55
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  8000084127

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.63
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000032797

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:10.05

 All tests were passed




Server wird beendet - Lösche Semaphor 185335820.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:48.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997197
  j =  2                              :             1400
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5449
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:55.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7581
p-value of test                       :  1.2e-3


-----------------------------------------------
CPU time used                    :  00:02:41.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4427
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:57.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:58.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:05.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:06.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7130
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:57.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:04:02.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    2.13
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    4.26
p-value of test                       :  6.5e-3

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:13.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:43.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.83
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.94
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.62
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.12
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.10
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.98
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.45
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.92
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.73
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  466.37
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:43.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1410.32
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:59.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6990.37
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.61
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:04.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.24
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.19
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:32.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5044.20
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:54.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45948
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869948
  j =  1                              :        399908111
  j =  2                              :            45934
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46083
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870083
  j =  1                              :        399907837
  j =  2                              :            46077
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:27.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:18.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:45.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:58.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:36.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.74e-4
p-value of test                       :  3.7e-3

Kolmogorov-Smirnov- statistic = D-    : 1.53e-6
p-value of test                       : 1 -  9.4e-5    *****

Anderson-Darling statistic = A2       :    6.49
p-value of test                       :  5.9e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:35.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:34.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.23
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.99
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.85
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.28
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:51.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.13
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:40.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.18
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.86
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.84
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17567.00
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.25
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.39
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.50
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.27
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.78
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.80
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.39
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.27
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.85
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.20
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.40
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.16
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  415.88
p-value of test                       :    0.9975


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.78
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.76
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.41
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.86
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.30
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.09
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.49
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.08
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.32
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5154.83
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.37
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.01
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.03
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.80
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.21
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.69
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.50
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:34.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.97
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :   -0.94
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:23.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.60
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   0.097
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:23.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   0.038
p-value of test                       :    0.48

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 6.12e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.28e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.54
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.80
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.10
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:05.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.77
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:07.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9816.14
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10042.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:47.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4946.87
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:47.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.57
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:49.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.37
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3899.80
p-value of test                       :    0.9924

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11559.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11844.34
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.62
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000019453

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.14
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999817622

Normal statistic for number of bits   :   -1.44
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.43

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.70
p-value of test                       :    0.04

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:21.28
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 54  SampleMean, r = 10              5.9e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 186384396.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5366
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:54.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4442
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4509
p-value of test                       :  4.8e-3


-----------------------------------------------
CPU time used                    :  00:01:59.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:05.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:06.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:56.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:01.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.68
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:14.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:39.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.72
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.01
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.41
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.52
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.13
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.70
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.76
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.42
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.16
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:44.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1427.20
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:00.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7140.65
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:41.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.60
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.65
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:03.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.79
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.09
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:33.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4876.39
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:58.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45334
p-value of test                       :    0.9946


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869334
  j =  1                              :        399909336
  j =  2                              :            45326
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45957
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869957
  j =  1                              :        399908092
  j =  2                              :            45945
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:27.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:17.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:45.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:59.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.47e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 7.94e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:24.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:39.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:37.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.39
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:49.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.53
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.13
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.05
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.19
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.67
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.22
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:43.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.30
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.25
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.30
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17240.62
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.23
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.82
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.89
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.20
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.29
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.96
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.58
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.83
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.05
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.11
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:38.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.47
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.81
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.13
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.10
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.89
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.74
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.21
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.02
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.70
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.04
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.64
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.47
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4905.44
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.20
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.51
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.01
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.29
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4941.33
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.02
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.13
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.57
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:24.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.66
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :   -1.76
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:23.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.93e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.98e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 7.99e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.07
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.98
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.15
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:06.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.08
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:07.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9944.95
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9801.99
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:47.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4989.13
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4967.48
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:49.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.31
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.10
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11948.77
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:28.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11858.44
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:29.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.68
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000079699

Normal statistic for number of bits   :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.18
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999970016

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9904

Tests on the sum of all N observations
Standardized normal statistic         :   0.052
p-value of test                       :    0.48

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:47.73

 All tests were passed




Server wird beendet - Lösche Semaphor 187367436.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:48.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5486
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:55.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:40.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:57.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:06.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:06.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:00.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:01.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    2.13
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     960
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.15
p-value of test                       :    0.9989

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.46
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     632
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.73
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:13.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:41.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.67
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.51
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.19
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.35
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:11.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.60
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.05
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.76
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:43.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1349.21
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:04.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7058.97
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:43.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.68
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.38
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:03.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.96
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.45
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:33.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5012.82
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:57.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45619
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869619
  j =  1                              :        399908762
  j =  2                              :            45619
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46096
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870096
  j =  1                              :        399907808
  j =  2                              :            46096
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:27.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:19.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:46.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:01.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 5.41e-3
p-value of test                       :    0.9933

Anderson-Darling statistic = A2       :    3.63
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:56.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:35.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.79e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 3.76e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 7.64e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:24.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.14
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:38.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.71
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:50.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.18
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.73
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.20
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   45.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.76
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.05
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.54
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17409.64
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.33
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.52
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.80
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.78
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.14
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.68
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.73
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.79
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.83
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.74
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.94
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.06
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.43
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.83
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.56
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.69
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.45
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.40
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.91
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.91
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.11
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.22
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.06
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.91
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.43
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.27
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.55
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4896.71
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.08
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.98
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.14
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:21.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.92
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:22.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 9.74e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 6.56e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.57
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.99
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:03.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.71
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:06.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10070.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9995.84
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:37.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4985.82
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4778.77
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:32.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.87
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4233.01
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11912.10
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11681.48
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.79
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999931811

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.15
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999985241

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.66
p-value of test                       :    0.05

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:00:41.13

 All tests were passed




Server wird beendet - Lösche Semaphor 188416012.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:48.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5501
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:42.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4459
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:36.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:36.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4226
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7178
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:02.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:02.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:54.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:59.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.63
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    2.37
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:52.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.36
p-value of test                       :  2.1e-3

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:11.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.09
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:36.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.95
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.83
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.33
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.80
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.10
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.46
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.09
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.69
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.70
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.62
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:50.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1403.98
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:00.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7270.51
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.05e-3
p-value of test                       :    0.9959

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   48.80
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.97
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:01.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.10
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.99
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:37.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5006.37
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:19.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45729
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869729
  j =  1                              :        399908544
  j =  2                              :            45725
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45756
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869756
  j =  1                              :        399908494
  j =  2                              :            45744
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:29.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:18.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:45.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:00.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:52.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.63e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 3.94e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.46e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 2.31e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:38.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:39.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:48.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.13
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.27
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.61
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.91
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:43.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.00
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.58
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:32.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:30.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.87
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9939

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17433.02
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.17
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.70
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.30
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.41
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.22
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:40.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.34
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.58
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.14
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.99
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.98
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:40.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.16
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.65
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  576.02
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.90
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.95
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:48.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.94
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.10
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.69
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.93
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.56
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.90
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.68
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.92
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.28
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.40
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.38
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.26
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4926.39
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.23
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.92
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:34.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.26
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:14.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.74
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :   -0.11
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:12.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:11.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.69e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:46.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.81e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 8.14e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.57
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.97
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.63
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:13.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  244.57
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:10.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9756.82
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9778.07
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:04:01.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4844.88
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:48.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4931.20
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:50.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.98
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3846.12
p-value of test                       :    0.9988

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11986.68
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11801.88
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:30.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.24
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999943163

Normal statistic for number of bits   :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.93
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999971006

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:10.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.80

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:17:26.21

 All tests were passed




Server wird beendet - Lösche Semaphor 168329229.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5425
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:44.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:37.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:36.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:53.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:55.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:02.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:02.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7181
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:55.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:58.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.61
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.44
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    4.59
p-value of test                       :  4.5e-3

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:10.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    3.79
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     182
p-value of test                       :  6.2e-3

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:39.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.27
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.20
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.82
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.15
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.84
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.29
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.55
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.71
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:47.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1434.78
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:06.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7334.46
p-value of test                       :  8.1e-3

-----------------------------------------------
CPU time used                    :  00:01:47.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.21
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:07.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.34
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.94
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:39.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4887.95
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:20.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45810
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869810
  j =  1                              :        399908381
  j =  2                              :            45808
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46140
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870140
  j =  1                              :        399907723
  j =  2                              :            46134
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:30.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:16.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :  2.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:44.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:59.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:54.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:34.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 4.98e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 8.88e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9950

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.039
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.19
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.22
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.61
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.88
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.23
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.76
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.27
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:29.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:32.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.43
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  2.1e-3

Anderson-Darling statistic = A2       :    4.44
p-value of test                       :  5.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17906.03
p-value of test                       :  5.7e-3



-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.60
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.00
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.61
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.05
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.48
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.81
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.93
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.62
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.28
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.53
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.86
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.60
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.23
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.43
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.58
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.14
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.48
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.40
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.37
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.27
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.39
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.42
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4917.71
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.95
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.90
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:34.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.66
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.55
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4852.09
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.80
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.17
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:34.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.20
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:30.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.41
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:32.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
p-value of test                       :    0.9998    *****

Anderson-Darling statistic = A2       :    3.86
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.92
p-value of test                       :    0.9982

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.78
p-value of test                       :    0.04

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 8.52e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.94
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.95
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9924

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.46
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:11.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.75
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:08.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9926.64
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10007.19
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:04:18.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:51.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4720.01
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:51.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4031.32
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3801.66
p-value of test                       :    0.9998    *****

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11812.97
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:31.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11893.79
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:32.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.77
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000007639

Normal statistic for number of bits   :   0.060
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.12
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000196765

Normal statistic for number of bits   :    1.56
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.082
p-value of test                       :    0.47

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.13
p-value of test                       :    0.98

Sample variance                       :    1.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:12:19.67
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 98  HammingIndep, L=300, r=26       0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 169508877.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1472
p-value of test                       :  2.0e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334592
  j =  1                              :        599997056
  j =  2                              :             1472
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:48.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4172
p-value of test                       :    0.9939


-----------------------------------------------
CPU time used                    :  00:01:38.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:37.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:55.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:56.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:05.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:05.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:58.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:01.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     641
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    2.15
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:16.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.53
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:46.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.66
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.99
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.29
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.25
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.33
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.30
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.83
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.85
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.40
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:46.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.22
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:01.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7078.88
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.66
p-value of test                       :  6.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.43
p-value of test                       :  5.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   14.24
p-value of test                       :    0.9934

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.28
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:13.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.48
p-value of test                       :    0.9929


-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.33
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:39.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4999.02
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:09.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45503
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869503
  j =  1                              :        399908996
  j =  2                              :            45499
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45972
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869972
  j =  1                              :        399908058
  j =  2                              :            45968
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:30.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:18.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.45e-3
p-value of test                       :    0.9952

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:43.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:00.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:56.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.32e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 6.75e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:44.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:44.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.17
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.96
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.20
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.72
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.37
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:48.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.97
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.37
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:29.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:10.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.93
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17174.54
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.73
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.86
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.85
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.80
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.22
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.75
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.87
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.06
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.15
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.25
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.85
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.20
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  442.98
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.69
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.71
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.33
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.48
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.19
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.66
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.53
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.57
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.94
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4972.04
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.97
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.84
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:36.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.98
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.08
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.43
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.57
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.28
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.71
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :  -0.064
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:28.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.04
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :   -1.19
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:25.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.51
p-value of test                       :    0.07

Sample variance                       :    0.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 8.20e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 6.27e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.72
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.11
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.40
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:08.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:09.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9923.64
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9863.26
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:04:24.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4931.05
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:53.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5055.22
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:57.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4353.41
p-value of test                       :  5.2e-3

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4141.56
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11607.65
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:32.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11713.82
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:32.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.68
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999966884

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.20
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000106180

Normal statistic for number of bits   :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.01
p-value of test                       :    0.02

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.69
p-value of test                       :    0.05

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:12:29.89

 All tests were passed




Server wird beendet - Lösche Semaphor 170590221.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5248
p-value of test                       :    0.9907


-----------------------------------------------
CPU time used                    :  00:03:50.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:39.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:39.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:57.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4463
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:07.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:07.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7144
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:04:05.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:04:12.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.57
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:15.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:43.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.66
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.69
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.02
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.57
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.26
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.64
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.84
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.99
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.24
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:29.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.65
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:57.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1391.30
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:03.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7044.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.90
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.68
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:19.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.49
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.67
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:40.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5016.73
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:00.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45881
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869881
  j =  1                              :        399908240
  j =  2                              :            45877
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45940
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869940
  j =  1                              :        399908122
  j =  2                              :            45936
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:31.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:18.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:04.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:57.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:38.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 7.36e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 5.37e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:24.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.45
p-value of test                       :  7.2e-3

-----------------------------------------------
CPU time used                    :  00:00:24.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.94
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:24.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:48.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:49.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.27
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.06
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.43
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.00
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.18
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.22
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.01
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:50.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.95
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.84
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:29.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.04
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17397.35
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.28
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.92
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.97
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.10
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.79
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.20
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.29
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.53
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.15
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.29
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.68
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.15
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.61
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.47
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.71
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.40
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.94
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  448.52
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.53
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.96
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.69
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.29
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.23
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.19
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.96
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.89
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.93
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5053.20
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  436.88
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.38
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.75
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :    1.06
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:28.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.45
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:27.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   0.049
p-value of test                       :    0.48

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 6.33e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.17e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.13
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.63
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.18
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:06.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.63
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:07.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9952.99
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9842.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:12.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:04:28.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5015.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4730.51
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:59.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4008.31
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.94
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12105.09
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:34.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11654.64
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:35.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.83
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999973070

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.07
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000017230

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :  -0.077
p-value of test                       :    0.53

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 8.16e-4
p-value of test                       :    0.9992    *****

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.74
p-value of test                       :    0.96

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:11:59.31

 All tests were passed




Server wird beendet - Lösche Semaphor 171769869.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997169
  j =  2                              :             1414
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5329
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:51.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:39.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:39.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4211
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:57.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:05.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:05.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:56.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:04:01.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:48.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:15.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.72
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:42.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.69
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.91
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.69
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.39
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.65
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.92
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.34
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.23
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.88
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:42.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1397.16
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:00.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6994.41
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.80
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.66
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:02.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.85
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.78
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:34.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5108.53
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:59.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46332
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870332
  j =  1                              :        399907337
  j =  2                              :            46330
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45517
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869517
  j =  1                              :        399908969
  j =  2                              :            45511
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9909


-----------------------------------------------
CPU time used                    :  00:02:28.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:18.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.94
p-value of test                       :  9.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9960


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:01.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:54.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:34.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 7.56e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.63e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.77
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:35.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:35.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.82
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.74
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.38
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.55
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.24
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.38
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.79
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:42.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.87
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.00
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.71
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.79
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17501.82
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.40
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.64
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.50
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.64
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.61
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   71.32
p-value of test                       :  4.1e-4    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.81
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.19
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.22
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.12
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.17
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.73
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.13
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.34
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.19
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.76
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.37
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.24
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.62
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   46.79
p-value of test                       :    0.9944


-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.98
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.13
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.81
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.47
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.26
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.47
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.76
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4924.22
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.43
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.24
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.21
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:24.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.13
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    1.72
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:26.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.9e-3

Anderson-Darling statistic = A2       :    4.19
p-value of test                       :  7.4e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.42
p-value of test                       :  7.8e-3

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 8.69e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:47.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.60e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.28
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.92
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.22
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:06.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.23
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:09.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9850.99
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  2.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.96
p-value of test                       :  3.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9607.38
p-value of test                       :    0.9975

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:47.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4961.88
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:49.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4895.87
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:51.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.06
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4035.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11933.17
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11704.56
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.49
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000046648

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.59
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000089515

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.96e-3
p-value of test                       :    0.9970

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.92
p-value of test                       :    0.03

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:57.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 75  RandomWalk1 H (L=50, r=25)      4.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 172982285.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:43.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5341
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:51.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:39.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:39.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4213
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7149
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:03.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7180
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:04.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:55.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:00.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    3.67
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.08
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    2.11
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     567
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:14.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.85
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:44.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.56
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.67
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.55
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.06
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.00
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.93
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.21
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.21
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.36
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.84
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:44.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1321.83
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:00.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6990.85
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:45.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:15.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.66
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:02.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.99
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.00
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:34.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5078.92
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:00.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45852
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869852
  j =  1                              :        399908296
  j =  2                              :            45852
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46494
p-value of test                       :  2.1e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870494
  j =  1                              :        399907015
  j =  2                              :            46488
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 6.75e-3
p-value of test                       :    0.9912

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:28.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:17.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:44.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:58.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:54.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:34.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.61e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.57e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 6.87e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:35.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.90
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:48.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.45
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.41
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.42
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.72
p-value of test                       :    0.9946

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.52
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.06
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.82
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.18
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.92
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:29.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.40
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17459.51
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.96
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.16
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.48
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.28
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.46
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.31
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.80
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.09
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.10
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.07
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.53
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.90
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  568.70
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.34
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.89
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.38
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.41
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.36
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.02
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.03
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.68
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.67
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5044.52
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.54
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.90
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.84
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.15
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5138.37
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.59
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.51
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.61
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:26.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.36
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:29.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.90e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:46.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.26e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 9.86e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.95
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.42
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.95
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:08.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.48
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:08.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9779.22
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10138.96
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:59.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5038.67
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4789.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:51.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4192.74
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.88
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11817.18
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11830.28
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   88.18
p-value of test                       :  2.3e-3


-----------------------------------------------
Total number of bits:  7999830987

Normal statistic for number of bits   :   -1.34
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.78
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999931541

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:12.14

 All tests were passed




Server wird beendet - Lösche Semaphor 173899789.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1253
p-value of test                       :    0.9988

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334373
  j =  1                              :        599997494
  j =  2                              :             1253
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5390
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:51.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:39.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7474
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:39.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:57.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:04.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7193
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:05.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:55.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:01.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.73
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     954
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.13
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.65
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    2.38
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     267
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:16.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:45.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.86
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.29
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.07
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.51
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.42
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.29
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  195.03
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.63
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:43.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1469.81
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:57.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6860.20
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:42.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.28
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.55
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:01.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.52
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.14
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:34.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5132.62
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:05.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45974
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869974
  j =  1                              :        399908053
  j =  2                              :            45972
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45842
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869842
  j =  1                              :        399908319
  j =  2                              :            45836
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:28.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:18.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:45.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9990    *****

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:00.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:55.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:33.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.68e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:35.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:35.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.18
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.20
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.32
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.85
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.14
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.19
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.79
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:41.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.19
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.48
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.03
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17340.08
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.46
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.27
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.30
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.78
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.86
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.44
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.46
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.17
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.66
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.03
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.63
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.93
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.97
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.47
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.89
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  551.44
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.18
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.19
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.59
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.18
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.91
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.45
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.23
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.23
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.54
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5102.53
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.48
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.54
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.74
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:24.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.51
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :   -1.36
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:27.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.83

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.84e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 7.34e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:47.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.35
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.61
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.00
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:07.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.24
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:07.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10145.81
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9784.82
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:46.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4818.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:00.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.70
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:01.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.45
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11732.00
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:29.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12071.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:30.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.73
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  7999980009

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.22
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999933980

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.48
p-value of test                       :    0.07

Sample variance                       :    2.29
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:23.70

 All tests were passed




Server wird beendet - Lösche Semaphor 174850061.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  3.8e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5371
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:50.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4440
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:39.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:39.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4235
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:04.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:04.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:55.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:00.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.39
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:47.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    5.01
p-value of test                       :  2.8e-3

Stat. AD after spacings (mNP2-S)      :    3.59
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.59
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:13.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    2.13
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:43.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.35
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.41
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.76
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.60
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.44
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.42
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.38
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.55
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  391.81
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:44.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1546.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:00.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6998.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.44
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.61
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:01.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.35
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.33
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:34.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4882.61
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:04.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46045
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870045
  j =  1                              :        399907915
  j =  2                              :            46035
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45677
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869677
  j =  1                              :        399908646
  j =  2                              :            45677
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:29.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:18.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:45.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:00.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:55.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:33.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.69e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.35e-5
p-value of test                       :    0.9928

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.06e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:34.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.021
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:35.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.91
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.93
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:48.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.29
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.39
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.06
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:43.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.56
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.19
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.40
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.60
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17649.99
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.26
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.82
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.02
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.01
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.33
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.03
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.53
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.18
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.52
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.11
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.28
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.56
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.02
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.54
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.10
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.28
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.04
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.11
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.62
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.44
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.30
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.22
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4940.22
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.14
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.18
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.39
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.18
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5153.45
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.34
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.57
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.46
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:24.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.64
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:26.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.34e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:47.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.00e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 7.38e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.72
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.35
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.20
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:07.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.17
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:07.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9909.72
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9869.39
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:54.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4867.38
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:48.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4920.13
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:50.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4508.10
p-value of test                       :  1.4e-5    *****

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4313.42
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11929.72
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11676.99
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:30.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.64
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000057157

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.10
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999944441

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.18
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:45.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  2  SerialOver, r = 22              3.8e-4
 97  HammingIndep, L=300, r=0        1.4e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 175865869.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:40.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5405
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:52.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:40.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:39.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:55.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7145
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:03.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:04.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:55.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:00.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.28
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.66
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     635
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:13.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:43.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.51
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.55
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.07
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.57
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.82
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.06
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  262.55
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.25
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:42.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1376.79
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:00.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7080.79
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:41.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.94
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:02.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.52
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  148.06
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:34.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4990.65
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9937


-----------------------------------------------
CPU time used                    :  00:03:08.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45922
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869922
  j =  1                              :        399908161
  j =  2                              :            45912
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45820
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869820
  j =  1                              :        399908361
  j =  2                              :            45818
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:28.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:17.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:44.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:59.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:55.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.07e-3
p-value of test                       :    0.9956

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:33.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 8.50e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.029
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:34.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:39.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.20
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.04
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.73
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.25
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.76
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.73
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:40.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.22
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.45
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17420.77
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.13
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.24
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.79
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.04
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.58
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.74
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.89
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.51
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.54
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.14
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.97
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.60
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.96
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.88
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.93
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.21
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.43
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.77
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.90
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.45
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.54
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  320.23
p-value of test                       :    0.9922


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.77
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.33
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.60
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.47
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.89
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4978.41
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.90
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.14
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.00
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :   -3.36
p-value of test                       :    0.9996    *****



-----------------------------------------------
CPU time used                    :  00:02:26.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.88
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :   -0.92
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:25.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.78

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 7.96e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.43e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 6.27e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.82
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.15
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.34
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:06.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:07.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9891.60
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10006.35
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.075
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:51.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4782.90
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:49.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.71
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:51.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.79
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4057.42
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11518.48
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:28.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11589.66
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.53
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000077419

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.35
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000029329

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:47.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0               0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 176783373.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5436
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:52.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:40.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:39.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4226
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:55.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:03.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:04.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:54.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:04:01.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:46.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     564
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:13.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.98
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:37.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.96
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.29
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.00
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.94
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.87
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  478.89
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:43.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1367.11
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:01.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7100.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.03
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.10
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:02.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.66
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.09
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:35.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4863.49
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:56.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45907
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869907
  j =  1                              :        399908187
  j =  2                              :            45905
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46042
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870042
  j =  1                              :        399907919
  j =  2                              :            46036
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:29.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:18.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:44.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:59.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:55.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:34.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 9.13e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:22.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.96e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:21.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:33.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:34.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.61
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.58
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.55
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.27
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.07
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.56
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.72
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.49
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:28.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.85
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17478.57
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.36
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.72
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.79
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   56.40
p-value of test                       :  2.0e-4    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.34
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.74
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.78
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.50
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.22
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.06
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.05
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.05
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.60
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.54
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.99
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.33
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.23
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.53
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.36
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  100.44
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.62
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.89
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5167.03
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.42
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.63
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.27
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.05
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.34
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  331.37
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.66
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.07
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:28.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.36
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :    0.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:26.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.85e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 9.38e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.24e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 5.48e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.04
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.01
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:07.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:06.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10305.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9777.36
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:04:05.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :  1.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    5.01
p-value of test                       :  3.0e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4606.86
p-value of test                       :    0.9982

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.15
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:50.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.53
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4222.96
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11742.50
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11900.96
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:29.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.32
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999992639

Normal statistic for number of bits   :  -0.058
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.07
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000120925

Normal statistic for number of bits   :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.25e-3
p-value of test                       :    0.9911

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.37
p-value of test                       :  9.0e-3

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:42.18
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 R (L=50, r=0)       2.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 177766413.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5370
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:52.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:39.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:55.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:56.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:03.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:03.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:53.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:59.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     841
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.19
p-value of test                       :    0.9919

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:14.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:42.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.26
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.42
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.94
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.76
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.82
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.31
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.83
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.82
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.75
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  492.71
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:43.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.24
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:59.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7042.52
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   14.58
p-value of test                       :    0.9919

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.10
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:01.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.57
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.75
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:34.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4915.19
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:03.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45611
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869611
  j =  1                              :        399908782
  j =  2                              :            45603
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45971
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869971
  j =  1                              :        399908062
  j =  2                              :            45963
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:29.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:18.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 1.91e-3
p-value of test                       :    0.9980

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:45.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.12
p-value of test                       :    0.9998    *****


-----------------------------------------------
CPU time used                    :  00:02:00.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:55.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:15.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:33.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.31e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.96e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.72e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:21.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:21.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:33.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.83
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:48.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.63
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.11
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.64
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.14
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.72
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.01
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.21
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.75
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17635.97
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.59
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.25
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.79
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.23
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.59
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.42
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.36
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.92
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.33
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.79
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.42
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.44
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.40
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.51
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.44
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.71
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.41
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.70
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.41
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.90
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.65
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.93
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5165.38
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.02
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.44
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.98
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.11
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4866.31
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.03
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.79
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.65
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:24.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.50
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:24.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 4.11e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 5.98e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.23
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.26
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:07.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.38
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:08.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10034.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10018.62
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    3.11
p-value of test                       :  9.4e-4    *****

-----------------------------------------------
CPU time used                    :  00:04:03.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.72
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:49.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4843.17
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:51.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.75
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.45
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11870.92
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:29.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11783.79
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.54
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999951932

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.73
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999893765

Normal statistic for number of bits   :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.14
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:54.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 49  MaxOft AD, t = 32               0.9998 
 94  HammingCorr, L = 1200           9.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 178683917.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  1.1e-3


-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:50.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1272
p-value of test                       :    0.9939

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334392
  j =  1                              :        599997456
  j =  2                              :             1272
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5506
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:52.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:40.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:39.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:04.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:04.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:53.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7519
p-value of test                       :  9.9e-3


-----------------------------------------------
CPU time used                    :  00:03:59.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.53
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    2.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:03.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.19
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:15.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:42.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.95
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.99
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.88
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.30
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.23
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.40
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.64
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.74
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:44.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.53
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:01.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7067.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:43.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.71
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:03.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.93
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.02
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:35.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5068.12
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:55.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46116
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870116
  j =  1                              :        399907770
  j =  2                              :            46112
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45896
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869896
  j =  1                              :        399908211
  j =  2                              :            45890
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:33.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:26.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:51.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:06.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:56.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:35.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.62e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 7.72e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:35.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.93
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.72
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.66
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.02
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.45
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.07
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.73
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.09
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.62
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:29.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   99.47
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17504.82
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.74
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.46
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.87
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.54
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.27
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.69
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.78
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.08
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.29
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.77
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  202.15
p-value of test                       :  1.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.62
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.96
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.70
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.70
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.77
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.19
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  567.84
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.58
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.66
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.92
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.64
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5071.57
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.18
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.47
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.86
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.52
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5102.70
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.95
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.16
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.14
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :    1.68
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:24.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.55
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:24.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.63e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 7.58e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.24
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.48
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.30
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:08.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.88
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:08.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9884.89
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9885.44
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:11.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:04:31.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.01
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:49.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.16
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:50.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.73
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3944.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11623.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11713.66
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.74
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000168535

Normal statistic for number of bits   :    1.33
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.73
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000183991

Normal statistic for number of bits   :    1.45
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.09

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:30.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:17.97

 All tests were passed




Server wird beendet - Lösche Semaphor 179732493.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1257
p-value of test                       :    0.9983

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334377
  j =  1                              :        599997486
  j =  2                              :             1257
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5538
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:55.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:40.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:39.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:57.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:05.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:04.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:56.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:59.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.49
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    2.14
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:13.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    3.39
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:45.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.03
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.27
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.32
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.26
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.85
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.20
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.46
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.87
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.46
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.62
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:06.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6953.66
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.75
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:06.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.19
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.72
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:36.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5111.77
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:56.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45927
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869927
  j =  1                              :        399908151
  j =  2                              :            45917
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46027
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870027
  j =  1                              :        399907951
  j =  2                              :            46017
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.12
p-value of test                       :    0.9998    *****


-----------------------------------------------
CPU time used                    :  00:02:30.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:17.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:02.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:36.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.49e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:39.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.040
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:40.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.25
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.66
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.67
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:51.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.49
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:55.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.42
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:44.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.74
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.34
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.81
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:17.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.70
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17647.80
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.66
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.95
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.77
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.14
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.60
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.55
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.59
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.57
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.56
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.58
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.19
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.01
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.01
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.49
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.86
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.17
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.40
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.87
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.84
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.00
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.43
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.05
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4884.48
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.79
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.44
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.31
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.58
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5123.39
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.38
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.30
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.18
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :    2.14
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:25.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.37
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   -1.67
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:24.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 8.96e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.30e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 8.97e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.88
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.86
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.67
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:04.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.47
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:07.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9801.55
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9964.77
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:04:18.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5040.10
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:51.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:53.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3901.56
p-value of test                       :    0.9920

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.39
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11507.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:30.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11906.04
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:31.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.10
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000017137

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.10
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999723566

Normal statistic for number of bits   :   -2.19
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:10.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:39.93
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 46  MaxOft AD, t = 8                0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 180781069.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:39.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1274
p-value of test                       :    0.9929

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334394
  j =  1                              :        599997452
  j =  2                              :             1274
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5381
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:53.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:56.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:03.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:03.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:54.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:04:00.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.86
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.94
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    8.35
p-value of test                       :  8.2e-5    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     985
p-value of test                       :  2.7e-3

Stat. AD (mNP2)                       :    6.39
p-value of test                       :  6.5e-4    *****

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     567
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    4.24
p-value of test                       :  6.7e-3

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.84
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    5.73
p-value of test                       :  1.3e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     350
p-value of test                       :  2.6e-3

Stat. AD (mNP2)                       :    2.40
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:12.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:44.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.91
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.09
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:10.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.05
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.27
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.88
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.81
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.07
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:44.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.51
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6768.22
p-value of test                       :    0.9910

-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.98
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:02.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.06
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.08
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:33.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4867.93
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:00.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45633
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869633
  j =  1                              :        399908737
  j =  2                              :            45627
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45937
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869937
  j =  1                              :        399908129
  j =  2                              :            45931
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :  6.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:29.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 4.10e-3
p-value of test                       :    0.9954

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:18.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:45.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:01.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:55.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:33.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:32.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:33.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.45
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:48.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.71
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.82
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.00
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.18
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:51.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.17
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:37.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.85
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.39
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.06
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.15
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.55
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17132.15
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.07
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.21
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.18
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.50
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.66
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.31
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.19
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.08
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.36
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.94
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.33
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  189.84
p-value of test                       :  8.6e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.92
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  167.96
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.48
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.89
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.11
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.23
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.11
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.11
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.78
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.33
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.26
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.35
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.46
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.02
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.30
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.86
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.66
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.21
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.58
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:27.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.93
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :    1.49
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:25.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.71

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.84
p-value of test                       :    0.03

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.28e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 7.83e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:46.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 5.05e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.19
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.35
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.89
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:05.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.07
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:08.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9877.21
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10051.84
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:03:44.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4744.62
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4821.05
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:51.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4018.00
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4016.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11952.81
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11786.14
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:29.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.68
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  7999966110

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.25
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999943343

Normal statistic for number of bits   :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.62
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.22
p-value of test                       :    0.99

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:07.86
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP1, t = 3          8.2e-5
 22  ClosePairs mNP2, t = 3          6.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 181895181.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:50.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5307
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:53.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:41.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:58.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:05.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:05.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:54.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:04:01.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:47.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     641
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.16
p-value of test                       :    0.9981

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.95
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    2.58
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     264
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:15.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.14
p-value of test                       :    0.9992    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:44.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.28
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.15
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.64
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.46
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.43
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.59
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.49
p-value of test                       :    0.9910

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.67
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.11
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:42.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1494.78
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:01.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7224.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.97
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.57
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:04.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.00
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.79
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:33.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5002.45
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:00.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45696
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869696
  j =  1                              :        399908610
  j =  2                              :            45692
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45924
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869924
  j =  1                              :        399908155
  j =  2                              :            45918
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:29.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:18.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:44.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:59.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:34.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 3.85e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:33.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    3.17
p-value of test                       :  7.5e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:32.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.05
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:49.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.99
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:51.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.85
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.66
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.79
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.81
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.08
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:39.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.52
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17352.91
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.24
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.92
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.49
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.68
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.29
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.74
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.63
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.88
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.32
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.63
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.75
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.94
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.87
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.91
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.24
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.64
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.82
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.29
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  171.17
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.54
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.89
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.93
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.84
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.58
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.13
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  303.44
p-value of test                       :    0.9991    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.58
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5088.67
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.01
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.47
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.00
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :   -1.42
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:24.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.17
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:25.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.49e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 7.57e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:46.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.51e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 9.90e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.91
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.85
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.16
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:07.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:07.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10069.47
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9910.19
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:49.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5005.88
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:51.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4008.04
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3990.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11679.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11921.71
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:29.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.28
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000008398

Normal statistic for number of bits   :   0.066
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.18
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000093922

Normal statistic for number of bits   :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.60
p-value of test                       :    0.06

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:38.09
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs mNP1, t = 16         0.9992 
 58  AppearanceSpacings, r = 27      7.5e-4
 79  RandomWalk1 H (L=10000, r=15)   0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 182845453.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:50.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1250
p-value of test                       :    0.9991    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334370
  j =  1                              :        599997500
  j =  2                              :             1250
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5459
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:55.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:42.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:58.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:04.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:04.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:55.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:59.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.94
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    2.11
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    2.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.58
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:12.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9900

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:40.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.64
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.32
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.55
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.10
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.92
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.65
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.17
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.91
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.97
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6975.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.32
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.49
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:04.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.76
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.10
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:33.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5129.84
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:59.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45935
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869935
  j =  1                              :        399908132
  j =  2                              :            45931
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45680
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869680
  j =  1                              :        399908643
  j =  2                              :            45674
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:27.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 7.68e-3
p-value of test                       :    0.9904

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:18.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:44.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:59.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:55.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.27e-3
p-value of test                       :    0.9976

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:33.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 8.11e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:21.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:35.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:35.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.63
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:49.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.27
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.99
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.91
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.16
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.41
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:38.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.72
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.95
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.10
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   96.16
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17195.38
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.10
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.81
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.72
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.13
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.92
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.69
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.28
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.49
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.30
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.31
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.18
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.37
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.69
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.41
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.07
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.88
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.75
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.95
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.03
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.30
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.49
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.03
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4854.93
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.92
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.99
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.36
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  445.35
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.68
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.70
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.62
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.27
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    1.91
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:23.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.07
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:23.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
p-value of test                       :    0.9925

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -2.03
p-value of test                       :    0.98

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.12e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 5.35e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.06
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.38
p-value of test                       :    0.9946

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:05.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:07.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9964.70
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.65e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10198.76
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:46.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4778.84
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:49.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.30
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:50.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4180.02
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.13
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11837.66
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11951.23
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:30.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.15
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000035041

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.13
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000050560

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:59.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 183861261.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5415
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:58.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:43.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4241
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:58.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:58.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:06.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:04.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:59.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:01.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:49.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.72
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.85
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     337
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    2.50
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:13.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.79
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.24
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.16
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.91
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:11.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.71
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.90
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.94
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.77
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  479.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:43.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1506.36
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:01.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6926.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.35
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.86
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:03.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:46.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.71
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:34.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5013.58
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:57.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46327
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870327
  j =  1                              :        399907349
  j =  2                              :            46321
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45343
p-value of test                       :    0.9939


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869343
  j =  1                              :        399909314
  j =  2                              :            45343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:28.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:18.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:45.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:00.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:56.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:33.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.27e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:34.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:34.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.87
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.26
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.62
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.93
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.61
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.23
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.92
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.06
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.29
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17278.86
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.21
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.60
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.88
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.43
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.02
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.77
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.35
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.11
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.38
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.63
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.84
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.08
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.00
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.28
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.92
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.42
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.82
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  550.98
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.88
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.68
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.05
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.83
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5048.72
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.26
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  155.17
p-value of test                       :    0.9918


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.84
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.37
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.13
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.60
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.52
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.07
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -1.49e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:24.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.28
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:24.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.80

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.18
p-value of test                       :    0.9965

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.13e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.83
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.93
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.18
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:07.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:08.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9807.63
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9851.56
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:51.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.06
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:49.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.53
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:52.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4239.50
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.31
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11874.74
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:29.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11872.22
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:31.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.06
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999934475

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.37
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000014803

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.53
p-value of test                       :    0.06

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   0.015
p-value of test                       :    0.49

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:10.34

 All tests were passed




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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5457
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:58.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:43.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:43.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:57.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4222
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:58.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:06.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:05.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:57.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:04:01.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.85
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:11.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:41.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.61
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.22
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.31
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.96
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.37
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.67
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.21
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.40
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  387.19
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:44.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1343.32
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:01.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7262.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:42.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.70
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:16.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.65
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:05.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.45
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.02
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:33.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4911.71
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:56.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45780
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869780
  j =  1                              :        399908443
  j =  2                              :            45774
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46380
p-value of test                       :  9.9e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870380
  j =  1                              :        399907241
  j =  2                              :            46378
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:28.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:17.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:44.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:59.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:55.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:33.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.64e-4
p-value of test                       :  5.0e-3

Kolmogorov-Smirnov- statistic = D-    : 5.69e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.30e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 6.41e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:21.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:33.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:32.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.11
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.43
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.63
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.10
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.06
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.73
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:39.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    3.58
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.00
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.80
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.24
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.13
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17375.04
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.79
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.42
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.91
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.62
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.81
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.20
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.98
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.59
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.50
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.90
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.22
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.84
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.48
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.22
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.94
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.50
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.89
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.09
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.04
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.81
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.45
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.67
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4932.70
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.51
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.60
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.42
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.98
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.47
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.13
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.82
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.54
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :   -1.53
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:22.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.06
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :    2.13
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:23.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.13

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.57
p-value of test                       :    0.94

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.33e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.18
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.32
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.36
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:07.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.05
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:08.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10041.68
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9970.04
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.027
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:41.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4766.77
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4969.25
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:49.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.30
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.51
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11935.57
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11765.47
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:29.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.16
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999986921

Normal statistic for number of bits   :   -0.10
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.46
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999914195

Normal statistic for number of bits   :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   0.019
p-value of test                       :    0.49

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:00.62

 All tests were passed




Server wird beendet - Lösche Semaphor 185925645.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1258
p-value of test                       :    0.9981

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334378
  j =  1                              :        599997484
  j =  2                              :             1258
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5347
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:59.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:42.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4240
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:58.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:58.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:05.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:06.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:01.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:01.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.21
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:51.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:17.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.75
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    2.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:42.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.93
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.34
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.57
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.55
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.74
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.50
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.35
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.53
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.19
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:44.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:02.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7028.89
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:42.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:03.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.80
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.71
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:33.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5140.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:59.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45724
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869724
  j =  1                              :        399908553
  j =  2                              :            45722
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45977
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869977
  j =  1                              :        399908050
  j =  2                              :            45969
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:29.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:19.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:45.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:59.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:56.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:33.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:37.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:34.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.09
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.88
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.22
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.04
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.15
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.44
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:40.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.74
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  4.0e-3

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.65
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17435.24
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   58.69
p-value of test                       :  9.8e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.31
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.98
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.13
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.82
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.62
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.08
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.78
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.68
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.01
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.81
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.46
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.58
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.88
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.87
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:46.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.93
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.84
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.27
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.29
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.39
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.82
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.63
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4928.13
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.08
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.28
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.11
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.69
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4899.95
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.98
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.54
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.65
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :   -1.15
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:24.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.20
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:25.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.98e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:46.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.93e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.71
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.48
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.90
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:06.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.62
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:09.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9940.31
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9711.55
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.03
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:46.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4997.25
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:50.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4905.53
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:52.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4031.17
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.44
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11828.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11793.75
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.88
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000063139

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.26
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999988403

Normal statistic for number of bits   :  -0.092
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.64
p-value of test                       :    0.95

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.21
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.030
p-value of test                       :    0.49

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.88

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:01.07

 All tests were passed




Server wird beendet - Lösche Semaphor 186941453.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5324
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:59.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:43.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:43.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:57.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:58.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7159
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:06.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:06.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:56.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:04:02.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:51.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.74
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:15.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.21
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    2.15
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:14.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.21
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:45.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.68
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.61
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.71
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:10.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.63
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.91
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.00
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.69
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.72
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1380.90
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:59.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6782.78
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.74
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.07
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:04.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.00
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  152.22
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:33.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5006.90
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:58.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45855
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869855
  j =  1                              :        399908295
  j =  2                              :            45845
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45675
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869675
  j =  1                              :        399908652
  j =  2                              :            45671
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 5.86e-3
p-value of test                       :    0.9926

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:28.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:18.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:45.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:58.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:55.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:16.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:34.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.57e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 2.68e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:34.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:33.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.51
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:49.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.25
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:51.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.87
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.40
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.81
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.36
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.78
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:38.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.59
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.84
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:15.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.69
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17226.54
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.65
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.38
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.90
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.01
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.89
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.79
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.24
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.49
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.71
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.79
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.06
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.36
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.77
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  103.56
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.29
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.08
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.68
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.41
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.17
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.84
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.10
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5083.62
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.31
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.17
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.10
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.93
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5209.30
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.46
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.60
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.79
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   -1.89
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:24.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.19
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   -1.06
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:24.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    2.66
p-value of test                       :  4.4e-3

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.04
p-value of test                       :    0.02

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.74e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 5.52e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.02
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.52
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.94
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:03.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.46
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:06.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9904.80
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9969.31
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:55.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:39.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5068.26
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.31
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:50.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.96
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11567.97
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11605.95
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.54
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999903821

Normal statistic for number of bits   :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.31
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000111706

Normal statistic for number of bits   :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.81

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:41.60

 All tests were passed




Server wird beendet - Lösche Semaphor 187957261.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5343
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:45.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:38.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:53.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:58.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:07.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:07.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:58.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:01.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:52.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.45
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    3.30
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:09.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.63
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:39.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.08
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.14
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.87
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.79
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.62
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:10.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.25
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.55
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.92
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  201.05
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:33.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  388.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:22.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1373.28
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:21.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7127.04
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:28.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.73
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:10.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.91
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:46.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.32
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5004.99
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:26.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46004
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870004
  j =  1                              :        399907996
  j =  2                              :            45996
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45642
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869642
  j =  1                              :        399908716
  j =  2                              :            45642
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:29.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:18.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:44.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:59.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:54.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:35.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.15e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 3.76e-4
p-value of test                       :  3.5e-3

Anderson-Darling statistic = A2       :    4.39
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.29e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:45.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:51.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.19
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.52
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.17
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.43
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:55.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.84
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:16.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.63
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:30.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.82
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:34.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:11.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.20
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:47.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17691.50
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:49.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.99
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.19
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.07
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.48
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.54
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.39
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.44
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.82
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.25
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.74
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.69
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.83
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.28
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.30
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.69
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:40.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.79
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.45
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.67
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.21
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.52
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:41.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.06
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.53
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.14
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.48
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.02
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:34.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.83
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.60
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4952.44
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.31
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.21
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.13
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :    1.60
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:28.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.33
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :   -1.25
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:27.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.73e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 4.80e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:46.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.96e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:46.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.22
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:31.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.89
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.14
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:09.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.81
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:11.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10002.24
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10043.62
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:04:20.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4858.26
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:52.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5046.47
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:53.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4285.43
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.64
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11844.79
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:36.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11616.30
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:33.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.45
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000087826

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.73
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000074806

Normal statistic for number of bits   :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.72
p-value of test                       :    0.04

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:10.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.12
p-value of test                       :    0.98

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:21:55.26

 All tests were passed




Server wird beendet - Lösche Semaphor 168361998.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5320
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:48.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:38.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:38.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:54.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:02.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:03.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:54.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:57.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     862
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:49.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.86
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.82
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:17.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:46.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.79
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.26
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.31
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.31
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.27
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  466.45
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:42.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1501.93
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:03.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6936.45
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:47.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.72
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.27
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:06.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.78
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.65
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:36.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4968.18
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:12.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45774
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869774
  j =  1                              :        399908456
  j =  2                              :            45766
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45880
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869880
  j =  1                              :        399908247
  j =  2                              :            45866
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:28.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :  3.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:17.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:44.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:59.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:54.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:35.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.47e-4
p-value of test                       :  3.3e-4    *****

Kolmogorov-Smirnov- statistic = D-    : 7.33e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    4.89
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:36.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:36.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.52
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.67
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.86
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.42
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.85
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.39
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:45.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.33
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.55
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.78
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.83
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.57
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17106.29
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.47
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.44
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.08
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.32
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.06
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.52
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.74
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.71
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.79
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.35
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.98
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.68
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.20
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.71
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.12
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:47.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.01
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.13
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  546.19
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.62
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.24
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.71
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.72
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4900.95
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.21
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.98
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.40
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.93
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.38
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.82
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.00
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.12
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :   -1.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:24.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.12
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:26.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -1.97
p-value of test                       :    0.98

Sample variance                       :    0.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.14e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 7.32e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:47.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.82e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 7.51e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.29
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.59
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.23
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:09.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.70
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:10.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9827.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.39
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:04:12.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4931.33
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:49.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.14
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:49.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4034.81
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12115.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:30.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11648.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:32.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.84
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999998168

Normal statistic for number of bits   :  -0.014
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:10.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.31
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999908408

Normal statistic for number of bits   :   -0.72
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :  -0.090
p-value of test                       :    0.54

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:12:16.79

 All tests were passed




Server wird beendet - Lösche Semaphor 169738254.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5441
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:49.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:39.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:37.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:55.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:57.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:05.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:05.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:57.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:04.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.41
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    2.12
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    2.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:16.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:44.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.42
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.48
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.92
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.42
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.45
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.11
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.23
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.67
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.30
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  503.52
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1393.87
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:59.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6975.20
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:49.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.21
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.01
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:15.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.28
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:47.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.29
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:39.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4883.14
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:01.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46228
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870228
  j =  1                              :        399907546
  j =  2                              :            46224
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45646
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869646
  j =  1                              :        399908713
  j =  2                              :            45636
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:28.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:15.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:42.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:00.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:36.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 5.73e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.23e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:43.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.53
p-value of test                       :    0.9943

-----------------------------------------------
CPU time used                    :  00:01:43.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.85
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.47
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.08
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.03
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.25
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.22
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:46.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.59
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.61
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.20
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:30.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.35
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:40.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17323.74
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.83
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.56
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.77
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.82
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.73
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.93
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.36
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.96
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.36
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.57
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.68
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.83
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  560.20
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.01
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.52
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.63
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.45
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.41
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.06
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.92
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.69
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.56
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5085.69
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.16
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.87
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:36.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.86
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.56
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4957.84
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.21
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.80
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.55
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:23.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.19
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:24.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.59
p-value of test                       :    0.06

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.95e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:46.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.52e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.79
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.74
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.73
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:08.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:08.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9885.50
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.33e-3
p-value of test                       :    0.9955

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10299.03
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:04:23.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4661.53
p-value of test                       :    0.9904

-----------------------------------------------
CPU time used                    :  00:01:54.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4773.95
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:56.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3975.46
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.23
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11891.26
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11729.08
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:32.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.37
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000042628

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.75
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  7999947060

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    2.99
p-value of test                       :  1.4e-3

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:11:29.98

 All tests were passed




Server wird beendet - Lösche Semaphor 170754062.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5446
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:48.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:39.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:38.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:03.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:03.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:56.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:02.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.11
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:46.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.30
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    6.45
p-value of test                       :  6.1e-4    *****

Stat. AD after spacings (mNP2-S)      :    3.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.90
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:14.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.99
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:42.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.05
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.45
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.69
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.09
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.94
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.69
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.54
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.51
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.64
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:45.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1274.59
p-value of test                       :    0.9992    *****

-----------------------------------------------
CPU time used                    :  00:02:00.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7098.02
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:42.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.91
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.75
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:03.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.39
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.85
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:52.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5163.00
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:33.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:22.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45708
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869708
  j =  1                              :        399908587
  j =  2                              :            45702
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45998
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869998
  j =  1                              :        399908007
  j =  2                              :            45992
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:27.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:17.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:45.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:00.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:54.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:32.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 8.57e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:22.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:33.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.79
p-value of test                       :    0.9973

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.75
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:47.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.41
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.85
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.03
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.36
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:42.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.38
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.56
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.66
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.53
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:09.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  157.06
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17346.83
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.48
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.29
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.46
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.10
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.28
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.54
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.26
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.97
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.26
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.39
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.96
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.68
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.38
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.83
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.35
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.18
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.01
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.67
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.85
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.18
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.91
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.16
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5019.42
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.37
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.20
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.33
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.63
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.46
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.62
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.49
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.19
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:24.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.47
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :    1.37
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:26.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 6.44e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:46.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 7.49e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.37
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.66
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.69
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:08.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.56
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:08.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10094.35
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10087.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:43.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5029.82
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4839.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4042.16
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11883.21
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11779.12
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:30.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.10
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999899582

Normal statistic for number of bits   :   -0.79
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.52
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999986507

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   0.017
p-value of test                       :    0.49

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.65
p-value of test                       :    0.95

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.48
p-value of test                       :    0.07

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:14.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs mNP2, t = 5          6.1e-4
 36  Gap, r = 0                      0.9992 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 171900942.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5418
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:50.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:39.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:41.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:58.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:08.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:07.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7125
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:57.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:03.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    2.90
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     855
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.35
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:14.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:43.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.14
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.92
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.41
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.70
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.46
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.53
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:42.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1455.70
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:18.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6988.23
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.97
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.14
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:03.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.72
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.56
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:35.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4998.01
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:18.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45727
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869727
  j =  1                              :        399908550
  j =  2                              :            45719
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46255
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870255
  j =  1                              :        399907492
  j =  2                              :            46251
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:29.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 7.05e-4
p-value of test                       :    0.9993    *****

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.26
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  2.8e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:18.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:44.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:59.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:55.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:32.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.54e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.33e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 8.01e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:21.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:35.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:33.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.26
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.46
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.91
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:49.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.17
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.91
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.16
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.23
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   62.11
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.90
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.77
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17589.57
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.22
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.25
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.94
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.34
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.06
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.89
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.14
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.49
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.80
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.09
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.39
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.36
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.97
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.07
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.14
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.66
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.37
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.25
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.95
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.15
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.42
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.78
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5075.43
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.49
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.31
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.13
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5173.84
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.69
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.66
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.88
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:24.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.71
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:24.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    2.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   0.071
p-value of test                       :    0.47

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.24e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 9.63e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 3.83e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.70
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.93
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.18
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:09.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.68
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:09.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9865.75
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9768.01
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:53.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.95
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.12
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:50.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.96
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4173.56
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11743.34
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:28.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12025.02
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:30.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.80
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999927536

Normal statistic for number of bits   :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.75
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000015865

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:09.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :  -0.093
p-value of test                       :    0.54

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.62
p-value of test                       :    0.05

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:25.92

 All tests were passed




Server wird beendet - Lösche Semaphor 172687374.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5338
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:49.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:39.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:37.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:56.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:04.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:04.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:58.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:02.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     958
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:47.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.21
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    3.51
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     336
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:17.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:45.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.32
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.80
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.68
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.98
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  374.72
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1409.59
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:00.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7078.71
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:50.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.69
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.88
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:09.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.96
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.20
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:37.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5193.73
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:56.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45630
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869630
  j =  1                              :        399908740
  j =  2                              :            45630
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45792
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869792
  j =  1                              :        399908421
  j =  2                              :            45782
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.37
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:32.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :  4.8e-3

Anderson-Darling statistic = A2       :    4.21
p-value of test                       :  7.0e-3


-----------------------------------------------
CPU time used                    :  00:02:20.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:03.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:55.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:34.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.61e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 3.32e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.78
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:22.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:37.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.88
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.72
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.86
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.43
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.29
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.64
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.59
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.93
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.06
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:40.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17173.70
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.92
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.39
p-value of test                       :    0.9906


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.50
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.86
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.46
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:38.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.94
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.27
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.52
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.59
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.60
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.10
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.22
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.58
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.62
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.51
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.34
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.52
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.99
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  100.71
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.01
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.94
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.63
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4818.06
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.97
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.99
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.65
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.09
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4967.17
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.86
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.65
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.65
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :  -0.051
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:27.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.51
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:27.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.66
p-value of test                       :    0.95

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 6.18e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 2.21e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.51
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.30
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.69
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:09.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.16
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:08.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10203.28
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9953.80
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:11.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:04:27.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4779.41
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:53.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4928.94
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:55.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4072.79
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.11
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11996.04
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:33.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12396.50
p-value of test                       :  1.2e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:31.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   85.49
p-value of test                       :  4.1e-3


-----------------------------------------------
Total number of bits:  8000081424

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.81
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000059710

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:15.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.72

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 3.17e-3
p-value of test                       :    0.9967

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.23
p-value of test                       :    0.99

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:49.86
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 100  HammingIndep, L=1200, r=25      1.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 173637646.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:40.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:52.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:40.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:40.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:58.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:59.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:09.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:09.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:04:05.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7161
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:04:10.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     865
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:49.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.40
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:14.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     174
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:44.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.48
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.28
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.09
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.41
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:11.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.42
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.36
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.83
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  267.92
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  378.15
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:53.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1443.98
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:56.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7204.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:50.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.64
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:15.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.69
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.69
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:37.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4975.98
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:02.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46157
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870157
  j =  1                              :        399907688
  j =  2                              :            46153
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46031
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870031
  j =  1                              :        399907944
  j =  2                              :            46019
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:33.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:20.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:51.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:06.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:37.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 9.68e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:42.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:43.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.61
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.75
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.54
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.04
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   11.69
p-value of test                       :    0.9982

-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.68
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.68
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.34
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  103.53
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17496.63
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   64.29
p-value of test                       :  2.6e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.08
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.86
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.90
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.29
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.85
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.32
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.99
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.97
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.17
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.20
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.49
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.64
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.04
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.70
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.27
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.03
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.87
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.40
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.71
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.97
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.06
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.89
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.17
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.56
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:37.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.68
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.87
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4940.72
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.70
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  245.99
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.00
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -1.12
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:25.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.36
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:26.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:46.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 3.40e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.82
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.50
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.17
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:07.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.15
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:08.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10042.74
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9953.70
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:10.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.38
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.050
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:04:32.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.75
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:56.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4913.95
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:00.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4033.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.00
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11753.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:35.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11952.98
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:35.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.25
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999907820

Normal statistic for number of bits   :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.70
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000042349

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 7.55e-3
p-value of test                       :    0.9919

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.23
p-value of test                       :    0.99

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.80
p-value of test                       :    0.04

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:21.89

 All tests were passed




Server wird beendet - Lösche Semaphor 174718990.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  6.9e-3


-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5467
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:52.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7504
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:40.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4226
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:57.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:04.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7178
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:04.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:55.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:00.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.89
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    2.09
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.26
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:18.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:46.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.42
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   19.39
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.78
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.44
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.31
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.07
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.90
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.00
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.29
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:44.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1388.35
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:00.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6843.41
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:44.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.41
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:02.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.03
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.01
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:35.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5053.47
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:02.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45390
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869390
  j =  1                              :        399909223
  j =  2                              :            45384
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45886
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869886
  j =  1                              :        399908236
  j =  2                              :            45870
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:28.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:20.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:00.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:55.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:34.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.62e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 7.01e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:22.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:37.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.89
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.06
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.39
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.45
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.45
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.86
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.37
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:45.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.13
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:29.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.46
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17482.78
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.44
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.89
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.92
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.60
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.66
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.14
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.48
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.32
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.26
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   33.98
p-value of test                       :  8.5e-3


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.87
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.03
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.22
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.23
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.58
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.93
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.51
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.17
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.25
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.59
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.43
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.18
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.52
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.31
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.90
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.16
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.63
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4778.39
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.30
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.69
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.49
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:25.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.82
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:25.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.17e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:46.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.85e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.08
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.03
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.14
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:08.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.16
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:07.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9969.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9873.91
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:55.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4929.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:49.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9917

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.81
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:51.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.32
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.80
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11903.92
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11927.99
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:29.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.05
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999799331

Normal statistic for number of bits   :   -1.59
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.49
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000015028

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:54.01

 All tests were passed




Server wird beendet - Lösche Semaphor 176029710.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5441
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:52.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:40.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:39.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:56.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:57.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:04.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:04.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:56.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:02.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.75
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:18.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.85
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.97
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:50.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.91
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.24
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.94
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.34
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.76
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.61
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.92
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.60
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.90
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:59.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7189.44
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:40.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.13
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.24
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:03.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.39
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.30
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:35.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5223.50
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:55.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46069
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870069
  j =  1                              :        399907864
  j =  2                              :            46065
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45586
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869586
  j =  1                              :        399908830
  j =  2                              :            45582
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:27.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:17.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:45.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:01.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:54.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:34.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.19e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.90e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.92e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : -2.63e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:21.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:35.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:37.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   41.66
p-value of test                       :    0.9936

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.45
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.63
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.96
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.17
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.77
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.30
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:43.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.87
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.67
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.36
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.20
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 9.29e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.43
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   93.78
p-value of test                       :    0.9929

-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17143.95
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.09
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.58
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.30
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.40
p-value of test                       :    0.9927


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.54
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.68
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.62
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.39
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.51
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.66
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.53
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.00
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  448.46
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.41
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.27
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.46
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.14
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.74
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.24
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.54
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.00
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.01
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.83
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.00
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.99
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.28
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.45
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.81
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.18
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.43
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.06
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :   -1.40
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:25.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.76
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :    0.16
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:25.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   0.092
p-value of test                       :    0.46

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.47e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 7.94e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.28e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 7.09e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9936

-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.10
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.52
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.78
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:07.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.52
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:08.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9814.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9980.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:46.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4964.84
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:48.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.53
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:50.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4118.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4183.67
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11790.33
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:28.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11890.49
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:29.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.78
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000017473

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.87
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999906596

Normal statistic for number of bits   :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    2.69
p-value of test                       :  4.0e-3

-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:19.15

 All tests were passed




Server wird beendet - Lösche Semaphor 177078286.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5387
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:50.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:39.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:39.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4429
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:57.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:04.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:05.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:54.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:00.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.75
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.39
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:48.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:17.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    2.41
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     130
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:51.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.80
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.00
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.04
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.87
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.40
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.75
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.02
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  202.19
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  473.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:43.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1437.88
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7429.34
p-value of test                       :  7.4e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:44.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.29
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:16.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   13.99
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.43
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5035.67
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:56.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46123
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870123
  j =  1                              :        399907758
  j =  2                              :            46115
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45799
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869799
  j =  1                              :        399908405
  j =  2                              :            45793
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:27.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:17.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  6.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.95
p-value of test                       :  9.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9968


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:44.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:59.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:54.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:34.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 3.23e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.32e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:26.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:34.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.64
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.75
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.40
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.74
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:48.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.59
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.95
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.83
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:43.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.40
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.94
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.093
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:10.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  101.22
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17529.13
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.25
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.56
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.27
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.12
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.17
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.57
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   15.65
p-value of test                       :    0.9981


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.83
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.51
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.11
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.99
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.69
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.51
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.56
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.16
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.46
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.96
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.09
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.27
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.02
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.68
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.49
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5085.10
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  329.40
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.58
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.33
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.70
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5023.77
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.30
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.56
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.86
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   -1.80
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:24.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.20
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :  -0.095
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:26.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.23

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.93e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 5.93e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 6.75e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.46
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.38
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.99
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:09.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.99
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:08.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10153.38
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.43
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10329.13
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:49.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4767.74
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:48.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4868.78
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:49.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.42
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.33
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12050.95
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11766.01
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.06
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999908042

Normal statistic for number of bits   :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.42
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000031783

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.03
p-value of test                       :    0.02

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.57
p-value of test                       :    0.06

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:13.19
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 37  Gap, r = 20                     7.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 178028558.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  9.0e-3


-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5361
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:51.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:40.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:57.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:05.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:04.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:54.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:00.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:47.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    2.29
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:16.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:50.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.88
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.54
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.90
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.95
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.53
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.58
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.38
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.13
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.57
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.92
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:40.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1349.32
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:56.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7237.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:39.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.18
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.06
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:01.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.22
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  166.68
p-value of test                       :  2.6e-3


-----------------------------------------------
CPU time used                    :  00:01:34.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4935.62
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:58.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46170
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870170
  j =  1                              :        399907663
  j =  2                              :            46164
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45298
p-value of test                       :    0.9967


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869298
  j =  1                              :        399909405
  j =  2                              :            45296
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:27.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:19.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:45.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :  4.0e-3

Anderson-Darling statistic = A2       :    4.28
p-value of test                       :  6.5e-3


-----------------------------------------------
CPU time used                    :  00:01:58.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:55.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:34.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:22.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.15e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 2.77e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.37
p-value of test                       :    0.9910

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:34.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:35.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.00
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:48.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.04
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.09
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:48.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.57
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.57
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.17
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.09
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.82
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:29.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.46
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17606.59
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.13
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.77
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.73
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.45
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.66
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.44
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.50
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.87
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.00
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.06
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.55
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.17
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.36
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  167.06
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.62
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.34
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.68
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.24
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.92
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.87
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.71
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.60
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.11
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.47
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.21
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.56
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.18
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5046.31
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  426.08
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  237.87
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.96
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:27.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.31
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :   -1.64
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:26.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.83

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.91e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 5.60e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.05
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.45
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.13
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:09.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.71
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:09.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.08e-5
p-value of test                       : 1 -  2.1e-5    *****

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10402.42
p-value of test                       :  2.5e-3

-----------------------------------------------
CPU time used                    :  00:00:58.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10158.50
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:44.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.24
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:49.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.56
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:50.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.71
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.15
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11744.46
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11748.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:30.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.58
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999936536

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.41
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000055717

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         : 2.72e-3
p-value of test                       :    0.50

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.71
p-value of test                       :    0.96

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:18.17

 All tests were passed




Server wird beendet - Lösche Semaphor 179044366.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:40.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5452
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:52.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:39.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:39.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:55.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:05.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:04.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:55.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:01.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    3.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.12
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    2.73
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:14.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.88
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:42.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.03
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.53
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.35
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.52
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.77
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.31
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.30
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  269.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.84
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:42.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1405.62
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:59.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7231.70
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:40.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.86
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:03.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.79
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.78
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4990.09
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:59.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46227
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870227
  j =  1                              :        399907547
  j =  2                              :            46225
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45811
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869811
  j =  1                              :        399908382
  j =  2                              :            45803
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.44
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:28.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:18.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:45.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:55.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:33.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.47e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.92e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 5.53e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:21.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:33.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.17
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.56
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.88
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.69
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:47.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.13
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.96
p-value of test                       :  7.8e-3

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.98
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:43.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  8.0e-3

Kolmogorov-Smirnov- statistic = D-    : 3.28e-3
p-value of test                       :    0.9966

Anderson-Darling statistic = A2       :    3.78
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   20.22
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.29
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.32
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:38.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17675.64
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.60
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.63
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.31
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.45
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.16
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.14
p-value of test                       :    0.9943


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.28
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.86
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.90
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.99
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.66
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.48
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.72
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.58
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.65
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.80
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.54
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.17
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.80
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.08
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.50
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.75
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5082.90
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.45
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.10
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:37.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.92
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.44
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.11
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.50
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.98
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.25
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:25.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.51
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:25.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :  -0.043
p-value of test                       :    0.52

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 4.82e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:47.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.90e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 7.51e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.09
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.68
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.20
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:07.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.44
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:09.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9989.26
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10190.12
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.080
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:45.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:48.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4955.50
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:50.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4035.25
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3995.07
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12025.53
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11855.45
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:30.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.63
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000151783

Normal statistic for number of bits   :    1.20
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.23
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999989408

Normal statistic for number of bits   :  -0.084
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:27.47

 All tests were passed




Server wird beendet - Lösche Semaphor 180060174.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:51.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5410
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:52.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:40.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:39.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:55.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:56.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:03.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:04.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7491
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:55.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:04:00.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:13.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:43.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.18
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.79
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.15
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.78
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.61
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1367.39
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:01.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7096.53
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:43.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.04
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.06
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:02.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.04
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.55
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:35.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4870.85
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:56.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46114
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870114
  j =  1                              :        399907773
  j =  2                              :            46112
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45941
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869941
  j =  1                              :        399908120
  j =  2                              :            45937
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:28.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:17.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 3.93e-3
p-value of test                       :    0.9958

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:45.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:59.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:00.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:40.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.55e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:34.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.069
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.08
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.82
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.84
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.63
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.82
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.34
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:43.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.45
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.01
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.42
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:28.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:28.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.79
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17310.80
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.20
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.47
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.14
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.48
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.07
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.62
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.70
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.42
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.47
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.31
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.18
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.93
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.97
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.84
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.58
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.05
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.64
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.01
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.91
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.87
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.47
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4916.12
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.83
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.16
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.57
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5137.82
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.58
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.55
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.57
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:24.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.67
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :   -1.41
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:22.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  2.0e-3

Kolmogorov-Smirnov- statistic = D-    : 6.06e-3
p-value of test                       :    0.9936

Anderson-Darling statistic = A2       :    4.28
p-value of test                       :  6.7e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.65
p-value of test                       :    0.9960

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 7.26e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.71e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.43
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.06
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.19
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:07.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.53
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:07.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10180.50
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9951

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10015.15
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.066
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:50.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5071.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:49.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4942.49
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:50.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.32
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.33
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11934.83
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11937.51
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:31.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.86
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000015847

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.94
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999790520

Normal statistic for number of bits   :   -1.66
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :  -0.028
p-value of test                       :    0.51

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:59.70

 All tests were passed




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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:39.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1266
p-value of test                       :    0.9963

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334386
  j =  1                              :        599997468
  j =  2                              :             1266
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1484
p-value of test                       :  7.2e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334604
  j =  1                              :        599997032
  j =  2                              :             1484
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1239
p-value of test                       :    0.9997    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334359
  j =  1                              :        599997522
  j =  2                              :             1239
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5339
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:54.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:40.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:39.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:56.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4444
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:06.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:06.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:00.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:04:02.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     938
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:49.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     567
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.60
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:15.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:37.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.93
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.68
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.95
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.98
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.92
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.67
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.87
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.49
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.97
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.17
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1473.92
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:03.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6893.02
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.32
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.72
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:09.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.88
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   92.45
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:37.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4901.64
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  1.5e-3


-----------------------------------------------
CPU time used                    :  00:02:56.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45564
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869564
  j =  1                              :        399908878
  j =  2                              :            45552
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46047
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870047
  j =  1                              :        399907909
  j =  2                              :            46041
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:30.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:18.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:46.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:01.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:55.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.26e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 6.32e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:37.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:38.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.76
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:50.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.80
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.34
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.71
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.70
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:45.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.02
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:29.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.24
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17740.57
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.36
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.87
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.85
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.43
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.17
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.70
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.02
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.02
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.46
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.89
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.08
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.09
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  445.28
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.22
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.76
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.92
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.79
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  562.09
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.06
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.97
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.60
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.96
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5080.45
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.68
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.00
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.31
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.78
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.47
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.73
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.00
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.91
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:27.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.47
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:24.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.25e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 8.30e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.50e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.21
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.81
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:05.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.24
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:07.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9821.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10024.81
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:10.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:04:19.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4946.79
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:52.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5015.99
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:55.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4049.84
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.62
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11958.70
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:31.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11697.31
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:31.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.72
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000004918

Normal statistic for number of bits   :   0.039
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.55
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000058081

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.46
p-value of test                       :  6.9e-3

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:11.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:00.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 10  CollisionOver, t = 14           7.2e-4
 12  CollisionOver, t = 21           0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 182026254.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5403
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:54.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:39.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7475
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:39.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:57.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:04.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:05.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:56.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:01.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.79
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.80
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.69
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.90
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:15.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:46.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.15
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.99
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.86
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.17
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.81
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.09
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.78
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.14
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.16
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:45.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.18
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:00.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7071.44
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.00
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.08
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:02.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.10
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.26
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:35.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5029.02
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:00.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45984
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869984
  j =  1                              :        399908034
  j =  2                              :            45980
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46344
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870344
  j =  1                              :        399907314
  j =  2                              :            46340
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:27.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:18.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 6.55e-3
p-value of test                       :    0.9926

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:45.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :  3.4e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    5.36
p-value of test                       :  2.0e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9968


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:00.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:55.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:34.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 8.43e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.74e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.64e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.08
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:32.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.24
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:34.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.29
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:49.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.72
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.72
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.09
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:49.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.35
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.30
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.60
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.88
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.23
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.58
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17320.98
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.30
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.19
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.18
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.25
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.58
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.38
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.88
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.39
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.62
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.91
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:38.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.82
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.43
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.84
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.31
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.70
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.68
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.48
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.84
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.35
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.75
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.44
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.66
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4802.51
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.27
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.25
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.73
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.49
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4805.59
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.41
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.30
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.99
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :    1.79
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:23.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.88
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :    1.05
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:25.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.78

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.84e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 8.28e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:46.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.66
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.36
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.95
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:06.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.96
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:08.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9949.72
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10050.96
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:42.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5048.13
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:50.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4224.08
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3997.05
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12035.14
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11944.88
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:30.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.20
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999928787

Normal statistic for number of bits   :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.53
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999965552

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9941

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.73

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:26.44

 All tests were passed




Server wird beendet - Lösche Semaphor 183238670.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:39.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:50.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5279
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:50.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:40.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:56.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4456
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:57.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:05.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:04.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:55.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:00.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:48.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    2.47
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     272
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:16.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    2.17
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:41.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.72
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.40
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:09.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.77
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.60
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.97
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  483.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:43.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1462.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:01.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7162.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:42.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.11
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.45
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:03.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.18
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.80
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:33.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5118.82
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:59.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46040
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870040
  j =  1                              :        399907922
  j =  2                              :            46036
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46216
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870216
  j =  1                              :        399907571
  j =  2                              :            46210
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:28.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:18.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:45.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:00.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:55.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :  4.6e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    5.55
p-value of test                       :  1.6e-3

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.96e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.70
p-value of test                       :  3.5e-3

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:32.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:33.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.14
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.71
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.58
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.17
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.83
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.36
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:38.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.04
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.55
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.18
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17214.91
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.58
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.69
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.38
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.94
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.85
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.33
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.11
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.49
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.43
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.69
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:39.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.03
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.98
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.36
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.14
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.78
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.77
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.96
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.67
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.52
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.78
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.99
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.21
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4896.40
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.81
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.26
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.70
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.32
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.05
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.48
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.17
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.05
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :    1.64
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:21.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.13
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:21.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.96
p-value of test                       :    0.98

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.30e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.12e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.22
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.44
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.15
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:07.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.37
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:08.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.08e-3
p-value of test                       :    0.9902

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10290.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9985.05
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:55.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:48.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4981.72
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4955.71
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:50.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.41
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4020.55
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12067.94
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11758.80
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:30.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.23
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000006337

Normal statistic for number of bits   :   0.050
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.62
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000040195

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.72
p-value of test                       :    0.96

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:03.94

 All tests were passed




Server wird beendet - Lösche Semaphor 184156174.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:39.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1483
p-value of test                       :  7.8e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334603
  j =  1                              :        599997034
  j =  2                              :             1483
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5422
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:57.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4144
p-value of test                       :    0.9984


-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:44.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:00.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:01.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7137
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:12.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:10.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7463
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:07.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:04:11.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.73
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     942
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:52.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    3.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    2.32
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:17.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.48
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:43.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.93
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.06
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.09
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.85
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:11.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.92
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.89
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.48
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.91
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.16
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.82
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:10.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6829.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:55.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.51
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.85
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:18.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.16
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.53
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5220.43
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:00.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46167
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870167
  j =  1                              :        399907672
  j =  2                              :            46155
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45621
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869621
  j =  1                              :        399908763
  j =  2                              :            45611
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:33.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:20.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:51.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9958


-----------------------------------------------
CPU time used                    :  00:02:08.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:37.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.64e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 9.20e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:24.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:26.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:42.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:43.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.39
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.34
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.38
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.10
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:16.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.09
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.70
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17227.18
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.42
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.81
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.84
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.35
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.30
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.57
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.96
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.74
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.02
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.38
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.58
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.78
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.83
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.37
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.37
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.86
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.78
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.79
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.82
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.71
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.44
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.66
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5166.02
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.56
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.40
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:36.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.79
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.10
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.75
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.35
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.25
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.55
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :   -1.46
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:25.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.63
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:23.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.20

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.18e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 6.75e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.02
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.07
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.36
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:05.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.67
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:07.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9988.91
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10024.08
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:04:28.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4981.53
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:56.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4810.74
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:59.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4223.48
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.70
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11929.05
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:35.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11805.24
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:36.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.68
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999905663

Normal statistic for number of bits   :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.66
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999977804

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   0.080
p-value of test                       :    0.47

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:56.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           7.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 185204750.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:48.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:24.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1469
p-value of test                       :  2.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334589
  j =  1                              :        599997062
  j =  2                              :             1469
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5397
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:55.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:39.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:57.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:58.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:06.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:06.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:56.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:02.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.98
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     844
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.16
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:14.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.90
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:40.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.65
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.57
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.97
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.84
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.33
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.77
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.14
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.65
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.50
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:42.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1455.64
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:00.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6907.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.80
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-3
p-value of test                       :    0.9982

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.78
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:03.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.90
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.59
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:32.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5041.26
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:11.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:57.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45957
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869957
  j =  1                              :        399908093
  j =  2                              :            45943
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46096
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870096
  j =  1                              :        399907813
  j =  2                              :            46086
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:28.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:17.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:45.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:59.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:55.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:36.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.32e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    3.80
p-value of test                       :  7.3e-5    *****

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:35.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.11
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.51
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.10
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.47
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:49.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.61
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.99
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.59
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:39.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.37
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.20
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.29
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.47
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.54
p-value of test                       :  8.5e-3

-----------------------------------------------
CPU time used                    :  00:01:17.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.05
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17553.89
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.87
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.78
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.57
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.58
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.42
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.57
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.13
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.19
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.44
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.09
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.87
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.42
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.98
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.80
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.55
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.09
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.39
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.34
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.83
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.55
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.40
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5137.07
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.31
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  238.96
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.36
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.99
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4896.58
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.95
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.72
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.43
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:24.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.15
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :    2.20
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:02:24.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   0.076
p-value of test                       :    0.47

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 5.49e-3
p-value of test                       :    0.9942

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.55
p-value of test                       :    0.9946

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.38e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:46.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.40e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 9.42e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.38
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.97
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:05.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.08
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:07.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10174.32
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9831.72
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:44.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4967.12
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    3.96
p-value of test                       :  9.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4675.85
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:51.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4226.04
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4178.51
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11931.77
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11848.05
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:29.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.67
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999984866

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.71
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999956141

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.61
p-value of test                       :    0.95

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:13.35
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 55  SampleCorr, k = 1               7.3e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 186286094.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:48.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1257
p-value of test                       :    0.9983

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334377
  j =  1                              :        599997486
  j =  2                              :             1257
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5489
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:55.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:41.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:56.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:06.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:07.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:57.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:01.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.22
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.72
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:13.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    2.46
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     121
p-value of test                       :    0.9916

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:42.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.86
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.48
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.53
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.09
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:10.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.72
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   29.65
p-value of test                       :    0.9972

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.36
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.53
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.21
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:43.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.52
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:00.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6855.47
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.25
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:03.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.46
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.44
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:33.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5134.78
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:56.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45848
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869848
  j =  1                              :        399908305
  j =  2                              :            45846
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45780
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869780
  j =  1                              :        399908444
  j =  2                              :            45772
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:28.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:18.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:45.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:59.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:34.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 5.48e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 5.81e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:35.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:37.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.76
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.56
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.21
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:48.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.01
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.01
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.37
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 4.11e-4
p-value of test                       :    0.9996    *****

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.59
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.22
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.43
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17477.18
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.03
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.72
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.36
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.30
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.49
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.51
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.78
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.12
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.61
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.51
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.23
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.84
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.37
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.84
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.36
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.94
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.34
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.21
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.60
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.39
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.31
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.99
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.70
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  317.33
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.37
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.12
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.35
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4856.95
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.03
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.45
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.21
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:25.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   26.79
p-value of test                       :  8.3e-3


-----------------------------------------------
Normal statistic for number of jumps  :   -2.80
p-value of test                       :    0.9975



-----------------------------------------------
CPU time used                    :  00:02:25.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.47e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 9.86e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.94
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.68
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.46
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:05.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.16
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:08.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10040.80
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9866.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:45.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.56
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:49.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.85
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:50.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4338.68
p-value of test                       :  8.0e-3

-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4017.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11749.01
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11759.57
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:29.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.27
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000099997

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.87
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999910268

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:31.64

 All tests were passed




Server wird beendet - Lösche Semaphor 187334670.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:48.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:59.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:43.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:00.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4466
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:01.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:10.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:04:08.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:09.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.83
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    3.44
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.10
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:14.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.63
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:42.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.20
p-value of test                       :    0.9910

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.09
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    5.04
p-value of test                       :    0.9988

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.26
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.68
p-value of test                       :    0.9934

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.88
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.53
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.20
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:31.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.00
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:55.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1504.47
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:03.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6962.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:55.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.74
p-value of test                       :  1.3e-3

Anderson-Darling statistic = A2       :    4.61
p-value of test                       :  4.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   48.82
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.76
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:18.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.68
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:46.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.17
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:41.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5011.94
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:59.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45908
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869908
  j =  1                              :        399908187
  j =  2                              :            45902
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45922
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869922
  j =  1                              :        399908159
  j =  2                              :            45916
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:32.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:21.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:52.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:09.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:56.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:38.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.61e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.43e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:29.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.00
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:47.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.45
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.73
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.40
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.79
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.14
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:50.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.25
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17405.34
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.99
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.22
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.67
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.96
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.46
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.80
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.91
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.31
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.15
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.90
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.25
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.97
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.08
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.81
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.97
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.44
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.01
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.70
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.18
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.06
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:46.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.55
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.58
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4976.76
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.30
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.73
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.00
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.89
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4870.15
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.91
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.10
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :    1.07
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:24.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.44
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :   -0.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:23.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.55
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 4.52e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 7.99e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.38
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.87
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.77
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:03.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.94
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:02.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9824.19
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9800.83
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:57.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.43
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:47.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4787.07
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:50.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4348.23
p-value of test                       :  6.0e-3

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4178.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11838.03
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11678.32
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:29.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.83
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999898379

Normal statistic for number of bits   :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.28
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000039253

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.47
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.66
p-value of test                       :  3.9e-3

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    2.50
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:31.21

 All tests were passed




Server wird beendet - Lösche Semaphor 188350478.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:48.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5409
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:42.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:36.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:36.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:55.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:02.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:02.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:54.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:59.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:50.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.16
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.00
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:12.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.72
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:35.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.57
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   49.35
p-value of test                       :  9.4e-5    *****

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.58
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.51
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.74
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.81
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.21
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  475.96
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:45.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1551.68
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:58.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7046.09
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.59
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.76
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:02.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.67
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.70
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4851.42
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:03.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45787
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869787
  j =  1                              :        399908431
  j =  2                              :            45777
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46147
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870147
  j =  1                              :        399907707
  j =  2                              :            46145
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:16.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 2.37e-3
p-value of test                       :    0.9974

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:30.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:18.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:45.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:00.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:52.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:22.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.06e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.017
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:35.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:37.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.05
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:47.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.54
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:47.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.27
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.90
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.40
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:37.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.88
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:33.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.63
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:32.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.57
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.41
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17226.84
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:54.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.96
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.92
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.56
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.49
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.95
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.96
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.66
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.78
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.87
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.18
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.47
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.72
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.18
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.97
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.27
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:48.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.55
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.77
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.82
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.77
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.53
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:48.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.33
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.99
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5090.17
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.83
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  237.14
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.22
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.83
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.47
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.43
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.49
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.74
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:24.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.08
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :   -1.23
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:13.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.95e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.00e-2
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.48e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.90
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.28
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.90
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:09.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.87
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:12.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10040.58
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9925.59
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:04:02.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.23
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:49.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4945.78
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:49.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4243.98
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4216.25
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11730.81
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11941.18
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:29.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.27
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000004918

Normal statistic for number of bits   :   0.039
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.57
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999951242

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :  -0.043
p-value of test                       :    0.52

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:29.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:16:07.19
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 29  SimpPoker, r = 25               9.4e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 168394767.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997319
  j =  2                              :             1339
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5464
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:43.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:37.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:36.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4226
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:54.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7111
p-value of test                       :    0.9924


-----------------------------------------------
CPU time used                    :  00:03:02.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:02.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:54.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7457
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:00.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.81
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:47.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.07
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9917

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:11.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:39.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.05
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.48
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.68
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.12
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:11.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.40
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.01
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.92
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.20
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.15
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:43.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1387.48
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:59.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7072.30
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:43.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.59
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.93
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:02.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.52
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.79
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5158.48
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:05.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45970
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869970
  j =  1                              :        399908066
  j =  2                              :            45958
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46097
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870097
  j =  1                              :        399907809
  j =  2                              :            46091
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:14.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9907

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:32.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:19.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:46.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:00.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:54.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:33.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 2.53e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.78e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 3.05e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.040
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:34.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.96
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:48.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.08
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.97
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.91
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:48.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.88
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.24
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.52
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:37.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.47
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.90
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.42
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:30.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.37
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:30.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.40
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 8.11e-3
p-value of test                       :    0.9913

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17868.43
p-value of test                       :  9.8e-3



-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.77
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.90
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.63
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.38
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.96
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.45
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.06
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.15
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.76
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.87
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.83
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.00
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.21
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.20
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.42
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:48.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.19
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.00
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.37
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.50
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.04
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:47.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.74
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.92
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4988.19
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.50
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.23
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.66
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.26
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.32
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.63
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.52
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.63
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:27.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.44
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:19.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    2.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.85e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.89e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.22
p-value of test                       :    0.9964

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:29.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.87
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.47
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:07.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.85
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:10.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9922.77
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10178.40
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.03
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:57.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.66
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:48.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4758.84
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:49.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.40
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4029.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11680.49
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11873.25
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:29.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.88
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999963119

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.01
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999877331

Normal statistic for number of bits   :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:30.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:40.04

 All tests were passed




Server wird beendet - Lösche Semaphor 169115663.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5439
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:43.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4206
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:37.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7188
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:35.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:54.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4451
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:55.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7491
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:02.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:03.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:53.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:59.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.44
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     936
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.17
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.71
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.60
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:13.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.95
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:40.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.36
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.00
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.21
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.44
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.23
p-value of test                       :  9.7e-3

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.04
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.12
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.05
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.52
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.83
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:42.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.32
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:59.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6968.87
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:42.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.20
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.26
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:00.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.37
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.14
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:34.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5199.54
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:01.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45653
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869653
  j =  1                              :        399908695
  j =  2                              :            45651
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45966
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869966
  j =  1                              :        399908071
  j =  2                              :            45960
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  7.4e-3

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:32.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:18.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:45.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:00.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:55.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:33.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:32.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:33.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.97
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:48.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.13
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.00
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.98
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:47.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.43
p-value of test                       :    0.9954

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.72
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:37.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.55
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    4.20
p-value of test                       :  7.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17945.03
p-value of test                       :  3.1e-3



-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.25
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.85
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.13
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    9.99
p-value of test                       :    0.9946


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.63
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.27
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.45
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.46
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.32
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.78
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.86
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.48
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.83
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  180.36
p-value of test                       :  6.5e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.59
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.07
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.85
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  421.82
p-value of test                       :    0.9952


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.20
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  109.44
p-value of test                       :  4.7e-3


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.06
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.35
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4911.04
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.12
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.84
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.63
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5039.68
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.18
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.03
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.42
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:27.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.24
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:24.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    3.48
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -1.74
p-value of test                       :    0.96

Sample variance                       :    2.46
p-value of test                       :  8.4e-3

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 4.30e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.90e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 8.90e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.26
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:28.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.45
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.85
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:07.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.87
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:08.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9937.39
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10015.40
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:59.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5041.14
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:50.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.07
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:51.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.51
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4183.10
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11713.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11901.85
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:30.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.87
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999836735

Normal statistic for number of bits   :   -1.29
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.53
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000069115

Normal statistic for number of bits   :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.53
p-value of test                       :    0.06

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:46.34

 All tests were passed




Server wird beendet - Lösche Semaphor 170065935.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1269
p-value of test                       :    0.9952

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334389
  j =  1                              :        599997462
  j =  2                              :             1269
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5326
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:47.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:39.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:55.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4500
p-value of test                       :  7.0e-3


-----------------------------------------------
CPU time used                    :  00:01:59.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:20.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:46.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:46.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:04:22.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:05:28.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     863
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     553
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:13.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.03
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:40.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.68
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.06
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:11.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.79
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.18
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.65
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:50.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  390.97
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:34.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.85
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:45.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7099.10
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:40.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.84
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.35
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:17.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.99
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.65
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:39.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5111.12
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:59.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45740
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869740
  j =  1                              :        399908525
  j =  2                              :            45730
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45912
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869912
  j =  1                              :        399908176
  j =  2                              :            45912
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 9.58e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:39.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:28.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:58.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:18.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:38.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.52e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 8.36e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 7.08e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:24.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.096
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:24.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.029
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:43.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.095
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:44.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.13
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:40.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.48
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:40.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.21
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.20
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:40.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.44
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.43
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:51.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.33
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.89
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.00
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.94
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17299.44
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.06
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.51
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.91
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.28
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.51
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.42
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.43
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.44
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.99
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.08
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.34
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.63
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.87
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.64
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.98
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.26
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.18
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.96
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.33
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.62
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.39
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.58
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4882.37
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.21
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.47
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.79
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.84
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5077.47
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.49
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.71
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.86
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :    1.11
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:25.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.70
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :   -1.05
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:26.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   0.087
p-value of test                       :    0.47

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.22e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:46.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.03e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.01
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.72
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  155.96
p-value of test                       :    0.9907

-----------------------------------------------
CPU time used                    :  00:02:07.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.80
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:08.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9798.03
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.58
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10329.85
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:13.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:04:33.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.23e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5064.91
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:55.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4846.23
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:58.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4196.92
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4240.48
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11678.84
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:34.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11884.30
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:35.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.01
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999871595

Normal statistic for number of bits   :   -1.02
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.85
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  7999972554

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.92

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:21:10.14

 All tests were passed




Server wird beendet - Lösche Semaphor 171081743.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:39.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:50.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5324
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:47.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:38.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7171
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:36.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:54.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:55.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:02.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7476
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:02.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:52.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:58.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:46.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.13
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.79
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     266
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:16.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    2.16
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:44.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.45
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.20
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.67
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.14
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.10
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.89
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.47
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.56
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.32
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.29
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:46.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1508.82
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:04.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7213.46
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.38
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.79
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:04.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.53
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  151.46
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5055.19
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:58.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46067
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870067
  j =  1                              :        399907868
  j =  2                              :            46063
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45525
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869525
  j =  1                              :        399908953
  j =  2                              :            45519
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:29.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:16.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:00.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:35.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:40.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:39.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.47
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.55
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.74
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.16
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.68
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.23
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:44.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.54
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.56
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:28.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.71
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.17
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:37.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17250.44
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.61
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.49
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.89
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.42
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.44
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.84
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.20
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.74
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.97
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.34
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.22
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.87
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  561.60
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.68
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.07
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.64
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.83
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.83
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.01
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.62
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.46
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.13
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5086.02
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.09
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.10
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.65
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.51
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4833.79
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.64
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.78
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.51
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:25.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.61
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:24.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:09.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 8.60e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:46.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 4.73e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.94
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.20
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:07.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.10
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:09.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10049.70
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10145.74
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:04:16.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4780.96
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:52.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4831.32
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:52.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.84
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4216.72
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11713.83
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:29.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12113.75
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:31.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.38
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000073528

Normal statistic for number of bits   :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.24
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000035866

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:09.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 4.51e-3
p-value of test                       :    0.9953

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.89
p-value of test                       :    0.97

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9980

Tests on the sum of all N observations
Standardized normal statistic         :  -0.034
p-value of test                       :    0.51

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:12.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.17e-3
p-value of test                       :    0.9912

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.77
p-value of test                       :    0.04

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:44.69

 All tests were passed




Server wird beendet - Lösche Semaphor 172457999.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5376
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:52.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:41.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:58.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:59.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:09.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7487
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:10.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:04:08.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:04:14.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.92
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:49.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.76
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:09.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.18
p-value of test                       :    0.9945

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:37.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.18
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.58
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.18
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.84
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.10
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.99
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.34
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:55.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1498.19
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:00.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7067.59
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:53.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9926

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.25
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.89
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:09.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.16
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.96
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:39.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5091.84
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:29.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:14.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45532
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869532
  j =  1                              :        399908940
  j =  2                              :            45524
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46009
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870009
  j =  1                              :        399907983
  j =  2                              :            46007
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:30.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:22.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:52.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:07.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:37.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.14e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.95e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.56e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:43.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.93
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.01
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.88
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.38
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.71
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.03
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.92
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:52.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.47
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.25
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.52
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.97
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.94
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17679.78
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.01
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.57
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.69
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.58
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.43
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.48
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.58
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.69
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.93
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.75
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.75
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.20
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.40
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.76
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.09
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.06
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.16
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.75
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.74
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.86
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.81
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.14
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4911.46
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.04
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.23
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.93
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.55
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5130.99
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  332.45
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.00
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.95
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:26.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.23
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :  -0.078
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:26.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.038
p-value of test                       :    0.48

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 5.85e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:46.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 7.72e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.75
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:37.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.02
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:35.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.76
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:19.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.09
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:14.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :  1.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    4.90
p-value of test                       :  3.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9625.82
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9923.37
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:14.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:04:38.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4803.10
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:52.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5002.36
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4012.46
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4187.89
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11773.21
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:31.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12086.02
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:33.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.79
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000032116

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.27
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000000958

Normal statistic for number of bits   : 7.57e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:11.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  3.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.96
p-value of test                       :  9.5e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.30
p-value of test                       :    0.99

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:12:51.96

 All tests were passed




Server wird beendet - Lösche Semaphor 173604879.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1257
p-value of test                       :    0.9983

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334377
  j =  1                              :        599997486
  j =  2                              :             1257
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5488
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:53.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4234
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:41.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:56.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4433
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:58.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:06.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:05.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:54.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:00.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:48.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.91
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     331
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:15.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.51
p-value of test                       :  5.5e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:45.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.87
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.50
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.27
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.96
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.90
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.89
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.25
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.70
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.64
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.66
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:43.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1401.26
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:59.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7054.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:41.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.80
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.19
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:01.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.60
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.42
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5015.42
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:04.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46032
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870032
  j =  1                              :        399907941
  j =  2                              :            46022
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46040
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870040
  j =  1                              :        399907920
  j =  2                              :            46040
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:27.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :  1.5e-5    *****

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    6.33
p-value of test                       :  7.1e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9987


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:18.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:59.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:54.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:36.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.90e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 4.84e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 4.98e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:33.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.54
p-value of test                       :  5.5e-3

-----------------------------------------------
CPU time used                    :  00:01:33.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.77
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.22
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:51.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.99
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.73
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.27
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.95
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:43.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.57
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:29.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.00
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:37.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17453.27
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   56.93
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.02
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.61
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.21
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.69
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.38
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.91
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.07
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.14
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.30
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.62
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.02
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.95
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.39
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.73
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.84
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.37
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  579.63
p-value of test                       :  7.8e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.96
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.12
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.24
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.33
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5084.73
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.56
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.90
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.79
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.66
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.13
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.36
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.23
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.03
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:25.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.35
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :   -1.09
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:25.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.56e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:46.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.97e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.62
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.80
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.31
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:07.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.54
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:07.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10217.11
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10072.62
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:49.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.42
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:48.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.11
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:50.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4006.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11653.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11798.04
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.19
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999931472

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.55
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000041899

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.60
p-value of test                       :    0.95

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:11.04

 All tests were passed




Server wird beendet - Lösche Semaphor 175112207.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:42.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5281
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:52.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:40.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:57.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:04.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7512
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:05.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:54.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:59.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.94
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    2.17
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:49.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.14
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.13
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.21
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:15.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.16
p-value of test                       :    0.9974


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.19
p-value of test                       :  7.7e-3

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:45.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.16
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.20
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.13
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.73
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.29
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.85
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.90
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:44.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.15
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:59.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7150.11
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:44.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:02.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.20
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.32
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:35.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5077.77
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:15.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46195
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870195
  j =  1                              :        399907615
  j =  2                              :            46185
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45689
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869689
  j =  1                              :        399908625
  j =  2                              :            45683
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:28.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 9.26e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:19.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:44.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  6.6e-3

Kolmogorov-Smirnov- statistic = D-    : 3.77e-3
p-value of test                       :    0.9960

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:00.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:35.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.28e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 5.48e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:39.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.64
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.01
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.56
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.23
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:48.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.45
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.68
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.66
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.58
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.49
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.72
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17105.44
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.22
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.06
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.43
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.68
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.53
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.44
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.51
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.58
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.85
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.33
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.34
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.04
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.99
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.01
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.52
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.08
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.34
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.45
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.06
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.87
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.50
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5162.67
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.78
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.67
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.60
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.24
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4931.71
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.12
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.35
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.28
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:25.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.29
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :   -1.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:25.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :  -0.092
p-value of test                       :    0.54

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 5.08e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.97e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 8.75e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.33
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.87
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:06.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.55
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:06.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10147.52
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10032.45
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.033
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.014
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:55.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4946.31
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:49.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4778.65
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:51.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4049.82
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11787.93
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11794.50
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:29.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.94
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000017578

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.97
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999943622

Normal statistic for number of bits   :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.77
p-value of test                       :    0.04

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   0.025
p-value of test                       :    0.49

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:07.07

 All tests were passed




Server wird beendet - Lösche Semaphor 176128015.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:43.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5459
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:52.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:40.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:40.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:57.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:04.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:05.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:56.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:01.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    2.40
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     831
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    2.91
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:15.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     124
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:49.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.45
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.75
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.37
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:10.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.18
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.70
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.16
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.17
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.20
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:43.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1378.81
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:00.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7096.83
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.16
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.86
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:02.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.98
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.86
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:34.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5034.25
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:12.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45678
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869678
  j =  1                              :        399908646
  j =  2                              :            45674
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45485
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869485
  j =  1                              :        399909036
  j =  2                              :            45473
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:27.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:18.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 3.40e-3
p-value of test                       :    0.9964

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:01.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:55.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:35.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.083
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:38.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:38.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.88
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:48.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.75
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.71
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.77
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.80
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.27
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.01
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:45.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.76
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.41
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.05
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:29.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:29.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.60
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17367.63
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.58
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.79
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.81
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.83
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.15
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.89
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.98
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.38
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.00
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.79
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.95
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.19
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.84
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.88
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.07
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.44
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.71
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.45
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.00
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.23
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.94
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.92
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.43
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.13
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.02
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.30
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.87
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.23
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.05
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.24
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.68
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:25.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.01
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:25.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.71

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 9.02e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:46.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.19
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.05
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.95
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:06.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.25
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:06.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9941

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9997.71
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10024.24
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.095
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:45.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5055.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4936.32
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:51.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4302.61
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4253.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11963.74
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11836.09
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:29.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.80
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999974423

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.52
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000034627

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:50.29

 All tests were passed




Server wird beendet - Lösche Semaphor 177143823.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5407
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:52.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:40.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7154
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:40.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4251
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4462
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:56.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:03.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:04.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:55.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:04:00.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     938
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:14.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:46.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.23
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.96
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.20
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.70
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:10.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.09
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.94
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.97
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.11
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  487.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:44.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.18
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:00.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7130.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:45.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.58
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.97
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:02.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.07
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.09
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:35.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4840.75
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:13.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45995
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869995
  j =  1                              :        399908013
  j =  2                              :            45989
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45637
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869637
  j =  1                              :        399908733
  j =  2                              :            45623
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:27.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:17.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:44.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 5.22e-3
p-value of test                       :    0.9942

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:55.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:35.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.68e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.74e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:35.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 1.77e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:35.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.58
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:47.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.66
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.16
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.42
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:48.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.48
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.36
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:45.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.93
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.26
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.88
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:32.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.51
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17194.75
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.24
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.18
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.42
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.73
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.97
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.92
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.90
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.44
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.52
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.86
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.78
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.42
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.95
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.80
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.88
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.84
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.79
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.35
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.77
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.98
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.79
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.49
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4930.42
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.20
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.82
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.28
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.04
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4888.61
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.04
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.74
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.77
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :   -1.40
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:24.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.87
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :    1.46
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:26.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.17

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.78e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:46.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.41e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 8.08e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.18
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.49
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.42
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:08.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.36
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:08.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9761.51
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10122.26
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.81
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:50.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4776.97
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4805.52
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:49.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4005.77
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4195.69
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11668.74
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:29.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11742.08
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:29.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.48
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000143923

Normal statistic for number of bits   :    1.14
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.88
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000012598

Normal statistic for number of bits   :   0.100
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:06.84

 All tests were passed




Server wird beendet - Lösche Semaphor 178126863.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:55.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5461
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:51.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:56.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4239
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:57.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7461
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:05.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7088
p-value of test                       :    0.9965


-----------------------------------------------
CPU time used                    :  00:03:04.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:54.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7453
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:00.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:50.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.88
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:17.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:47.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.51
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.19
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.07
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.21
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.31
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.53
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.97
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.54
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.29
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.92
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:41.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1397.22
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:58.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6997.22
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:43.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:11.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:01.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.97
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  147.04
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:34.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5216.49
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:12.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45926
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869926
  j =  1                              :        399908150
  j =  2                              :            45922
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45630
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869630
  j =  1                              :        399908744
  j =  2                              :            45622
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:27.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :  5.3e-3

Anderson-Darling statistic = A2       :    4.49
p-value of test                       :  5.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  4.3e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:17.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:44.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:58.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:32.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.94e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.38e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.92e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.082
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.093
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:36.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:34.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.73
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.98
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   15.76
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.05
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.86
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:44.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.38
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.50
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.26
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17533.83
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.51
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.42
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.23
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.29
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.72
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.51
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.81
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.07
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.23
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.79
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.50
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.17
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.18
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.25
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.27
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.22
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.00
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  566.54
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.51
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.72
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.22
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.71
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4942.60
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  322.09
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.22
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.66
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.25
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4976.78
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.80
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.71
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.65
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:23.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.86
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :   -1.41
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:24.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.96
p-value of test                       :    0.03

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.36e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 9.27e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:46.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.73e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.01
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.24
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.07
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:08.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.35
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:07.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10037.10
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.33
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:55.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:53.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:49.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4933.84
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:50.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4049.96
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11811.70
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11642.11
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:29.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.28
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999887717

Normal statistic for number of bits   :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.13
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999917969

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.97
p-value of test                       :    0.02

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:48.30
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 62  WeightDistrib, r = 0            0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 179175439.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5418
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:55.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:42.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:00.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:01.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:11.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:11.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:10.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:14.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.17
p-value of test                       :    0.9959


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    3.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:15.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    3.14
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    3.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:44.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.17
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.80
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.96
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.01
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.51
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.86
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.15
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.94
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.43
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:53.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1423.92
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:01.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7103.78
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:53.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.07
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.67
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:13.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.34
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.30
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:40.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4843.77
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:29.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:04.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45807
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869807
  j =  1                              :        399908390
  j =  2                              :            45799
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45910
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869910
  j =  1                              :        399908186
  j =  2                              :            45898
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:31.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:21.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:54.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:08.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:56.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:38.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.12e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.73e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 2.99e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:24.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:44.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:48.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.65
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.25
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.45
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.82
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.43
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.63
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.69
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:29.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.24
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.67
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.31
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17270.70
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.93
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.73
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.35
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.81
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.90
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:38.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.52
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.82
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.58
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.61
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.82
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.55
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.62
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.76
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.69
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.21
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.00
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.37
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.74
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.05
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.03
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.56
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.31
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4987.57
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.58
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.57
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.69
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.92
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.58
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  425.18
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.75
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.60
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :   -1.77
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:24.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.41
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:26.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   0.000
p-value of test                       :    0.50

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.59e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:47.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 2.46e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.85
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.34
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.59
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:11.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.12
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:12.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10088.71
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.00
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:10.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:04:33.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4772.90
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:52.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4812.31
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:56.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3936.55
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4214.94
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11873.77
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:34.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11816.86
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:36.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.55
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000063667

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.22
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000081280

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :  -0.097
p-value of test                       :    0.54

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.14e-3
p-value of test                       :    0.9935

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.56
p-value of test                       :  5.2e-3

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:12:12.70

 All tests were passed




Server wird beendet - Lösche Semaphor 180125711.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5373
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:54.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4166
p-value of test                       :    0.9953


-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7189
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:41.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:58.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7180
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:05.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7490
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:06.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:55.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:04:01.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.32
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.44
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     632
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:14.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:43.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.50
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.02
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.99
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.20
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:10.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.58
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.52
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.48
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.84
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  477.53
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:43.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.18
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:00.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7073.30
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:40.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.48
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.42
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:03.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.50
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.53
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:29.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4995.71
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:05.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45799
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869799
  j =  1                              :        399908409
  j =  2                              :            45785
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45712
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869712
  j =  1                              :        399908579
  j =  2                              :            45706
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.89e-3
p-value of test                       :    0.9941

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:28.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:18.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:46.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:59.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.18e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 7.76e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:22.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:38.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:38.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.37
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.85
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.37
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.68
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.64
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:44.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.69
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.80
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.98
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.87
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17764.26
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.71
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.96
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.12
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.95
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.57
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.41
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.62
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.57
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.42
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.63
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.45
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.15
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  429.25
p-value of test                       :    0.9901


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  101.82
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.44
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.79
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.24
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.36
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.26
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.14
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.50
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.06
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.42
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.35
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.08
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.48
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.31
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.30
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.96
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  251.81
p-value of test                       :  7.6e-3


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.85
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :   -2.87
p-value of test                       :    0.9980



-----------------------------------------------
CPU time used                    :  00:02:23.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.96
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :    0.40
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:24.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.81
p-value of test                       :    0.97

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.41e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 9.51e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.87e-3
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.65
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.82
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.30
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:07.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.97
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:06.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10045.00
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10159.78
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:40.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4844.77
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:47.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4838.33
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:49.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.60
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3954.52
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11977.72
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11962.64
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.02
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000191533

Normal statistic for number of bits   :    1.51
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.31
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999862004

Normal statistic for number of bits   :   -1.09
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:07.46

 All tests were passed




Server wird beendet - Lösche Semaphor 181436431.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1500
p-value of test                       :  1.5e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334620
  j =  1                              :        599997000
  j =  2                              :             1500
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5483
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:52.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:40.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:43.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:57.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:58.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:08.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:09.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:00.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:04:01.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:47.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    4.21
p-value of test                       :  6.9e-3

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:13.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.54
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:43.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.85
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.84
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.28
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.16
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.90
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:11.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.44
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  189.14
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.90
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:48.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.51
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:01.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7122.35
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:47.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:15.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:05.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.30
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:46.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.92
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5091.64
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:11.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:57.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45818
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869818
  j =  1                              :        399908369
  j =  2                              :            45808
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45656
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869656
  j =  1                              :        399908689
  j =  2                              :            45654
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:28.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:16.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:44.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:59.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:56.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:36.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.69e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 6.77e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.44e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:39.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:41.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.75
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.77
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:55.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.07
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.94
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.88
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:45.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.68
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.77
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.33
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17426.55
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.52
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.35
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.37
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.34
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.83
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.89
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.31
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.99
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.53
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.06
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.37
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.07
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.51
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.79
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.33
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.65
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.68
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.60
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.83
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.04
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.69
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.04
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.16
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.92
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.61
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  439.89
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.07
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5034.54
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.11
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.37
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.39
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :   -1.79
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:23.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.09
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:23.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-3
p-value of test                       :    0.9982

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.32
p-value of test                       :  6.4e-3

Tests on the sum of all N observations
Standardized normal statistic         :    3.05
p-value of test                       :  1.1e-3

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.70e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.08
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.23
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.02
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:06.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:06.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.08
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9803.69
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:04:02.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4707.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4958.05
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:48.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.20
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.55
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11833.13
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11660.50
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:28.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.19
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000150064

Normal statistic for number of bits   :    1.19
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.60
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999995783

Normal statistic for number of bits   :  -0.033
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   0.017
p-value of test                       :    0.49

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.094
p-value of test                       :    0.46

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:03.35
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           1.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 182419471.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5496
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:53.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:41.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:56.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:57.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7500
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:06.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:06.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:56.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7147
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:04:00.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.63
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    2.58
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:15.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     175
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:40.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.19
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.14
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.87
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.93
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.71
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.99
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.36
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  494.08
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:44.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.00
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:00.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7001.53
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:42.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.09
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.43
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:06.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.18
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.67
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:33.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5066.13
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:00.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46083
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870083
  j =  1                              :        399907840
  j =  2                              :            46071
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45481
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869481
  j =  1                              :        399909041
  j =  2                              :            45475
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:27.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:19.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:45.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:58.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:34.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 9.09e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:36.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.66
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.06
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.82
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.48
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.87
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:06.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.39
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.58
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.41
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.07
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17626.30
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   58.79
p-value of test                       :  9.6e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.23
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.63
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.16
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.00
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   61.41
p-value of test                       :  3.8e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.34
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.45
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.24
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.51
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.22
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.89
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.97
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.27
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.78
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.97
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.91
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.76
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.10
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.99
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.08
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.97
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.54
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.07
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.16
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.59
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.80
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.03
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.29
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.92
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :  -0.060
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:23.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.62
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :    1.36
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:24.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.52
p-value of test                       :    0.94

Sample variance                       :    2.40
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.91e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 7.28e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.75e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.17
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.19
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.75
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:07.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:06.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.15e-3
p-value of test                       :    0.9957

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10261.17
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9656.01
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:50.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.93
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.25
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:49.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.00
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11887.45
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12038.24
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.65
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  7999956930

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.76
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999878804

Normal statistic for number of bits   :   -0.96
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.28

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :  -0.050
p-value of test                       :    0.52

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:25.62

 All tests were passed




Server wird beendet - Lösche Semaphor 183402511.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:56.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:56.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1476
p-value of test                       :  1.5e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334596
  j =  1                              :        599997048
  j =  2                              :             1476
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5458
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:57.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4469
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7169
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:42.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:59.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4238
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:01.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7534
p-value of test                       :  6.1e-3


-----------------------------------------------
CPU time used                    :  00:03:12.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:13.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:09.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:10.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.79
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    2.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:49.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.28
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.82
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     547
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    3.06
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     328
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:13.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:43.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.60
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.29
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.80
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.55
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:11.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.81
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.17
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.90
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.14
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:53.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1395.43
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:04.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7118.37
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.23
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.51
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:15.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.82
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.40
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:37.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5227.13
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:01.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46063
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870063
  j =  1                              :        399907878
  j =  2                              :            46055
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45527
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869527
  j =  1                              :        399908948
  j =  2                              :            45523
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:32.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:20.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:52.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:07.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 4.14e-3
p-value of test                       :    0.9955

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:38.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.38e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:24.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:47.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.94
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.00
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.19
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:50.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.66
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.75
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.68
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.20
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.86
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.96
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.96
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:43.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17230.57
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.08
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.00
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.75
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.00
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.51
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.79
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.12
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.92
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.44
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.23
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:38.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.28
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.39
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.74
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.29
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.00
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.22
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.79
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.57
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.38
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.31
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.29
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.72
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5014.89
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.25
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.30
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.52
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.37
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4961.73
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.59
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.30
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    2.75
p-value of test                       :    0.9970


-----------------------------------------------
Normal statistic for number of jumps  :   0.097
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:24.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.17
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:23.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.13e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 2.88e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.37
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.36
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:07.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.69
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:06.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9893.76
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.26e-3
p-value of test                       :    0.9945

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    4.31
p-value of test                       :  6.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10426.58
p-value of test                       :  1.4e-3

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:04:18.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4778.30
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:54.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9970

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.83
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:57.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.66
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.98
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11509.56
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:33.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11752.43
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:33.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.86
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000045472

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.32
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000164461

Normal statistic for number of bits   :    1.30
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    1.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.90

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:11:01.62

 All tests were passed




Server wird beendet - Lösche Semaphor 184418319.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:39.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5489
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:57.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:42.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:56.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:58.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:05.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:05.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:56.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:00.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.33
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:16.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.57
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:46.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.29
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.29
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.68
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.80
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:11.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.88
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.16
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:42.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1356.17
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:02.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7098.65
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:41.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.73
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.74
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:02.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.99
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:33.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5190.02
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:01.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45677
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869677
  j =  1                              :        399908649
  j =  2                              :            45671
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45898
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869898
  j =  1                              :        399908209
  j =  2                              :            45888
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:28.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:18.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:44.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:58.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:56.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:36.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.31
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:37.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.46
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:01:38.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.68
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.86
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.91
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.26
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.76
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:44.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.59
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.12
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.27
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:29.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.91
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:29.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   13.51
p-value of test                       :  1.2e-3

-----------------------------------------------
CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    3.38
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  101.58
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17443.79
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.23
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.01
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.63
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.07
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.47
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.64
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.36
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.75
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.61
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.52
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.83
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.41
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.72
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.46
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.20
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.37
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.40
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.44
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.68
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.80
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.92
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.41
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4947.69
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.80
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.47
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.21
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4982.78
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.90
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.35
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.47
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:23.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.81
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:25.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.90e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 9.15e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 5.85e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.82
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.89
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:05.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.73
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:06.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9861.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9950.68
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.049
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:42.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5078.76
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5070.51
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:49.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.89
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4225.60
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11590.93
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11861.81
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.73
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999950327

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.29
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999978581

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:18.43

 All tests were passed




Server wird beendet - Lösche Semaphor 185532431.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1465
p-value of test                       :  3.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334585
  j =  1                              :        599997070
  j =  2                              :             1465
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5339
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:58.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:43.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4445
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:59.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:07.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:07.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:04:01.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:04:06.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    2.14
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:49.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.04
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    2.12
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     328
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    3.06
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:16.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:47.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   19.50
p-value of test                       :  6.7e-3

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.48
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.05
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.18
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:10.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.07
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.66
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  192.70
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  390.65
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:47.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1398.39
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:06.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6832.10
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.20
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.79
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:07.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.84
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.13
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5005.25
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:04.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45884
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869884
  j =  1                              :        399908238
  j =  2                              :            45872
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45948
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869948
  j =  1                              :        399908109
  j =  2                              :            45938
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:31.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:17.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:46.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:02.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:57.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.50e-4
p-value of test                       :    0.9995    *****

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.52e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.34
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.07
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.94
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.73
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.92
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.99
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:45.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.39
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.23
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.85
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.99
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17201.15
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.07
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.76
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.83
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.44
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.49
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.12
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.68
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.38
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.44
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.41
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  206.26
p-value of test                       :  7.6e-4    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.49
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.87
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.81
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.90
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.18
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.35
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.20
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.53
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.00
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.95
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.23
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.38
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.19
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.76
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.68
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.69
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4860.86
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.85
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.67
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.65
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:26.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.91
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:24.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.60
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.41
p-value of test                       :    0.9921

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :  -0.087
p-value of test                       :    0.53

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 8.93e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.28e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 9.44e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.11
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.26
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:06.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.81
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:06.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10142.64
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10141.52
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:04:11.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4976.05
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:51.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.64
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:52.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3948.38
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3947.42
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11884.83
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:29.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11876.69
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:30.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.88
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999907094

Normal statistic for number of bits   :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.83
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000085483

Normal statistic for number of bits   :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.58
p-value of test                       :    0.94

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:12.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 H (L=1000, r=0)     7.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 186548239.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1484
p-value of test                       :  7.2e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334604
  j =  1                              :        599997032
  j =  2                              :             1484
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5339
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:56.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:40.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4184
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4144
p-value of test                       :    0.9984


-----------------------------------------------
CPU time used                    :  00:01:57.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:06.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:06.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:55.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:02.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.96
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    2.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:49.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    3.58
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:16.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:45.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.60
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.35
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.22
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.19
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:11.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.03
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.33
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1384.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:07.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6791.02
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:52.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:02.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.56
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.83
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:34.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5100.92
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:01.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45892
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869892
  j =  1                              :        399908216
  j =  2                              :            45892
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45867
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869867
  j =  1                              :        399908267
  j =  2                              :            45865
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:29.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:18.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:45.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.9916


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:00.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:55.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.48e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 3.98e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:21.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:38.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:40.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.26
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.60
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.96
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.68
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:49.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.73
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.03
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.78
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:45.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.95
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.34
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.15
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.43
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17401.41
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.02
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.73
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.13
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.23
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.72
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.20
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.92
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.43
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.90
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.60
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.65
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.55
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.36
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.90
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.87
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.56
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.65
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.89
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.49
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.77
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.73
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.70
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5090.42
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.69
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.85
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.85
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.32
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4897.21
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.47
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.20
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.14
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:24.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.94
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:24.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.73
p-value of test                       :    0.04

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 6.18e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.17e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.67
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.28
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.09
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:07.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.01
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:07.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9873.81
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10149.32
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:42.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4816.68
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:46.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4710.70
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:50.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.02
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3940.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11884.23
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11889.81
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.31
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000005668

Normal statistic for number of bits   :   0.045
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.60
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000101065

Normal statistic for number of bits   :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :  -0.012
p-value of test                       :    0.50

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:11.90
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           7.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 187564047.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:39.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1478
p-value of test                       :  1.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334598
  j =  1                              :        599997044
  j =  2                              :             1478
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5463
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:58.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:42.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:43.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:00.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:01.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:13.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:13.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:11.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:15.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    2.25
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     938
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:06.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:17.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:48.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.10
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.51
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.34
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.96
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.23
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.78
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.17
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.91
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:30.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  383.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:57.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1485.97
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:06.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7129.67
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.78
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:19.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.03
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:46.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.42
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:41.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5133.30
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:03.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46170
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870170
  j =  1                              :        399907664
  j =  2                              :            46162
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45909
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869909
  j =  1                              :        399908183
  j =  2                              :            45907
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:32.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:21.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:53.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:09.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:56.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:37.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 8.75e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 3.29e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.55
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.47
p-value of test                       :    0.9932

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:25.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:52.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:51.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.65
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.23
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  100.55
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.63
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.14
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:44.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.82
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.73
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.50
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.15
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:20.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.00
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:11.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.79
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:37.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17543.91
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.59
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.28
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.82
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.05
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.43
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.65
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.54
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.36
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.55
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.04
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.39
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.57
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.86
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.74
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.92
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:40.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.93
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.22
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.79
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.36
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.87
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:40.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.53
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  309.55
p-value of test                       :    0.9979


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5111.95
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.43
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.04
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:32.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.00
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.39
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4936.79
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.77
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.32
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.34
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:11.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.00
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :   0.070
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:11.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.01e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 8.02e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.78e-4
p-value of test                       :    0.9931

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.55
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.80
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:16.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.30
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:54.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.27
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:55.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10147.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10145.75
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:04:01.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5119.71
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:46.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4850.79
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:49.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4072.27
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4065.62
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11579.00
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11914.73
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:29.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.83
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999981644

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:58.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.28
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999927854

Normal statistic for number of bits   :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9959

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         : -1.38e-3
p-value of test                       :    0.50

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:32.55

 All tests were passed




Server wird beendet - Lösche Semaphor 188612623.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1481
p-value of test                       :  9.4e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334601
  j =  1                              :        599997038
  j =  2                              :             1481
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5381
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:42.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:36.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:35.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:55.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:56.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:03.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:02.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:55.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:00.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:49.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     561
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:10.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    2.33
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:38.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.71
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.66
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.54
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.28
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.24
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.38
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1515.52
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:59.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6877.02
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:42.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.70
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.59
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:02.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.26
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.12
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5049.82
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:02.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45695
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869695
  j =  1                              :        399908614
  j =  2                              :            45687
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46330
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870330
  j =  1                              :        399907343
  j =  2                              :            46324
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:14.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:30.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:19.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:46.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:00.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9932

-----------------------------------------------
CPU time used                    :  00:01:59.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9904

-----------------------------------------------
CPU time used                    :  00:01:44.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 7.15e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:22.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.61e-4
p-value of test                       :  5.4e-3

Kolmogorov-Smirnov- statistic = D-    : 1.33e-5
p-value of test                       :    0.9930

Anderson-Darling statistic = A2       :    4.00
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.081
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:33.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:34.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:48.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.37
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.75
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.80
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:46.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:52.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.77
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.00
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:37.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.50
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.55
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.46
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:32.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:32.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   98.19
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17290.95
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.51
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.56
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.93
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.14
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.26
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.61
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.83
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.10
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.89
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.07
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.56
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.30
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.34
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.05
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.56
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:48.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.08
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.71
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.48
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.31
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.68
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  452.29
p-value of test                       :  9.2e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.23
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5081.02
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.41
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.50
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.43
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.98
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4924.16
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.59
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.61
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.24
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:27.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.68
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :   0.012
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:13.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   0.092
p-value of test                       :    0.46

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.51e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.60e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 4.44e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.71
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.77
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.69
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:08.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.13
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:13.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10245.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10074.17
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.32
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.15
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:56.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:49.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4759.90
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:49.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.04
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4141.57
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11914.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11908.23
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:30.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.76
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000038455

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.41
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999952841

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:29.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:16:10.32
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           9.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 168427536.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5367
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:43.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:36.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:35.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:54.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4442
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:02.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:02.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:53.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:00.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.93
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:55.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.45
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    2.86
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.58
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.03
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:18.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:42.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.99
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.60
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.25
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.08
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.73
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:10.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.31
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.42
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.79
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.70
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.45
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:44.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1384.15
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:01.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7146.27
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:46.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.95
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.22
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:02.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.91
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:35.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4919.57
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:03.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46175
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870175
  j =  1                              :        399907654
  j =  2                              :            46167
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45983
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869983
  j =  1                              :        399908039
  j =  2                              :            45973
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:13.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:33.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:18.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:01.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:55.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:32.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 4.50e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:22.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:32.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:33.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.90
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:48.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.99
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.14
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.67
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.78
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.60
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:39.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.50
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.38
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:30.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.16
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:30.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.21
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17311.53
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.19
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.86
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.07
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.53
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.78
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.93
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.70
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.69
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.47
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.63
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.10
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.48
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.23
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.92
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.57
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.50
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.85
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.85
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.24
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.83
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.46
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.80
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4833.62
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.86
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.23
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.97
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.99
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5075.99
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.56
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.18
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.15
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:32.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.70
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :   -0.86
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:23.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.24e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 8.48e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.02e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.83
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.11
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.62
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:07.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.58
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:09.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9779.93
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9699.92
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:59.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4844.69
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:48.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.73
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:49.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.41
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4162.77
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11888.62
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11869.91
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.25
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000159358

Normal statistic for number of bits   :    1.26
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.94
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000181981

Normal statistic for number of bits   :    1.44
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.66e-3
p-value of test                       :    0.9929

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.89
p-value of test                       :    0.03

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:30.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:22.02

 All tests were passed




Server wird beendet - Lösche Semaphor 169017360.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1250
p-value of test                       :    0.9991    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334370
  j =  1                              :        599997500
  j =  2                              :             1250
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5337
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:42.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:36.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:34.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:54.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:55.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:02.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:02.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:53.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:58.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.92
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:51.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:18.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    2.20
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:46.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.04
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.56
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.80
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.92
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.59
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:42.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1360.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:59.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6923.64
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:43.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.85
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.76
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:00.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.83
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.08
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:32.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4888.55
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:01.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46032
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870032
  j =  1                              :        399907937
  j =  2                              :            46030
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45840
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869840
  j =  1                              :        399908321
  j =  2                              :            45838
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:33.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:20.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:45.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:00.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:55.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.38e-3
p-value of test                       :    0.9964

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:33.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 9.44e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 2.61e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:22.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.041
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:32.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:34.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.54
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.37
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.85
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.68
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.71
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.07
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.94
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:43.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.84
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.38
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.79
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.65
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17222.69
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.99
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.30
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.11
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.42
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.87
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.77
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.85
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.20
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.90
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.43
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.84
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.63
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.62
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.58
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.63
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.88
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  440.93
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.05
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.47
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.26
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.32
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.44
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.29
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.83
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.07
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.77
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.43
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.64
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.45
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:28.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.99
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:26.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.22e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.47e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 8.25e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.61
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.58
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  241.37
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:08.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.81
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:07.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9962.77
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10101.31
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.12
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:49.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4957.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:49.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.75e-5
p-value of test                       : 1 -  6.8e-5    *****

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5113.31
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:51.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4038.46
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.91
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11970.92
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11451.78
p-value of test                       :    0.9928

-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   83.17
p-value of test                       :  6.6e-3


-----------------------------------------------
Total number of bits:  8000061462

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.10
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000078469

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.2e-3

Anderson-Darling statistic = A2       :    4.42
p-value of test                       :  5.7e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.37
p-value of test                       :  8.9e-3

Sample variance                       :    0.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.07
p-value of test                       :    0.98

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:02.05
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 10  CollisionOver, t = 14           0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 170000400.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5290
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:44.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:36.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:35.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:53.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:54.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:02.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7161
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:02.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:52.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:59.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.90
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:46.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     330
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:10.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     178
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:37.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.61
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.71
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.86
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.21
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:11.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.83
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.61
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.84
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  196.88
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.27
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:46.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1318.77
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:02.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6940.02
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:47.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.41
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.35
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:06.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.67
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:46.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   92.44
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:36.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5092.00
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:00.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45892
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869892
  j =  1                              :        399908220
  j =  2                              :            45884
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45711
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869711
  j =  1                              :        399908579
  j =  2                              :            45709
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:31.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:20.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.51
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  6.4e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:03.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.18e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.49e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.04e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:36.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:36.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.06
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.25
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.31
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.00
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.77
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.71
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:42.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.91
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.63
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.61
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.61
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17228.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.97
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.43
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.68
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.90
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.14
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.80
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.67
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.24
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.16
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.14
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.35
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.53
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  564.60
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.24
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.02
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.33
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.73
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.30
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.09
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.92
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.31
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.79
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.51
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.68
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.13
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.56
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.11
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4988.50
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.24
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.12
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.90
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    1.27
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:23.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.91
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   0.083
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:22.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 7.30e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.55e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 9.84e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.14
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.74
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.01
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:06.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.84
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:07.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :  9.8e-4    *****

Anderson-Darling statistic = A2       :    3.96
p-value of test                       :  9.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10337.01
p-value of test                       :  9.1e-3

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9815.75
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.92
p-value of test                       :    0.9983

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:04:18.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4820.30
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:51.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4743.86
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:52.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4001.14
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4226.54
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11608.20
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:29.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11959.33
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:30.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.46
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999906737

Normal statistic for number of bits   :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.80
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999904643

Normal statistic for number of bits   :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 6.52e-3
p-value of test                       :    0.9931

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -2.13
p-value of test                       :    0.98

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:30.98

 All tests were passed




Server wird beendet - Lösche Semaphor 171048976.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5349
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:52.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:39.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:38.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:54.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:54.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:59.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:00.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:52.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:58.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.11
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.85
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:44.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    2.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:11.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:38.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.83
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.85
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.54
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.03
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.32
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.98
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  495.62
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:44.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1344.93
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:01.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7285.03
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:45.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.45
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.04
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:04.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.48
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:46.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.89
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:35.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5152.37
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:59.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46064
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870064
  j =  1                              :        399907874
  j =  2                              :            46060
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45570
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869570
  j =  1                              :        399908861
  j =  2                              :            45568
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:28.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:16.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:44.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 6.77e-4
p-value of test                       :    0.9993    *****

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  6.8e-3

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  4.8e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:00.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:57.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 6.59e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.30e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.67
p-value of test                       :    0.9962

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:21.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:36.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:36.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.36
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.81
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.12
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.93
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.49
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:37.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.05
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.34
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.17
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.83
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:39.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17174.21
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.14
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.97
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.27
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.11
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.91
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.79
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.09
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.32
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.16
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.15
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.66
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.88
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.23
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.14
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.24
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.37
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.27
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  558.48
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.43
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.83
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.74
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.19
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5119.28
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.13
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.93
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.13
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.08
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4988.26
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  319.39
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.36
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.23
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :    0.69
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:24.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.78
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:23.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 6.18e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.20
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.23
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.61
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:08.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.88
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:06.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10197.37
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9975.40
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.75
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:04:02.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4792.43
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:51.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4844.68
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:52.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3983.53
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3902.22
p-value of test                       :    0.9918

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11688.80
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:29.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11472.54
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:29.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.87
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999933035

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.16
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  7999936578

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.87

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   0.070
p-value of test                       :    0.47

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:33.25

 All tests were passed




Server wird beendet - Lösche Semaphor 172163088.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  1.0e-2


-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5436
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:57.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:40.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:40.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:56.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:03.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:02.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:51.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:58.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    3.58
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.36
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:11.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:38.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.03
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.99
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.61
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.77
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.72
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.96
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   82.24
p-value of test                       :  7.9e-3

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.63
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  396.07
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:44.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.97
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:00.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7016.51
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.35
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.58
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:02.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.95
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.82
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:32.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5147.16
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:13.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:57.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45893
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869893
  j =  1                              :        399908216
  j =  2                              :            45889
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45966
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869966
  j =  1                              :        399908073
  j =  2                              :            45956
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9981

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:28.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :  2.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:18.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:44.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:58.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:35.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.70e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:36.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.00
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.67
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.72
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.82
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:51.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.35
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:37.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.47
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.99
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.28
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.43
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17354.21
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.59
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.81
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.90
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.51
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.78
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.03
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.81
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.66
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.42
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.45
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.79
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.72
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.12
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  170.23
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.55
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.33
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.99
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.93
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.08
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.28
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.76
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.99
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4686.74
p-value of test                       :    0.9993    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.96
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.31
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.87
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.11
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.58
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.11
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.62
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.37
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:25.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.84
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :    1.56
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:23.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.57e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 7.10e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.23e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 7.77e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.37
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.03
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.11
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:07.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.53
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:05.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10047.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10169.65
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:47.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.99
p-value of test                       :  9.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4634.75
p-value of test                       :    0.9956

-----------------------------------------------
CPU time used                    :  00:01:49.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.72
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:50.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.77
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.26
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11975.36
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:29.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12098.51
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:30.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.07
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999968711

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.83
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999875273

Normal statistic for number of bits   :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 5.07e-4
p-value of test                       :    0.9995    *****

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -2.16
p-value of test                       :    0.98

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:25.94
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 J (L=10000, r=0)    0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 173211664.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1486
p-value of test                       :  6.0e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334606
  j =  1                              :        599997028
  j =  2                              :             1486
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5362
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:01.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:42.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:44.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4429
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:58.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:58.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7106
p-value of test                       :    0.9936


-----------------------------------------------
CPU time used                    :  00:03:06.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:06.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:54.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:57.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.72
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:51.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:16.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:45.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.37
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.81
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.97
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    5.91
p-value of test                       :    0.9966

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.11
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.98
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.86
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.87
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.45
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.05
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:42.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1470.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:59.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7075.36
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.64
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:07.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.44
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.69
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:34.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4967.70
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:01.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45760
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869760
  j =  1                              :        399908488
  j =  2                              :            45744
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45995
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869995
  j =  1                              :        399908013
  j =  2                              :            45989
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:29.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:16.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:43.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:58.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:55.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:34.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.12e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 2.37e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.010
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:21.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:36.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.84
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:47.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.76
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.15
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.97
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:49.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.86
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.11
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:38.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.66
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.11
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.56
p-value of test                       :  9.1e-3

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.72
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.35
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17504.79
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.69
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.13
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.58
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.34
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.32
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.99
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.99
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.25
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.06
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.06
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.26
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.92
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  551.03
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.82
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.07
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.77
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.02
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  572.56
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.20
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.92
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.54
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.27
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4897.24
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.70
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  159.06
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.11
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.76
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.02
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.41
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.84
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:34.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.06
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :    1.71
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:23.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.44
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :   -1.88
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:22.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.22e-3
p-value of test                       :    0.9956

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.21
p-value of test                       :    0.01

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.17
p-value of test                       :    0.9973

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.29e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.29e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.38
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.06
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.82
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:05.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.10
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:05.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10114.96
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10098.94
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.042
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:48.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4808.13
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.02
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:51.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.83
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4046.30
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11794.11
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:29.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11855.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:32.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.31
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000047824

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.37
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999979718

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.0e-3

Anderson-Darling statistic = A2       :    3.75
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.23
p-value of test                       :    0.01

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   0.093
p-value of test                       :    0.46

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:08.93
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14           6.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 174194704.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5440
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:04:01.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:44.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:45.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:59.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:07.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7198
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:06.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:54.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:58.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:52.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.14
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.73
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     269
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:17.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:44.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.33
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.74
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.74
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.51
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.26
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.59
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.61
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.73
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.56
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  470.52
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:44.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.24
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:00.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7181.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:43.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.21
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.94
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:04.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.60
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.08
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:33.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4951.05
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:54.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45969
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869969
  j =  1                              :        399908065
  j =  2                              :            45963
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46002
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870002
  j =  1                              :        399907996
  j =  2                              :            46002
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:28.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:16.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:43.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:58.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:59.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:40.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 9.85e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:21.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:37.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:36.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.76
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:49.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.73
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.35
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.45
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.01
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.05
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.39
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:37.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.40
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.80
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.71
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   10.18
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.35
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17425.47
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.29
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.81
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.90
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.62
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.89
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.57
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.12
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.92
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.95
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.79
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.03
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.23
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.59
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.53
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.08
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.74
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.67
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.15
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.51
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.93
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:43.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.97
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.40
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4947.56
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.40
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.70
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.70
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.03
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4944.85
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.51
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.49
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.23
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -2.05
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:21.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.75
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:21.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 7.47e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 6.89e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.91
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.49
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.03
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:05.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.58
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:06.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9862.14
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10102.97
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:42.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5007.24
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:47.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.05
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:50.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4020.98
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4033.13
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11727.40
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11811.91
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.88
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000091669

Normal statistic for number of bits   :    0.72
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.75
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999973613

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.50
p-value of test                       :    0.93

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:47.90

 All tests were passed




Server wird beendet - Lösche Semaphor 175243280.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5415
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:04:00.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:43.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7179
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:44.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:59.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:01.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:09.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:08.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:55.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:59.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:52.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:16.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    2.13
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:17.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     127
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:48.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.01
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.25
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.56
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.96
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.80
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.12
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.24
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  200.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.06
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:44.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1363.14
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:01.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6933.70
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.12
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:03.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.12
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.30
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:31.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4967.43
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:54.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45940
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869940
  j =  1                              :        399908123
  j =  2                              :            45934
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45713
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869713
  j =  1                              :        399908574
  j =  2                              :            45713
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:27.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:18.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:44.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:58.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:55.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9945

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:35.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.27e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 8.17e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.18
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:35.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:37.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.97
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.97
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.04
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.42
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.02
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.00
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    3.34
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.03
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   61.61
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.64
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.12
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.93
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.74
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17128.66
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.11
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.93
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.43
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.77
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.21
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.98
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.00
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.28
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.09
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.44
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.82
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.72
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.52
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.76
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.71
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.67
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.03
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.90
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.91
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.06
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:42.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.64
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.84
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4891.95
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.29
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  257.65
p-value of test                       :  3.7e-3


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.58
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.63
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4928.82
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  440.49
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.49
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:34.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.16
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :  -0.028
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:22.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.44
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:22.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.23
p-value of test                       :    0.9908

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.65e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 5.93e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.24
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.10
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.27
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:05.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.39
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:06.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10050.50
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9942.04
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:38.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4761.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4811.26
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:50.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4049.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.87
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11878.18
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:29.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11335.97
p-value of test                       :    0.9994    *****

-----------------------------------------------
CPU time used                    :  00:01:30.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.73
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000032239

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.72
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999951794

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :  -0.062
p-value of test                       :    0.52

Sample variance                       :    2.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.57

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.90

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:09.97
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 100  HammingIndep, L=1200, r=25      0.9994 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 176291856.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5442
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:59.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:42.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:44.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:00.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:02.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:11.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:09.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:58.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:00.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.14
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:51.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:09.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.9903

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:38.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.66
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.17
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.26
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.93
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.38
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.00
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.68
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.78
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.03
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:44.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.48
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:00.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6818.74
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:42.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.75
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.38
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:04.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.12
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  152.40
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5011.16
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:52.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45933
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869933
  j =  1                              :        399908139
  j =  2                              :            45923
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46317
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870317
  j =  1                              :        399907374
  j =  2                              :            46301
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:27.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:18.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:45.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:59.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:55.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:34.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.14e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 2.47e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 9.79e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:37.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   95.61
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   38.56
p-value of test                       :    0.9979

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.33
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.59
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.75
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.18
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:45.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.71
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.45
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.028
p-value of test                       :    0.9988

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:15.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.08
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17412.74
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.91
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   16.88
p-value of test                       :    0.9958


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.42
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.19
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.93
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.28
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.76
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.23
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.93
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.21
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:37.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.73
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.80
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.01
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.98
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.05
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.62
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.48
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.18
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.26
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.14
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.88
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.02
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4913.83
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.29
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.44
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.63
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.82
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.23
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.84
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.37
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.48
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:22.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.83
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:23.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.69e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 8.75e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.01
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.90
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.77
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:05.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:05.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10139.05
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9773.99
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:38.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4962.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:47.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.24
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:49.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4039.29
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4078.85
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11727.96
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12002.39
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:31.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.21
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000081193

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.71
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000017338

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:05.96

 All tests were passed




Server wird beendet - Lösche Semaphor 177340432.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5609
p-value of test                       :  5.6e-3


-----------------------------------------------
CPU time used                    :  00:04:04.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4234
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:45.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:48.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4480
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:02.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:03.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:16.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7180
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:16.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:04:09.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:06.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.09
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.20
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.51
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    4.22
p-value of test                       :  6.8e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     271
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:19.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.07
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.76
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.94
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:47.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.14
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.91
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.23
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.70
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.71
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:09.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.74
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.76
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.56
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.66
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.71
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:51.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.47
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:04.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7011.14
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:55.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.57
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.85
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:17.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4886.08
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:01.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45966
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869966
  j =  1                              :        399908073
  j =  2                              :            45956
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45870
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869870
  j =  1                              :        399908267
  j =  2                              :            45856
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:31.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:20.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:50.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:06.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:55.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:24.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.066
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:41.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:42.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.15
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.31
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.54
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.95
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.63
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.37
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.52
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.97
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.11
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17686.58
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.74
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.77
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.07
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.92
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.21
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.59
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.32
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.85
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.79
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.50
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.21
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.58
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.85
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.43
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.60
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.08
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.89
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.06
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.36
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.44
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.40
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.61
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5036.56
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  445.77
p-value of test                       :  9.3e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.46
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.99
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.33
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.26
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.35
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.11
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.19
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:23.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.36
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:23.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 3.97e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.25e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.64
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.54
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.66
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:06.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.90
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:04.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10013.43
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10023.49
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:10.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:04:30.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4835.46
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:54.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:58.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4226.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4180.43
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11873.55
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:34.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11961.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:36.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.43
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999900692

Normal statistic for number of bits   :   -0.79
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.71
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000099310

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :  -0.015
p-value of test                       :    0.51

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:38.02

 All tests were passed




Server wird beendet - Lösche Semaphor 178389008.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1465
p-value of test                       :  3.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334585
  j =  1                              :        599997070
  j =  2                              :             1465
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5388
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:59.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:43.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:45.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:59.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:00.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:08.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:05.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:54.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:59.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:50.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.93
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:12.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:40.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.58
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.61
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.61
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.94
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.19
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  475.79
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:44.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1486.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:01.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7068.95
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.00
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   86.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:04.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.62
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.83
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:33.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5071.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:54.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45780
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869780
  j =  1                              :        399908441
  j =  2                              :            45778
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46105
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870105
  j =  1                              :        399907794
  j =  2                              :            46097
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 6.49e-3
p-value of test                       :    0.9916

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :  5.3e-3

Anderson-Darling statistic = A2       :    5.07
p-value of test                       :  2.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  8.3e-4    *****


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 5.40e-3
p-value of test                       :    0.9933

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.82
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:27.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:17.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:44.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:57.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:35.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -3.31
p-value of test                       :    0.9995    *****

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:39.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:37.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.53
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.73
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.02
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.09
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.62
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:39.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.15
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.68
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.06
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.01
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  164.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17448.50
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.25
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.77
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.22
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.64
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.32
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.89
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.84
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.58
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.35
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   33.78
p-value of test                       :  9.0e-3


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.87
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.13
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  563.82
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.78
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.24
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.44
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.55
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.73
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.40
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.36
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.06
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5231.03
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.37
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.89
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.59
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  445.70
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4888.12
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.97
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.32
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.04
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :    1.58
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:22.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.08
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  : -1.49e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:21.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.88e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 8.42e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.48
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.34
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.09
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:04.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.42
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:06.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10197.59
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9819.01
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:45.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.81
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:49.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.83
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:50.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.24
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.36
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11713.29
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11743.13
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:29.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.56
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999845063

Normal statistic for number of bits   :   -1.22
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.78
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000101833

Normal statistic for number of bits   :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:55.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 46  MaxOft, t = 8                   8.3e-4
 56  SampleCorr, k = 2               0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 179470352.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:38.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5381
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:03.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4245
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:43.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:45.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:00.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4227
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:58.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:07.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:07.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:55.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:59.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:51.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:12.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.67
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.83
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.15
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.49
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.56
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.76
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.61
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  280.54
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.80
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:44.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1359.02
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:00.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7121.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.31
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.59
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:03.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.37
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.35
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5000.78
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:54.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46007
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870007
  j =  1                              :        399907989
  j =  2                              :            46001
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45671
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869671
  j =  1                              :        399908661
  j =  2                              :            45665
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:27.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 3.44e-3
p-value of test                       :    0.9962

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:18.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:45.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:58.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:02.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.50
p-value of test                       :  5.1e-3

-----------------------------------------------
CPU time used                    :  00:01:41.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 2.71e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.07e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 3.62e-4
p-value of test                       :  5.2e-3

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:40.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.55
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.27
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.52
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.62
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.10
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:40.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.49
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 2.50e-4
p-value of test                       :    0.9997    *****

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.57
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.08
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.26
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:39.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17191.80
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.32
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.76
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.01
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.73
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.42
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.46
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.34
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.82
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.44
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.79
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.24
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.58
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.48
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.22
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.62
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.45
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.62
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.87
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  173.98
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.89
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:43.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.56
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.55
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5121.15
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.87
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.28
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.97
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  446.21
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5044.66
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.95
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.99
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.00
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:22.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.97
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :   -0.86
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:22.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.96
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.44e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.27e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 8.19e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.32
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.21
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.87
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:03.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.48
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:06.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.59
p-value of test                       :  3.4e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.03
p-value of test                       :  8.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9653.20
p-value of test                       :    0.9934

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10178.03
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:44.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4783.59
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:49.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :  1.3e-3

Anderson-Darling statistic = A2       :    3.46
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5071.63
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.90
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4018.49
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11631.17
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:29.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11898.79
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:31.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.00
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999943331

Normal statistic for number of bits   :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.31
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999993275

Normal statistic for number of bits   :  -0.053
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :  1.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.50
p-value of test                       :  5.3e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.82
p-value of test                       :    0.9976

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :  -0.075
p-value of test                       :    0.53

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:28.73

 All tests were passed




Server wird beendet - Lösche Semaphor 180518928.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5643
p-value of test                       :  1.4e-3


-----------------------------------------------
CPU time used                    :  00:04:01.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:44.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:46.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:00.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:00.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7198
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:11.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:06.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:55.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:00.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:52.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    2.23
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     259
p-value of test                       :    0.9914

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:18.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    3.79
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:47.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.98
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.94
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.48
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.07
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.74
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.42
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.05
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.16
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:44.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.12
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:00.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7002.40
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:44.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.73
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.47
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:03.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.34
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.86
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:33.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5036.84
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:54.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45799
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869799
  j =  1                              :        399908406
  j =  2                              :            45791
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46073
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870073
  j =  1                              :        399907858
  j =  2                              :            46065
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:27.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:17.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:45.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:01.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:55.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:33.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.86e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:38.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.96
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.83
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.49
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.39
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.01
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:38.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.05
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.50
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.37
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.24
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:39.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  8.3e-3

Anderson-Darling statistic = A2       :    3.27
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17754.88
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:51.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.03
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.93
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.91
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.46
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.88
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.30
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.97
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.40
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.13
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.62
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.07
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.17
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.63
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.37
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.56
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.78
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.00
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.12
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.68
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.05
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.09
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.38
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4924.01
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.47
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.01
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.40
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.45
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4931.53
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.94
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.75
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.99
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :   -1.50
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:21.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.62
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :   -1.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:21.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 6.53e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.61e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 5.66e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.05
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.84
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.12
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:05.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.12
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:06.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.01
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10125.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:38.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4967.26
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4931.54
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:49.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.88
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4178.47
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11816.39
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11675.71
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:30.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.35
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999955145

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.23
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000011380

Normal statistic for number of bits   :   0.090
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:14.57

 All tests were passed




Server wird beendet - Lösche Semaphor 181567504.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:38.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5569
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:59.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:45.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4418
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:58.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:59.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:09.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:09.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:58.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7501
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:04:00.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.78
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:53.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.13
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:17.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    2.91
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:49.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.98
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.04
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.46
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.58
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.38
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.90
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   86.83
p-value of test                       :  3.1e-3

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.21
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.51
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  358.37
p-value of test                       :    0.9966

-----------------------------------------------
CPU time used                    :  00:01:44.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1445.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:01.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7081.11
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:04.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.61
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.12
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:33.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4920.38
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:11.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46003
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870003
  j =  1                              :        399907999
  j =  2                              :            45993
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45976
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869976
  j =  1                              :        399908051
  j =  2                              :            45970
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:28.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:18.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:45.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:00.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:54.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:33.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 9.65e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 2.54e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:39.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.16
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   99.89
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.24
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.28
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.89
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.78
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.41
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:39.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.66
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.09
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.54
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.50
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.05
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.38
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17232.61
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.53
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.40
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.12
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.30
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.46
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.82
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.81
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.46
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.85
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.43
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:36.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.54
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.49
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.21
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.43
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.75
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.25
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.42
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.48
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.40
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.34
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.13
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.74
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.68
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.66
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.12
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.64
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.02
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.80
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.36
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.42
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:21.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.31
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:21.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   0.033
p-value of test                       :    0.49

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.14
p-value of test                       :    0.98

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 9.93e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.55
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.19
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.76
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:04.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:06.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9896.39
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10073.47
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.94
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:40.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.96
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:48.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4976.58
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:50.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4273.04
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3998.23
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11762.36
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11946.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.97
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000042877

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.22
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999934742

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.045
p-value of test                       :    0.48

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:41.61

 All tests were passed




Server wird beendet - Lösche Semaphor 182616080.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5402
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:58.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:43.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:45.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:59.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4441
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:59.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:09.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:09.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:04:00.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:01.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:50.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.30
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.71
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    2.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:14.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.38
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     125
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:49.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.11
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.93
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.58
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.30
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.46
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.61
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.52
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.13
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.18
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.47
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1466.38
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:02.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6971.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:44.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.06
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.33
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:05.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.94
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.19
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:32.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5129.82
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:01.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46113
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870113
  j =  1                              :        399907776
  j =  2                              :            46109
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45659
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869659
  j =  1                              :        399908684
  j =  2                              :            45655
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:28.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:19.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:45.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:01.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:55.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:32.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.22e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.28e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:37.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:38.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.80
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:49.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.18
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.58
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.95
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.07
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.06
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.47
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:39.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.36
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.02
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.41
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17545.68
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.24
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.68
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.97
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.65
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.32
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.79
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.90
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.90
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.11
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.44
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.54
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.05
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.42
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.28
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.92
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.44
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.69
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.87
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.15
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.58
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5198.37
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.86
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.66
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.71
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  443.40
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.88
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.00
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.27
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.94
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:23.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.40
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :    1.11
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:23.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.55e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 7.47e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9907

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 5.62e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.83
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.45
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.23
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:05.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.14
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:05.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10073.23
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.3e-3

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10251.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.50
p-value of test                       :  6.2e-3

-----------------------------------------------
CPU time used                    :  00:03:40.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4895.51
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4977.74
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.99
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.58
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11700.63
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11814.81
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:29.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.53
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000032419

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   82.16
p-value of test                       :  8.0e-3


-----------------------------------------------
Total number of bits:  7999812954

Normal statistic for number of bits   :   -1.48
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.14

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:44.62

 All tests were passed




Server wird beendet - Lösche Semaphor 183631888.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:49.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5476
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:01.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:43.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:46.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:58.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4432
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:00.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:09.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:11.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:59.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:04:01.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:50.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.75
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.15
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    4.83
p-value of test                       :  3.5e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     676
p-value of test                       :  1.2e-3

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:17.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9915

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:43.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.20
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.07
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.00
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.61
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.95
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.74
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.57
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:44.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.24
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:01.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7250.35
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:44.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.67
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:02.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.00
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  146.68
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:31.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5109.97
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:04.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45774
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869774
  j =  1                              :        399908456
  j =  2                              :            45766
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45714
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869714
  j =  1                              :        399908574
  j =  2                              :            45710
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:27.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:18.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:45.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:00.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-3
p-value of test                       :    0.9987

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.84
p-value of test                       :  3.5e-3

-----------------------------------------------
CPU time used                    :  00:01:54.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:33.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.24e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 9.01e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:36.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:38.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.19
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.02
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.80
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.65
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.90
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.12
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:38.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.29
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.52
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.30
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.92
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:16.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.60
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17754.01
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.49
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.19
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.64
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   44.69
p-value of test                       :  6.3e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.97
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.59
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.66
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.30
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.91
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.65
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.62
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.30
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.94
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.64
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.66
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.72
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.57
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.98
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.21
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.86
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.69
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4967.54
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.83
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.99
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.75
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.23
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5122.03
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.50
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.93
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.16
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -0.48
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:21.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.23
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:21.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.38

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 4.00e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 2.76e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.85
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.13
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.41
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:06.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.71
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:05.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10116.04
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10099.78
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.073
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:41.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.36
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:48.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4970.52
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:50.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3923.73
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4036.00
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11734.78
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11931.49
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.89
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999987008

Normal statistic for number of bits   :   -0.10
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   32.51
p-value of test                       :    0.9910


-----------------------------------------------
Total number of bits:  8000037438

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    2.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:31.69

 All tests were passed




Server wird beendet - Lösche Semaphor 184680464.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:49.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5446
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:01.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:43.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:47.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:59.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4200
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:00.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:10.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:11.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:01.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:02.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:50.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:16.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.53
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    2.42
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:45.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.07
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.64
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.53
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.23
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.33
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.18
p-value of test                       :    0.9920

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.58
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.19
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:44.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1506.42
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:01.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7119.05
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:44.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.70
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.20
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:03.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.83
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.78
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:33.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4948.30
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:02.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45950
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869950
  j =  1                              :        399908102
  j =  2                              :            45946
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45833
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869833
  j =  1                              :        399908341
  j =  2                              :            45819
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:27.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:18.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:45.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:00.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:54.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:32.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.14e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:33.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:35.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.83
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.66
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.10
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.13
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.76
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.86
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:39.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.88
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.26
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.20
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17227.14
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.07
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.48
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.90
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.31
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.14
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:37.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.83
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.96
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.53
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.55
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.07
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  107.86
p-value of test                       :    0.9923


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.40
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.38
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.91
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.19
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.31
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.55
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.05
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.60
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.73
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.62
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.30
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.03
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.75
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.81
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.50
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.54
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5089.17
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.66
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.69
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.58
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :   0.016
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:21.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.26
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:21.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.50e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 8.85e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.89e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.56
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.75
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:05.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.85
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:05.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10037.04
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10168.63
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:40.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4928.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:48.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4820.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:49.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4223.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4012.34
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12000.01
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11827.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:30.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.03
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000029731

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.56
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999968120

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   0.082
p-value of test                       :    0.47

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.66

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:19.87

 All tests were passed




Server wird beendet - Lösche Semaphor 185729040.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5583
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:04:01.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:43.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:45.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:00.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:00.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:10.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:10.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:58.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:05.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:49.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.92
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:15.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:46.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.42
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.91
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.59
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.07
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.64
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:10.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.39
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.41
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  199.45
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.20
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:47.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1443.97
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:01.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6903.13
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:43.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.18
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.18
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:03.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.94
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.43
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:30.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5205.06
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:11.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:21.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46031
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870031
  j =  1                              :        399907942
  j =  2                              :            46023
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46207
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870207
  j =  1                              :        399907590
  j =  2                              :            46199
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  9.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.14
p-value of test                       :  7.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9965


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:26.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:17.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:45.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:00.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:33.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.98e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 4.45e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:27.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.024
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:21.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:32.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:33.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.60
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:49.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.05
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.48
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.22
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.49
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.06
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.02
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:39.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.83
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.99
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.13
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.27
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17270.88
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.84
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.83
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.17
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.34
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.23
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.54
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.47
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.37
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.68
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.67
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:40.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.17
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.05
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.39
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.21
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.59
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.53
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.28
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.06
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.64
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.18
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:50.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.80
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.96
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4817.54
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.80
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.38
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.58
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.79
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4960.46
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.14
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.24
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.62
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:22.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.41
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:22.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    5.29
p-value of test                       :  2.2e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -3.08
p-value of test                       :    0.9989

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 9.41e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.80e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.27
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.40
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.43
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:04.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.75
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:05.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.99e-3
p-value of test                       :    0.9926

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10329.62
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9976.92
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:40.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4980.32
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:50.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4148.88
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.35
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11751.37
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11785.93
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.46
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999998075

Normal statistic for number of bits   :  -0.015
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.63
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000180811

Normal statistic for number of bits   :    1.43
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.84
p-value of test                       :    0.03

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.76

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:00.46

 All tests were passed




Server wird beendet - Lösche Semaphor 186777616.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5520
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:00.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:43.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:45.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:00.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:01.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:11.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:11.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:59.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:05.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:51.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:15.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    3.95
p-value of test                       :  9.3e-3

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:46.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.28
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.62
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.08
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.30
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.21
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.10
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.86
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.85
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.72
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:44.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1376.49
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:00.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7000.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:42.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.52
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.26
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:03.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.40
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.06
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5009.78
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:20.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46187
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870187
  j =  1                              :        399907631
  j =  2                              :            46177
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45690
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869690
  j =  1                              :        399908625
  j =  2                              :            45680
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:26.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:18.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:45.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  7.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.32
p-value of test                       :  6.3e-3


-----------------------------------------------
CPU time used                    :  00:02:01.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:54.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:15.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:33.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.60e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 5.14e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.49e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:33.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:35.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.98
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.83
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.14
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.31
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.74
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:42.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.67
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.76
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.93
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.055
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.56
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:39.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17500.94
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.61
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.09
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.46
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.03
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.07
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.17
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.02
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.33
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.98
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.58
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.58
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.61
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.16
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.58
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.56
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.92
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.14
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.33
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.79
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.20
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.11
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.49
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5108.48
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.28
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.40
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.86
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.70
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5111.36
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.05
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.53
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.37
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:22.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.86
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :   -1.27
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:21.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 9.84e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.09
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.49
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 7.59e-3
p-value of test                       :    0.9919

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:03.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.16
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:04.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10029.42
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10145.55
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:40.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.61
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:48.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4784.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:50.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4201.04
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4000.04
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12009.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11938.52
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.86
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999927836

Normal statistic for number of bits   :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.91
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000121066

Normal statistic for number of bits   :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.38
p-value of test                       :    0.9913

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :  -0.029
p-value of test                       :    0.51

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:48.18

 All tests were passed




Server wird beendet - Lösche Semaphor 187826192.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:22.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:18.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:18.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:23.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:35.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5472
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:46.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:38.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:38.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4486
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:56.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4197
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:57.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:06.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:07.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:04.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:04:05.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.01
p-value of test                       :  8.8e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    2.49
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    2.16
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:42.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:17.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.71
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:48.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.58
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.97
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.55
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.18
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.15
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.37
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:29.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.86
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:53.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1481.15
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:07.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6930.65
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:55.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.52
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.69
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:17.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.80
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.40
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:43.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5125.87
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:31.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:06.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45634
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869634
  j =  1                              :        399908733
  j =  2                              :            45632
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46086
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870086
  j =  1                              :        399907832
  j =  2                              :            46078
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 7.59e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:30.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :  3.5e-3

Anderson-Darling statistic = A2       :    3.43
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:16.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:02.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:56.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:38.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 5.64e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:24.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:24.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:24.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:50.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:50.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.84
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.62
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.94
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.33
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.53
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.70
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:52.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.58
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.81
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:29.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.03
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17049.79
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.79
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.14
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.36
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.19
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.27
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.40
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.14
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.36
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.17
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.62
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.76
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.77
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  551.91
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.76
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.51
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  106.28
p-value of test                       :    0.9944


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.61
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.02
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   98.09
p-value of test                       :    0.9940


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.96
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:46.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.36
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.42
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5097.68
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.64
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.61
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.81
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.13
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.31
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.00
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.06
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.82
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:29.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.92
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:25.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 9.41e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.55e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.04
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.64
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.03
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:08.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.00
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:08.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9982.17
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10116.73
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:11.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:04:29.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4798.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5023.72
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4253.05
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4207.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12194.48
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:01:34.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12131.66
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:32.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.74
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000102043

Normal statistic for number of bits   :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.94
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000027967

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:24:13.36

 All tests were passed




Server wird beendet - Lösche Semaphor 168460305.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:47.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5279
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:49.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:39.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:39.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:55.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:56.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7453
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:04.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:04.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:54.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:03.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    1.95
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.59
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.78
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     328
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    4.48
p-value of test                       :  5.1e-3

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:16.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.97
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:45.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.28
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.90
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.89
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.52
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:11.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.68
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.21
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.33
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.14
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:44.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1427.66
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:00.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7270.45
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.65
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.42
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:03.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.46
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.66
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:34.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5126.08
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:58.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45849
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869849
  j =  1                              :        399908304
  j =  2                              :            45845
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46058
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870058
  j =  1                              :        399907884
  j =  2                              :            46058
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:24.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:15.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:44.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:57.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:54.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:33.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.01e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:22.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.66
p-value of test                       :  3.9e-3

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:32.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:32.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.08
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:49.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.56
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.99
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.20
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.98
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.42
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.68
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:42.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.78
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.76
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:31.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.54
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.13
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17512.52
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:55.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.94
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.70
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.38
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.79
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.62
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.41
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.14
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.67
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.48
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.46
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.82
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.89
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.91
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.22
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.08
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:46.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.92
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.88
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  544.76
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.45
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.07
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.83
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.37
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.18
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.59
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.09
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.64
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.26
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4972.29
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.82
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.22
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:36.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.02
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:28.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.83
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :    1.10
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:28.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.40e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 9.65e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:47.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.31e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 9.54e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.47
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:28.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.47
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.01
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:08.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.31
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:09.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10013.74
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10066.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:44.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4737.42
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4786.08
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:51.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4036.26
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11808.81
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11624.37
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.11
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000061000

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.33
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000141319

Normal statistic for number of bits   :    1.12
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:27.42

 All tests were passed




Server wird beendet - Lösche Semaphor 169902097.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:47.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5506
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:50.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4236
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:39.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:39.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:55.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:57.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7567
p-value of test                       :  1.9e-3


-----------------------------------------------
CPU time used                    :  00:03:04.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:04.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7498
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:54.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:04:02.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:50.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:19.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:49.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.26
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.74
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.63
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   36.35
p-value of test                       :  6.4e-3

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.03
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.93
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.19
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.30
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.53
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.55
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:43.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.97
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:57.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6927.29
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:47.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.58
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   14.58
p-value of test                       :    0.9919

-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.91
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:04.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.18
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.37
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:35.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5079.64
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:01.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45575
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869575
  j =  1                              :        399908852
  j =  2                              :            45571
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45720
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869720
  j =  1                              :        399908562
  j =  2                              :            45716
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:26.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:16.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:45.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:01.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:54.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:32.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.92e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.45e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:21.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:22.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.89
p-value of test                       :    0.9981

-----------------------------------------------
CPU time used                    :  00:01:34.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:37.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.37
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.85
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.91
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:55.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.64
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:40.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.64
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.46
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.04
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:30.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17525.79
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.48
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.22
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.15
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.76
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.00
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.52
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.82
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.08
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.71
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.14
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.47
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.99
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.70
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.23
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.82
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.53
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.98
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.26
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.86
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.94
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  322.71
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.04
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.59
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.07
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:36.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.08
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.33
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4843.00
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.55
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.50
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.78
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :    0.51
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:24.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.10
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:24.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 8.03e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.18
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.91
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.98
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:09.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.93
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:09.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9947.62
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10164.05
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.074
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:42.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4773.73
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:49.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4946.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:51.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.62
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.33
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11628.66
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.73
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:30.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.67
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999885143

Normal statistic for number of bits   :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.70
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000060985

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   0.052
p-value of test                       :    0.48

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:58.10

 All tests were passed




Server wird beendet - Lösche Semaphor 170917905.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1462
p-value of test                       :  4.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334582
  j =  1                              :        599997076
  j =  2                              :             1462
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5448
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:04:02.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:47.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:54.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:16.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:16.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:37.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:37.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:05:07.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:05:14.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.99
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.75
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.75
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:15.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:45.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.52
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.28
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.03
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.06
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.12
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.04
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.85
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.74
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.67
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:48.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1397.24
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:03.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7052.79
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:51.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.09
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:13.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.39
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.94
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:38.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5053.93
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:03.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45842
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869842
  j =  1                              :        399908318
  j =  2                              :            45838
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46047
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870047
  j =  1                              :        399907910
  j =  2                              :            46039
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:29.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:17.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:44.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:00.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:35.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:42.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:44.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.60
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.87
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.56
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.62
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.83
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.25
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:48.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.61
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:12.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.08
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:12.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:29.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.07
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.86
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:39.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17611.32
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.60
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.84
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.92
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.34
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.53
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.39
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.71
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :    7.46
p-value of test                       :    0.9997    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.68
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.85
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.72
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.48
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.56
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.06
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.90
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.14
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.69
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.67
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   92.61
p-value of test                       :    0.9983


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.40
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.44
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.92
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5155.76
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  436.12
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.92
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  321.72
p-value of test                       :    0.9908


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.38
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5180.87
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.92
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.62
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.11
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:25.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.72
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:26.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.98
p-value of test                       :    0.98

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 7.15e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 3.86e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.82
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.57
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.55
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:06.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.09
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:07.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10105.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9941.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:10.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:04:27.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.41
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:53.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.51
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:55.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4198.77
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4304.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11753.55
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:34.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11500.19
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:31.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.91
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999949268

Normal statistic for number of bits   :   -0.40
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.11
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999935396

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 4.33e-3
p-value of test                       :    0.9955

Anderson-Darling statistic = A2       :    3.48
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.71
p-value of test                       :    0.9967

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:16:36.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 75  RandomWalk1 J (L=50, r=25)      0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 171737105.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5545
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:50.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:39.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:38.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4160
p-value of test                       :    0.9965


-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7448
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:04.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:05.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:56.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:02.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:46.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.63
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:08.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.74
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:36.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.36
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.88
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.90
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.65
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.73
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.04
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.52
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:41.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.15
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:00.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7061.21
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:41.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.05
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:13.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  4.3e-3

Anderson-Darling statistic = A2       :    4.85
p-value of test                       :  3.6e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   94.48
p-value of test                       :  3.0e-3

-----------------------------------------------
CPU time used                    :  00:03:03.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.94
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.04
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:35.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5111.98
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:58.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46103
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870103
  j =  1                              :        399907797
  j =  2                              :            46097
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45816
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869816
  j =  1                              :        399908370
  j =  2                              :            45812
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:27.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:18.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:45.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:00.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:54.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:32.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.94e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:22.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:33.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:34.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.17
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.55
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.46
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.48
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.06
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.97
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.59
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.04
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.85
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.23
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.15
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17578.68
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.79
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.28
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.81
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.15
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.92
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.95
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.46
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.06
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.56
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.62
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.16
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.67
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.27
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.98
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.15
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:48.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.09
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.89
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  439.72
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.19
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.68
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:47.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.14
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.93
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.54
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.91
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:39.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.52
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.69
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.87
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.02
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.78
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:39.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.28
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:25.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.70
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :   -1.26
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:27.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    2.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.38e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:46.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.77e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.91
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.82
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  154.15
p-value of test                       :    0.9931

-----------------------------------------------
CPU time used                    :  00:02:07.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.20
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:09.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10179.00
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9919.82
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:46.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4934.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:48.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.92
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:50.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.98
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4182.87
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11834.36
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11890.69
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:29.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.43
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999975452

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.93
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  7999971417

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.69
p-value of test                       :  1.6e-5    *****

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    6.39
p-value of test                       :  6.9e-4    *****

Tests on the sum of all N observations
Standardized normal statistic         :   -3.05
p-value of test                       :    0.9989

Sample variance                       :    0.22
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:44.95

 All tests were passed




Server wird beendet - Lösche Semaphor 172883985.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:40.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5407
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:50.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:39.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:57.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:57.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:08.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:08.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:04:05.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:10.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9922

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     859
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    2.28
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:49.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    3.55
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:14.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:44.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.78
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.49
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.32
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.02
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.41
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.11
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.21
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  271.41
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.83
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:55.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1378.12
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:00.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7106.36
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:55.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.85
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.08
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:16.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.58
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:46.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.36
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:40.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5092.66
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:58.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45709
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869709
  j =  1                              :        399908584
  j =  2                              :            45705
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45852
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869852
  j =  1                              :        399908300
  j =  2                              :            45844
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:32.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:19.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:50.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:06.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:37.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 8.09e-6
p-value of test                       :    0.9974

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:24.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:24.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:49.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:47.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.03
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.12
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.60
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.14
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.25
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.00
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.94
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:48.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.73
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:29.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:29.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.63
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17291.98
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.18
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.01
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.25
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.33
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.54
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.71
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.79
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.65
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.29
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.11
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:38.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.95
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.71
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  544.70
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.12
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.10
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.09
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.44
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.14
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.43
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.84
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.29
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.57
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.76
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.80
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.84
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.38
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.42
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4864.67
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  435.08
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.26
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.17
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:28.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.52
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:26.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.0e-3

Anderson-Darling statistic = A2       :    4.83
p-value of test                       :  3.6e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.67
p-value of test                       :  3.8e-3

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.08e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:46.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.82e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 9.30e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.00
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:31.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.22
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.58
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:09.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.81
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:09.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9877.55
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9896.88
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:04:30.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4796.06
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:53.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.79
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4197.24
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.44
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11857.56
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:34.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11754.17
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:35.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.25
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999903476

Normal statistic for number of bits   :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.60
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999965729

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    1.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:15.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 6.02e-3
p-value of test                       :    0.9936

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.55
p-value of test                       :    0.94

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:49.13

 All tests were passed




Server wird beendet - Lösche Semaphor 173735953.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9967


-----------------------------------------------
CPU time used                    :  00:00:51.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5498
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:53.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:40.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4446
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7173
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:05.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:05.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:54.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:00.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.87
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     852
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:48.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.37
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    2.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:15.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     127
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:48.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.33
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.60
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.52
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.52
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:11.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.34
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  491.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.53
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7019.35
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:01.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.49
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.79
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4880.23
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:00.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45563
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869563
  j =  1                              :        399908875
  j =  2                              :            45561
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45476
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869476
  j =  1                              :        399909055
  j =  2                              :            45462
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:28.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:18.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:45.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:01.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:33.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.14
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:21.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:40.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:40.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.47
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:48.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.67
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.79
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.48
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.85
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:45.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.01
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.12
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.86
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   14.59
p-value of test                       :  2.2e-3

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.60
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17788.27
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.96
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.61
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.05
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.85
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.78
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.92
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.89
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.06
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.12
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.57
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.49
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.44
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.14
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.47
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.54
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.88
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.53
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.95
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.02
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.00
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.76
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.25
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5173.93
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.15
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  258.09
p-value of test                       :  3.5e-3


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.29
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.67
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4868.07
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.90
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.36
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.78
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:25.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.86
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:26.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   0.016
p-value of test                       :    0.49

Sample variance                       :    2.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 9.25e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:46.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.46e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 4.14e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.68
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.45
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.87
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:08.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.23
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:08.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9965.94
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10160.89
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.042
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:58.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.53
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:49.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.17
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4237.70
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4192.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11978.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11705.39
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:29.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.02
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999936764

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.17
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000010120

Normal statistic for number of bits   :   0.080
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.70
p-value of test                       :    0.04

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:40.39

 All tests were passed




Server wird beendet - Lösche Semaphor 174981137.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:50.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1520
p-value of test                       :  1.8e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334640
  j =  1                              :        599996960
  j =  2                              :             1520
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5411
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:52.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:40.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:39.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:56.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4247
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:04.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:05.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:55.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:01.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    3.47
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:46.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.18
p-value of test                       :    0.9953

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.16
p-value of test                       :    0.9978

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:13.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:40.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.84
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.45
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.98
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.57
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.98
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.29
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.14
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.01
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:00.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6883.74
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.33
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.27
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:02.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.22
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.39
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:35.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5103.76
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:57.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46016
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870016
  j =  1                              :        399907970
  j =  2                              :            46012
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45695
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869695
  j =  1                              :        399908620
  j =  2                              :            45675
  j =  3                              :               10
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:27.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:17.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:45.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:00.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:55.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:15.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 7.02e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:34.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:35.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.20
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:48.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.96
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.11
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.28
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.02
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.06
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:42.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.17
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.87
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   98.57
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17678.27
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:55.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.68
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.62
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.01
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.33
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.18
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.30
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.39
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.13
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.42
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.51
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.25
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.64
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.38
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.87
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.50
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.40
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.26
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.14
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.16
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.50
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.17
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.62
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.26
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.85
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.88
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.00
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.70
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.61
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.79
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.60
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:24.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.21
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:24.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :  -0.071
p-value of test                       :    0.53

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.20e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.77e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 4.73e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.00
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.21
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.17
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:07.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.11
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:08.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10089.20
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9946.29
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:46.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4729.32
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:49.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.01
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:51.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4172.11
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4231.33
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11874.63
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11797.49
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:30.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.41
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999966758

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.48
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999869945

Normal statistic for number of bits   :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :  -0.075
p-value of test                       :    0.53

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:26.96
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14           1.8e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 175996945.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  1.8e-3


-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5355
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:52.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:40.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7167
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:39.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:57.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:04.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:05.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:54.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7444
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:04:00.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    5.08
p-value of test                       :  2.6e-3

-----------------------------------------------
CPU time used                    :  00:01:48.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    2.33
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.84
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:15.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:43.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.72
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.65
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    4.34
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.61
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.54
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.74
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.63
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.80
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:43.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1390.61
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:00.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7141.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:42.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.94
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:13.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.11
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:03.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.82
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.63
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:35.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4994.34
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:56.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46048
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870048
  j =  1                              :        399907905
  j =  2                              :            46046
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45883
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869883
  j =  1                              :        399908235
  j =  2                              :            45881
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:28.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :  4.4e-3

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:18.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:45.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:59.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:55.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:33.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.26e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 4.26e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:37.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:37.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.81
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.33
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.48
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.17
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:47.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.91
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.18
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:42.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:29.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.33
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  159.52
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 4.58e-3
p-value of test                       :    0.9952

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17839.01
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.98
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.51
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.68
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.45
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.25
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.34
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.41
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.45
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.33
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.23
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.12
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.67
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.77
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.92
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.50
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.15
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.07
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.38
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  103.49
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.99
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.27
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.93
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4964.41
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.39
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.65
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.97
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.76
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4848.42
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.86
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.20
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.57
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :   0.057
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:24.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.03
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :   -1.39
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:24.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.59
p-value of test                       :    0.06

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.47e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.52e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   21.10
p-value of test                       :  6.9e-3

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.67
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.22
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:08.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.04
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:09.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9985.91
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10167.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.013
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:51.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4834.04
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:49.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4834.09
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:50.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.07
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11527.28
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11801.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:30.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.05
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999991838

Normal statistic for number of bits   :  -0.065
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.04
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999985049

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   0.071
p-value of test                       :    0.47

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:56.44
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 28  SimpPoker, r = 0                0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 176947217.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5441
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:53.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:39.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:38.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:04.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:05.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7193
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:55.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:00.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    3.22
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.07
p-value of test                       :  8.2e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.30
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    2.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:14.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:39.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.69
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:54.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.79
p-value of test                       :    0.9975

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.27
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.92
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.73
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.93
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.52
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  271.41
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.94
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:43.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1324.95
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:01.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7074.08
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:43.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.50
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.52
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:01.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.31
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.11
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:35.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5017.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:56.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45588
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869588
  j =  1                              :        399908828
  j =  2                              :            45580
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46305
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870305
  j =  1                              :        399907397
  j =  2                              :            46291
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:28.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:17.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:59.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9978

-----------------------------------------------
CPU time used                    :  00:01:55.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.83e-3
p-value of test                       :    0.9959

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:35.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.23e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 8.22e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.90e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.64e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:35.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:35.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.66
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.51
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.73
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.86
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.37
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.18
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.30
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:43.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.92
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.40
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.94
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:29.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.58
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17339.37
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.81
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.50
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.28
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.07
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.11
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.23
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.31
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.75
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.47
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.89
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.14
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.61
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.47
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.48
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.01
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.32
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.14
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.77
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.82
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.47
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.14
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5061.52
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.29
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.46
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.80
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  324.42
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.91
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.54
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.94
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.58
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :   -1.96
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:27.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.24
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:27.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:11.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 5.44e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.50e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 9.24e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.70
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.37
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.94
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:08.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.15
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:10.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10081.94
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9991.97
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:51.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4929.34
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4831.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:49.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4198.00
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4243.79
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11878.93
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11727.87
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:30.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.99
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000214534

Normal statistic for number of bits   :    1.70
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.73
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999867149

Normal statistic for number of bits   :   -1.05
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:08.42

 All tests were passed




Server wird beendet - Lösche Semaphor 177864721.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1265
p-value of test                       :    0.9966

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334385
  j =  1                              :        599997470
  j =  2                              :             1265
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5388
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:51.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:39.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:39.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:04.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:05.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:55.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:01.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:14.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:46.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.90
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.50
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.24
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:10.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.72
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.73
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.93
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:41.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.02
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:59.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7062.09
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:40.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.84
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.28e-3
p-value of test                       :    0.9934

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.09
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:01.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.43
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.79
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5100.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:59.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46222
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870222
  j =  1                              :        399907558
  j =  2                              :            46218
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46055
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870055
  j =  1                              :        399907896
  j =  2                              :            46043
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-3
p-value of test                       :    0.9977

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:29.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:18.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9953


-----------------------------------------------
CPU time used                    :  00:01:45.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:59.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:55.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:35.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.15e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:35.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:35.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.07
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.45
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.60
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.33
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:49.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.17
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.38
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.40
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.20
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.76
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17521.89
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.99
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.92
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.06
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.99
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.63
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.82
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.89
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.82
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.34
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.10
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.15
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.85
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.40
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.84
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.16
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.59
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.26
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.95
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.74
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.09
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.29
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.26
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5093.34
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.49
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.82
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.62
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.15
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.37
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.04
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.09
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.90
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  :   -1.45
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:24.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.48
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:25.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.87e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 7.28e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 6.40e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.18
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.74
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.14
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:05.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.32
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:08.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.84
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9925.27
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.040
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:46.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4752.58
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:48.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.65
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:52.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.45
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4147.54
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11934.06
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:29.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11754.36
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:29.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.55
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999787685

Normal statistic for number of bits   :   -1.68
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.90
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999994451

Normal statistic for number of bits   :  -0.044
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.83
p-value of test                       :    0.97

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:45.12

 All tests were passed




Server wird beendet - Lösche Semaphor 178913297.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:51.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5245
p-value of test                       :    0.9917


-----------------------------------------------
CPU time used                    :  00:03:51.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:39.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:39.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:56.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:04.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:55.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:01.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    2.93
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    2.83
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:14.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.86
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:43.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.27
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.91
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.07
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.85
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  282.02
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:42.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1363.68
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:01.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6943.55
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:40.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.52
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.27
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:02.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.39
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  146.60
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:35.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5062.64
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:02.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45894
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869894
  j =  1                              :        399908216
  j =  2                              :            45886
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46122
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870122
  j =  1                              :        399907760
  j =  2                              :            46114
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:28.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:18.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:45.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  5.6e-3

Anderson-Darling statistic = A2       :    3.71
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  7.4e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:58.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 3.86e-3
p-value of test                       :    0.9958

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:35.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.31e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.51
p-value of test                       :    0.9940

-----------------------------------------------
CPU time used                    :  00:01:35.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:34.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.18
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:49.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.09
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.73
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.72
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.75
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.94
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:44.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.89
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.99e-3
p-value of test                       :    0.9969

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.69
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.59
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:29.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:18.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.74
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.22
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17264.29
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.54
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.81
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.11
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.34
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.05
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.25
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.40
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.90
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.56
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.31
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.81
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.06
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.90
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.87
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.89
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.68
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.45
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.34
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.27
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.29
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.70
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.69
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4841.49
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.57
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.60
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.36
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.43
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.20
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.99
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.14
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:34.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.28
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:24.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.82
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:25.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 6.47e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 7.35e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.21
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.47
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.53
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:07.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.17
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:08.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10076.29
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9938.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.96
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:44.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4852.08
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4766.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:50.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4152.54
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3938.73
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11903.27
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11935.25
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:30.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.19
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000005647

Normal statistic for number of bits   :   0.045
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.60
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000011716

Normal statistic for number of bits   :   0.093
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :  -0.026
p-value of test                       :    0.51

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:58.29

 All tests were passed




Server wird beendet - Lösche Semaphor 179929105.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1274
p-value of test                       :    0.9929

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334394
  j =  1                              :        599997452
  j =  2                              :             1274
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5255
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:51.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:40.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:40.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:56.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:05.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:06.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7175
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:58.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:04:01.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.81
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.65
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     272
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:15.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    2.76
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:44.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.07
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.66
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.09
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.14
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.21
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.47
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.32
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:50.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1405.71
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:07.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6916.03
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.62
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   48.63
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.79
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:09.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.62
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.72
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:37.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4970.83
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:57.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45372
p-value of test                       :    0.9911


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869372
  j =  1                              :        399909264
  j =  2                              :            45356
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45945
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869945
  j =  1                              :        399908114
  j =  2                              :            45937
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:30.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:18.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:02.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:36.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.74e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.031
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:47.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.10
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:50.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.32
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.65
p-value of test                       :  8.4e-3

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.62
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.44
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.89
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:46.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.96
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.37
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.22
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:29.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.50
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.38
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:39.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17252.78
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.31
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.10
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.84
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.50
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.98
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:39.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.63
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.00
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.77
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.07
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.11
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.25
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.66
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.52
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.97
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.02
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.03
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.53
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.85
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.76
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.96
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.21
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.43
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4863.86
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.72
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  238.42
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:36.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.68
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.96
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5061.72
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  425.90
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.86
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.81
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:24.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.14
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:22.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.53e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 5.46e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 6.84e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.84
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.45
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.72
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:08.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:09.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10091.35
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10111.06
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:04:22.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.7e-3

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4733.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:52.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.77
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:54.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4007.83
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3885.58
p-value of test                       :    0.9952

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11812.82
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:33.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11728.99
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:32.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.06
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999985685

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.32
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999967343

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:11.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:52.17

 All tests were passed




Server wird beendet - Lösche Semaphor 180944913.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:11.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5451
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:52.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:39.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:38.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4429
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:57.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:04.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7056
p-value of test                       :    0.9990


-----------------------------------------------
CPU time used                    :  00:03:06.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:57.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:04:02.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.96
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     965
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     564
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:15.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.85
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:44.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.69
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.31
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.96
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.84
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.10
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.59
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.52
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.74
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:46.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1485.11
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:04.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7108.22
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:47.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.37
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:06.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.07
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.55
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5082.67
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:57.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46092
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870092
  j =  1                              :        399907819
  j =  2                              :            46086
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45956
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869956
  j =  1                              :        399908091
  j =  2                              :            45950
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:29.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:16.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:44.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 5.96e-4
p-value of test                       :    0.9994    *****

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:59.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:36.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.71e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 6.03e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:22.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:44.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:43.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.87
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.07
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.93
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.88
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.20
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.79
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.53
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:45.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.83
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.97
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.96
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:29.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.62
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:29.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.19
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16981.59
p-value of test                       :    0.9922



-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.13
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.98
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.41
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.61
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.79
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   65.37
p-value of test                       :  2.0e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.00
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.73
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.97
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.96
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.02
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.04
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.52
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.30
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.55
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.58
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.26
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.54
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.27
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.12
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.25
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.96
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5091.36
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.83
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  237.20
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.55
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.85
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.88
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.79
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.79
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.22
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:25.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.59
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:23.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:11.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.28

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 6.19e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.26e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.11
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.48
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9960

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.81
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:06.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  243.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:08.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10150.74
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9997.91
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:04:08.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5024.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:50.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4907.45
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:52.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.30
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4070.17
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12098.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:29.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12151.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:31.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.25
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000053965

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.34
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000121852

Normal statistic for number of bits   :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    2.37
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:46.62

 All tests were passed




Server wird beendet - Lösche Semaphor 182190097.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:51.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5429
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:54.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4437
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:40.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:39.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:06.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:07.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:04:00.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:03.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.68
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     849
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    2.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.92
p-value of test                       :  9.7e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.35
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.61
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     340
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    2.68
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:14.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    2.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:44.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.10
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.46
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.28
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.01
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.51
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.42
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.92
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.75
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.12
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1467.04
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:03.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6881.20
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:50.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.85
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.03
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:09.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.93
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   90.67
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:37.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5068.75
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:59.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45926
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869926
  j =  1                              :        399908151
  j =  2                              :            45920
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45656
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869656
  j =  1                              :        399908690
  j =  2                              :            45652
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:30.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:18.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:45.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:04.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:36.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 5.25e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.23e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:46.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:46.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.55
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.47
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.16
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.34
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.95
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.41
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.06
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.83
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.52
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:39.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17333.43
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.52
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.08
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.08
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.60
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.46
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.31
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.89
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.03
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.69
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.75
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.30
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.82
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.03
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.84
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.63
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.80
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.10
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.02
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.34
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.02
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.95
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.23
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4892.48
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.43
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.18
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.64
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.84
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5075.12
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.49
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.21
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.10
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :   -1.29
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:25.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.70
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:25.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.09e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 4.39e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.65e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.38
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.54
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.33
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:06.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.95
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:06.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9968.14
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10121.55
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:04:20.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4913.15
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:53.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4913.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:54.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4306.74
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4118.80
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11848.05
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:32.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11885.72
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:31.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.98
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000001417

Normal statistic for number of bits   :   0.011
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.74
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000002263

Normal statistic for number of bits   :   0.018
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:10.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    1.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:29.95

 All tests were passed




Server wird beendet - Lösche Semaphor 183205905.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:40.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5372
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:57.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:43.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:59.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4231
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:12.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7447
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:12.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:10.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:16.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:49.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.99
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:14.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.51
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.87
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     125
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:46.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.68
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.19
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.35
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.82
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.70
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.85
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  270.23
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:29.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.49
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.64
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:04.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6944.90
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:55.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.87
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.51
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:18.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.17
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.37
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:43.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4947.83
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:28.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:01.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46224
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870224
  j =  1                              :        399907556
  j =  2                              :            46216
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45554
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869554
  j =  1                              :        399908893
  j =  2                              :            45552
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:31.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:20.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:53.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:09.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:56.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:37.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.99e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.73e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:49.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:48.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.80
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.82
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.91
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.61
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.23
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:49.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.55
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.43
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.33
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.54
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17703.29
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.94
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.78
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.12
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.02
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.24
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.73
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.94
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.04
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.56
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.62
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.88
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.51
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.15
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.53
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.15
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.42
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.97
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.14
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.63
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  106.72
p-value of test                       :  7.7e-3


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.46
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.95
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4976.82
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.69
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.79
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.86
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  454.82
p-value of test                       :  7.4e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5093.64
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.44
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.14
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.29
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :  -0.060
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:25.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.68
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :   -1.02
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:25.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.54e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 7.47e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.44
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.31
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9902

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.16
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:05.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.69
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:05.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9840.21
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9803.80
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.56
p-value of test                       :  5.3e-3

-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.94
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:04:33.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5049.21
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:57.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4768.87
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:59.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4160.84
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4022.33
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11902.28
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:34.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12060.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:38.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.45
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999873314

Normal statistic for number of bits   :   -1.00
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.37
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999926447

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.38

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 9.29e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.93

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:28.52

 All tests were passed




Server wird beendet - Lösche Semaphor 184352785.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:38.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5412
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:57.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:41.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4436
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:57.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4471
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:58.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:06.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:06.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:55.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:04:00.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:46.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.9913

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:15.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:42.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.22
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.37
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.16
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.71
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.30
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.26
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.00
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.09
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.87
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.90
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:44.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1472.54
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:01.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7089.68
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:45.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.32
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.69
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.12
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  151.17
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:35.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5025.55
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:00.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45821
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869821
  j =  1                              :        399908361
  j =  2                              :            45815
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45850
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869850
  j =  1                              :        399908305
  j =  2                              :            45840
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:29.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:17.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:44.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 1.53e-3
p-value of test                       :    0.9984

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9944


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:58.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:57.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.03e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 8.03e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:41.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.085
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.12
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.54
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.42
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.94
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.23
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:43.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.59
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.86
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.26
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17387.81
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.12
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.04
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.23
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.13
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.16
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:38.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.70
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.40
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.08
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.15
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.37
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.88
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.90
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.49
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.88
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.31
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.22
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.57
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.82
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.36
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.66
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.22
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.33
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.29
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.96
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.56
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.46
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.90
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.91
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  457.01
p-value of test                       :  3.3e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.57
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   -1.22
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:26.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.11
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:24.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.68
p-value of test                       :    0.05

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.42e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 7.28e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.10e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.14
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.38
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.66
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:06.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.83
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:09.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10122.31
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10118.21
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:41.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4914.60
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4811.91
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:50.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4162.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.66
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11990.48
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:28.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11863.15
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:29.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.98
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000005707

Normal statistic for number of bits   :   0.045
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.69
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000006949

Normal statistic for number of bits   :   0.055
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.44
p-value of test                       :    0.07

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.3e-3

Anderson-Darling statistic = A2       :    4.55
p-value of test                       :  5.0e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.73
p-value of test                       :  3.1e-3

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.5e-3

Anderson-Darling statistic = A2       :    4.41
p-value of test                       :  5.8e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.50
p-value of test                       :  6.1e-3

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:25.15

 All tests were passed




Server wird beendet - Lösche Semaphor 185401361.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:40.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5370
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:56.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:42.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:44.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:01.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:02.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:12.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:11.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:08.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:04:13.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    3.72
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:49.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    2.42
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     560
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    2.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:14.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:45.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.33
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.01
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.03
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.90
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:11.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.18
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.38
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.17
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.64
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  486.54
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:56.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:06.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7325.62
p-value of test                       :  9.9e-3

-----------------------------------------------
CPU time used                    :  00:01:56.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.62
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.73
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:16.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.01
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:46.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.39
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:40.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5042.04
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:01.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45589
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869589
  j =  1                              :        399908825
  j =  2                              :            45583
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45806
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869806
  j =  1                              :        399908392
  j =  2                              :            45798
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:34.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:52.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:08.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:57.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:37.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.55e-4
p-value of test                       :  6.4e-3

Kolmogorov-Smirnov- statistic = D-    : 6.69e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.61e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.70e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:24.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:24.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:24.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 3.42e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:44.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -5.54e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.54
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.36
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.64
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.86
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:50.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.00
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.21
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.57
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.68
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  155.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17503.86
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.90
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.23
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.61
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.64
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.57
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:38.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.64
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.97
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.10
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.41
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.39
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.71
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.07
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.82
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   91.60
p-value of test                       :    0.9987


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.77
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.73
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.04
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.51
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.33
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.77
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.43
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.50
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.68
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.97
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.40
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:36.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.37
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.72
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5230.56
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  435.52
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.13
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.78
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:25.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.09
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:22.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.9e-3

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.55
p-value of test                       :    0.06

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 4.40e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.40
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.07
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.02
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:08.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.73
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:07.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10047.78
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9884.10
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:09.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:04:24.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4975.34
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:54.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4722.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:58.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.67
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4202.08
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11618.42
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:34.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12024.00
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:34.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.20
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999726761

Normal statistic for number of bits   :   -2.16
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.24
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000006451

Normal statistic for number of bits   :   0.051
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:32.47

 All tests were passed




Server wird beendet - Lösche Semaphor 186449937.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5336
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:54.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:40.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:57.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:06.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:06.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:57.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:04.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:49.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.70
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    3.36
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     338
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:14.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:46.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.13
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.58
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.01
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.36
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.92
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:32.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.79
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:31.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.99
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:31.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  516.29
p-value of test                       :  4.0e-3

-----------------------------------------------
CPU time used                    :  00:01:43.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1335.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:01.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6955.82
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:44.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.31
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.71
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:04.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.27
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.66
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:35.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5070.64
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:04.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45782
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869782
  j =  1                              :        399908439
  j =  2                              :            45776
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46100
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870100
  j =  1                              :        399907806
  j =  2                              :            46088
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:28.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:19.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:01.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:56.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  9.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 3.81e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 7.55e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:22.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:38.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:37.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.29
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.30
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.15
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.37
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.29
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.02
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:45.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.02
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.04
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.35
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17540.14
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.86
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.68
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.87
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.95
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.23
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   55.03
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.72
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.35
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.83
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.60
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.98
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.42
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.37
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  167.08
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.31
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.13
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.95
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.11
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  177.70
p-value of test                       :  9.4e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.52
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.32
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.24
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.54
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.45
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.82
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.47
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.83
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5039.72
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.22
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.07
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.30
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:22.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.15
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:24.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 9.80e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.88
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.35
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.73
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:06.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:05.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9928.05
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9865.55
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:41.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5047.96
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.15
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:51.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.52
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.87
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12024.51
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11909.46
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:30.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.92
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  7999951824

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.14
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000044839

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.19
p-value of test                       :    0.01

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.23

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.87

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:23.70

 All tests were passed




Server wird beendet - Lösche Semaphor 187662353.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5424
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:55.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:40.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:40.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:58.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:06.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:06.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:55.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:04:01.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    2.30
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.92
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.77
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:15.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.00
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:45.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.71
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.73
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.19
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.90
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.59
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  298.84
p-value of test                       :  2.0e-3

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.21
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:43.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1507.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:01.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7168.86
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.71
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.08
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:02.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.03
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  154.15
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:33.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4982.22
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:59.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45712
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869712
  j =  1                              :        399908578
  j =  2                              :            45708
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45663
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869663
  j =  1                              :        399908676
  j =  2                              :            45659
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:28.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:18.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 6.46e-3
p-value of test                       :    0.9927

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:44.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:00.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:55.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:33.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 9.31e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 8.73e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.080
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:36.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.78
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.15
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:48.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.62
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.58
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.45
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:39.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.45
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.79
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17147.61
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   60.25
p-value of test                       :  6.8e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.01
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.95
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.07
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.33
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:34.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.88
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.97
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.01
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.68
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.05
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:34.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.72
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.91
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.89
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.39
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.11
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.30
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.03
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.63
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.65
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.83
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.82
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.70
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5104.91
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.53
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.97
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.66
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.61
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5122.08
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.89
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.62
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:32.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   28.01
p-value of test                       :  5.5e-3


-----------------------------------------------
Normal statistic for number of jumps  :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:11.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.80
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:12.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   0.060
p-value of test                       :    0.48

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.59e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 4.69e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.04e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.51
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.41
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.04
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:54.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.39
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:54.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10236.97
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9919.60
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:51.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.038
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:22.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4913.22
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:32.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4836.03
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.23
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.62
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11704.87
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11789.10
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.55
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999994703

Normal statistic for number of bits   :  -0.042
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.09
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000138913

Normal statistic for number of bits   :    1.10
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   0.012
p-value of test                       :    0.50

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.43
p-value of test                       :    0.08

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   02:57:41.31

 All tests were passed




Server wird beendet - Lösche Semaphor 188710929.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1237
p-value of test                       :    0.9998    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334357
  j =  1                              :        599997526
  j =  2                              :             1237
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5317
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:42.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:36.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:34.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:55.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:02.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:02.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:55.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:01.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:51.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.99
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:08.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.78
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    3.32
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     126
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    2.29
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:32.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.53
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.78
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.28
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.79
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.99
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.09
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.62
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.31
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.66
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:50.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.07
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:00.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6955.60
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:50.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.65
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  1.0e-2

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.56
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:02.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.72
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.35
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:37.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5079.26
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:15.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:12.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45950
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869950
  j =  1                              :        399908102
  j =  2                              :            45946
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46412
p-value of test                       :  6.6e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870412
  j =  1                              :        399907181
  j =  2                              :            46402
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:14.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:29.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:18.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:45.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:00.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:53.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.29e-3
p-value of test                       :    0.9903

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:15.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:33.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 8.72e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:22.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 9.90e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:38.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.84
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:48.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.57
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.70
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:50.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.36
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.79
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:44.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.69
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.75
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.84
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:32.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.74
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:30.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.20
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17353.54
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.77
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   16.92
p-value of test                       :    0.9957


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.11
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.56
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.25
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.54
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.23
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.05
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.96
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.63
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.68
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.71
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.15
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.26
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:49.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.21
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.54
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.10
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.21
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.16
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:47.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.10
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.45
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.30
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.63
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  245.55
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.50
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.99
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.34
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.80
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.86
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.42
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :    1.49
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:16.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.65
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:12.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:14.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 6.35e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:46.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.80e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.06
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.70
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.24
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:11.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.75
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:11.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10188.18
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10155.21
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.29
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:49.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4956.16
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:48.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4887.82
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:50.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4251.35
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4170.97
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11589.67
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:28.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12092.86
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:30.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.28
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000028198

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.73
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000040747

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:16:44.68
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  5  CollisionOver, t = 3            0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 168493074.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5452
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:44.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:37.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:36.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:54.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4205
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:03.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:02.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:53.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:00.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:47.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.13
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:04.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:30.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.28
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.18
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.01
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.99
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.72
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.56
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  261.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.92
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:43.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1498.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:00.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6979.82
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:43.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 5.10e-3
p-value of test                       :    0.9948

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.44
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.59
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:02.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.72
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.28
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5075.45
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:05.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46042
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870042
  j =  1                              :        399907920
  j =  2                              :            46034
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45905
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869905
  j =  1                              :        399908196
  j =  2                              :            45893
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:31.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:18.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:45.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 3.76e-3
p-value of test                       :    0.9960

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:59.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:53.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:15.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:33.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 9.50e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.81
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:22.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:32.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:33.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.09
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:48.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.90
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:48.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.08
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.72
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.65
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:38.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.33e-3
p-value of test                       :    0.9955

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.60
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.01
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:30.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:30.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  100.36
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17631.65
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:55.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.43
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.64
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.84
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.86
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.87
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:39.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.61
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.63
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.80
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.47
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.81
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.26
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.03
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.78
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.54
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.50
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.87
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.47
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.78
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.12
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.72
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.23
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.33
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.30
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.58
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.61
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.98
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.50
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5007.14
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.12
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.55
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.73
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :   0.075
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:28.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.41
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:20.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :  -0.033
p-value of test                       :    0.51

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.26e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.29e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.07
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.47
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.96
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:07.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:10.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9940.79
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9977.18
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:58.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.96
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4843.62
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:49.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4266.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.61
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11900.83
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11861.80
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.54
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999931145

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.10
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000078901

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:19.46

 All tests were passed




Server wird beendet - Lösche Semaphor 169410578.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5469
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:43.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:37.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:35.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:54.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:55.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:02.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:02.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:53.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:59.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.39
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.83
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:15.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:44.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.09
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.48
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.35
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.28
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.02
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.63
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.14
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.59
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:42.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1427.94
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:58.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7080.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:43.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.58
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.70
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:00.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.83
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.66
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:34.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4972.17
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46101
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870101
  j =  1                              :        399907802
  j =  2                              :            46093
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45856
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869856
  j =  1                              :        399908293
  j =  2                              :            45846
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:33.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:19.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:45.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:59.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:55.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.63e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:22.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:22.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.01
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 2.05e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:35.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.44
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:47.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.89
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.40
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.62
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:48.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.21
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.40
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.10
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:41.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.52
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.47
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.86
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.04
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:29.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.87
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17263.11
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.40
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.73
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.33
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.95
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.99
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.13
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.03
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.29
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.43
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.84
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.53
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.41
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.58
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.68
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.39
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.73
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.96
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  446.39
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.08
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.04
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.63
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.35
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4915.02
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.66
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  238.74
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.54
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.73
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4907.33
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  332.98
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.12
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.89
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:24.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.69
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :   -0.54
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:22.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :  -0.027
p-value of test                       :    0.51

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:46.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.97e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.64
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.68
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:06.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.43
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:09.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10048.19
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10069.30
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:04:06.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  2.9e-3

Anderson-Darling statistic = A2       :    3.84
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5079.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:50.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:51.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.96
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4029.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11938.10
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11749.53
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:30.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.10
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000232435

Normal statistic for number of bits   :    1.84
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.26
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000132964

Normal statistic for number of bits   :    1.05
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.48
p-value of test                       :    0.07

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.63
p-value of test                       :    0.95

Sample variance                       :    0.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:28.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:12.13

 All tests were passed




Server wird beendet - Lösche Semaphor 170098706.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:39.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:50.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5463
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:44.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:36.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:34.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4438
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:54.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:55.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:01.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:02.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:53.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:58.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.70
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:46.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     644
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:12.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:39.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.20
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.79
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.31
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.54
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.06
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.76
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  470.67
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1367.43
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:01.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7276.57
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.29
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.07
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:05.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.87
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.17
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:33.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5236.93
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:00.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45961
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869961
  j =  1                              :        399908079
  j =  2                              :            45959
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45705
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869705
  j =  1                              :        399908592
  j =  2                              :            45701
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:30.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:20.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:46.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:01.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:57.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:34.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.78e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 2.55e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.16e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:33.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:33.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.27
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:48.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.49
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.11
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.57
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:48.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.01
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.78
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.48
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.82
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   17.43
p-value of test                       :  5.8e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.08
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17651.88
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.71
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.40
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.73
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.06
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.68
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   61.86
p-value of test                       :  4.7e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.14
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   45.24
p-value of test                       :  7.9e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.22
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   36.67
p-value of test                       :  3.7e-3


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.74
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.38
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.33
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.18
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.06
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.50
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.47
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  560.41
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.92
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.91
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.73
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.11
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5136.49
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.52
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.36
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.33
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.18
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5137.89
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.52
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.69
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.05
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    0.72
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:23.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.35
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:22.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.70
p-value of test                       :    0.96

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 6.37e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 7.66e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.82
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.14
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:07.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.65
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:07.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9830.01
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10195.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:50.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9919

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4858.96
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:50.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5024.90
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:51.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4195.93
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.53
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11736.79
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:28.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11910.23
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:30.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.45
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000107965

Normal statistic for number of bits   :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.00
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000119725

Normal statistic for number of bits   :    0.95
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9938

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.19
p-value of test                       :    0.9948

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.80
p-value of test                       :    0.96

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:55.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 69  MatrixRank, L=1000, r=26        5.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 171147282.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5530
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:51.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:39.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:38.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:54.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:54.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:00.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:59.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:51.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:58.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:45.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.85
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.95
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:11.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:41.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.69
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.63
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.01
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.70
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.35
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.82
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.64
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  270.57
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.25
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:43.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1479.99
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:01.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7063.46
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:42.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.23
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.54
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:03.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.86
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:47.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.10
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:33.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5068.97
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:00.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46013
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870013
  j =  1                              :        399907974
  j =  2                              :            46013
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45821
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869821
  j =  1                              :        399908360
  j =  2                              :            45817
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:29.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:17.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:43.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:59.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:57.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:37.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 6.51e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:22.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:35.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.010
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:35.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.82
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.78
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.34
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:48.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.48
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.46
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.49
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.93
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.97
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.89
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17140.98
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:52.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.05
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.33
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.28
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.15
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.55
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.23
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.72
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.99
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.46
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.92
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.79
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.03
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.89
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.35
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.03
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.60
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.84
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.52
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.07
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.63
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  318.39
p-value of test                       :    0.9937


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.40
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.68
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.48
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.22
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.15
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.87
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4905.27
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.91
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.21
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.79
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :    0.72
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:23.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.22
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :   -1.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:23.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.56
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.40
p-value of test                       :    0.9917

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 6.17e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.82e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 8.85e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.18
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.95
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.0e-3

Kolmogorov-Smirnov- statistic = D-    : 8.71e-3
p-value of test                       :    0.9906

Anderson-Darling statistic = A2       :    5.20
p-value of test                       :  2.5e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  142.33
p-value of test                       :    0.9993    *****

-----------------------------------------------
CPU time used                    :  00:02:08.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.29
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:06.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9768.58
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10168.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:50.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.13
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5017.20
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:52.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4004.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.64
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11624.13
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:30.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11580.51
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:31.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.68
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999847091

Normal statistic for number of bits   :   -1.21
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.23
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000027403

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :  -0.067
p-value of test                       :    0.53

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :  -0.078
p-value of test                       :    0.53

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.70
p-value of test                       :    0.04

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:43.43
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 88  PeriodsInStrings, r = 0         0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 172130322.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:40.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9958


-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5328
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:00.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:43.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:44.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:00.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:01.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:08.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:06.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7132
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:59.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7122
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:04:01.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.95
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.69
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:14.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:46.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.43
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.84
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.95
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.49
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.02
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  189.80
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:28.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.03
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1353.07
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:06.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7182.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:56.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.83
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.15
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:18.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.61
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.48
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:40.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4957.28
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:57.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45462
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869462
  j =  1                              :        399909079
  j =  2                              :            45456
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45783
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869783
  j =  1                              :        399908439
  j =  2                              :            45773
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:32.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:21.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:52.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:08.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:56.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:36.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 6.53e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.83e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:24.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.090
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:38.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:40.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.69
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.89
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.35
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.25
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.39
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.20
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.68
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.65
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.64
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.03
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.01
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17283.94
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.24
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.53
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.51
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.34
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.46
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.98
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.02
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.48
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.31
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.52
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.19
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.79
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.88
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.74
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.36
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.27
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.19
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  556.27
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.21
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.53
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.68
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.99
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4954.61
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.20
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.34
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.45
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.46
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4951.01
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.23
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.63
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.91
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :  -0.010
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:27.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.05
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:24.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    2.37
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 3.25e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 4.81e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.55
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.25
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.34
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:06.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.14
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:06.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9887.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9890.24
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:12.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:04:32.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4952.88
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:56.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.95
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:57.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4049.94
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4258.87
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11553.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:35.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12000.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:36.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.42
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999953264

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.01
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000046744

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  8.2e-3

Anderson-Darling statistic = A2       :    3.52
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.41
p-value of test                       :  8.0e-3

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.76
p-value of test                       :    0.96

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:09.82

 All tests were passed




Server wird beendet - Lösche Semaphor 173146130.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5497
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:57.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:41.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:03.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:02.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:52.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7177
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:59.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.93
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:13.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:43.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.89
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.56
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.17
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.68
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.96
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.77
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.37
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.19
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:42.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1382.91
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:59.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6997.63
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.43
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.80
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:04.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.85
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.96
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:35.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5078.37
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:02.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45765
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869765
  j =  1                              :        399908471
  j =  2                              :            45763
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46388
p-value of test                       :  8.9e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870388
  j =  1                              :        399907230
  j =  2                              :            46376
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:28.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:17.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:43.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:58.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:56.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  6.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:35.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.78e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:34.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.12
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.63
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.99
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.54
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.20
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.22
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:11.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.03
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.40
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.61
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.44
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17400.93
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.87
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.54
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.42
p-value of test                       :    0.9906


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.34
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.03
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.22
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.75
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.72
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.46
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.92
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.41
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.08
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.38
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.92
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.04
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.01
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.08
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.65
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.66
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.64
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.57
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.13
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4986.89
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.59
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.92
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.89
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.12
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4868.87
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.33
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.78
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:34.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.91
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :   -1.79
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:23.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.92
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   0.097
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:24.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.91e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.75e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 7.88e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.62
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.26
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.31
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:06.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.40
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:07.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9813.07
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9855.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:04:01.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5044.07
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  1.8e-3

Anderson-Darling statistic = A2       :    3.79
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5085.72
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:51.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4258.03
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3997.40
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12155.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:29.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11677.18
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:31.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.25
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999921374

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.40
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999915731

Normal statistic for number of bits   :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    2.00
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:57.59

 All tests were passed




Server wird beendet - Lösche Semaphor 174424082.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:38.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:48.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.99

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5474
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:01.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:43.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:58.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:57.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7477
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:06.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:05.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:04:00.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:03.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     273
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:14.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.07
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.45
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.65
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.37
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.46
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.72
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.24
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:29.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.02
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:53.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.28
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:10.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6767.65
p-value of test                       :    0.9911

-----------------------------------------------
CPU time used                    :  00:01:55.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.54
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.63
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:14.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.07
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.97
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:37.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5125.91
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:55.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45791
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869791
  j =  1                              :        399908421
  j =  2                              :            45785
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45964
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869964
  j =  1                              :        399908078
  j =  2                              :            45952
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:31.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:20.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9991    *****

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:52.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:09.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:58.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 1.71e-3
p-value of test                       :    0.9982

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:39.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.40e-4
p-value of test                       :  9.9e-3

Kolmogorov-Smirnov- statistic = D-    : 6.05e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    4.12
p-value of test                       :  7.7e-3

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.77
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:51.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:48.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.82
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.67
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.89
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.63
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.39
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.50
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:53.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.02
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.62
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.64
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.66
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:42.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17443.19
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.62
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.13
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.69
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.69
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.13
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   60.34
p-value of test                       :  6.7e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.24
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.04
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.47
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.15
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.92
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.01
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.83
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.10
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.10
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.91
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.05
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.81
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.40
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.43
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.22
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.43
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5076.21
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.15
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.33
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.37
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  461.59
p-value of test                       :  4.0e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.97
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.74
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.63
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.88
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :    1.37
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:26.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.84
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:24.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.8e-3

Kolmogorov-Smirnov- statistic = D-    : 5.49e-3
p-value of test                       :    0.9942

Anderson-Darling statistic = A2       :    4.57
p-value of test                       :  4.9e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.89
p-value of test                       :    0.9980

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.46e-3
p-value of test                       :    0.9909

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.13
p-value of test                       :    0.02

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 6.56e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.72e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.94
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.88
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.71
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:08.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.88
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:08.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9912.88
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10028.41
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:12.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:04:37.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4902.50
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:59.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4948.92
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:00.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.81
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.43
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11600.95
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:35.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12221.69
p-value of test                       :  5.3e-3

-----------------------------------------------
CPU time used                    :  00:01:35.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.33
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999949790

Normal statistic for number of bits   :   -0.40
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.72
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999928259

Normal statistic for number of bits   :   -0.57
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    1.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:27.07

 All tests were passed




Server wird beendet - Lösche Semaphor 175472658.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1463
p-value of test                       :  4.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334583
  j =  1                              :        599997074
  j =  2                              :             1463
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5354
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:52.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:40.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:39.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:56.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:04.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:03.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7179
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:54.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:00.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:15.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:45.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.52
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.52
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.83
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.37
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.07
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.60
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.69
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.36
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.17
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:00.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6955.59
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:40.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.26
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.61
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:01.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.97
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.65
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:33.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5012.14
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:54.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46084
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870084
  j =  1                              :        399907837
  j =  2                              :            46074
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45859
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869859
  j =  1                              :        399908285
  j =  2                              :            45853
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:29.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:17.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:44.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:58.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:35.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:21.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:36.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:37.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:48.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.50
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.22
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.21
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.20
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:38.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.89
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.00
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.91
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.33
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17271.72
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.99
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.34
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.67
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.56
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.59
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.81
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.69
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.83
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.38
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.08
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:37.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.87
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.00
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.88
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.49
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.08
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.33
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.83
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  446.11
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.36
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.49
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.19
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.19
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.66
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.49
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.25
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  442.08
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.38
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4928.57
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.28
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.00
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.48
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:24.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.09
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :    1.72
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:24.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.41e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 9.68e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 9.17e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.11
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.91
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:07.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:07.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9906.05
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10067.03
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.072
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:42.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4825.31
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    3.61
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4687.94
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:52.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4254.28
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3989.10
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11875.67
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11854.80
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.38
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999987611

Normal statistic for number of bits   :  -0.098
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.22
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999994481

Normal statistic for number of bits   :  -0.044
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:45.28

 All tests were passed




Server wird beendet - Lösche Semaphor 176554002.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5324
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:56.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:43.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4452
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:59.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:09.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:09.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:05.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7467
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:12.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9917


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:49.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.04
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.72
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    2.36
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:15.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:47.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.15
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.44
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.84
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.14
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.77
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.21
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.62
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.07
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:30.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  384.16
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1403.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:05.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6853.71
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:57.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.24
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:16.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.53
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.56
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:07.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5081.56
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:32.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:25.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46112
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870112
  j =  1                              :        399907783
  j =  2                              :            46098
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45763
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869763
  j =  1                              :        399908476
  j =  2                              :            45759
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:32.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:21.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:53.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:08.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:57.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.24
p-value of test                       :  6.8e-3

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:39.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 4.06e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.09e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 8.32e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:24.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:24.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:43.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.53
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.36
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.39
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.16
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.00
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.24
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.50
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.64
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.81
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17621.48
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.57
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.13
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.17
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.28
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.14
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.77
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.08
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.81
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.70
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.09
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.81
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.73
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.72
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  171.37
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.46
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.05
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.84
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.61
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.16
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.35
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  325.08
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.72
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4931.56
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.39
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.73
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.19
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.70
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.13
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.75
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  151.59
p-value of test                       :    0.9955


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.23
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:24.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.63
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:25.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.91
p-value of test                       :    0.03

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.2e-3

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.88
p-value of test                       :    0.03

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 4.72e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:46.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.39e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.03
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.61
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.95
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:06.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.01e-3
p-value of test                       :    0.9948

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  257.52
p-value of test                       :  3.8e-3

-----------------------------------------------
CPU time used                    :  00:02:06.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  2.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    4.27
p-value of test                       :  6.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9653.30
p-value of test                       :    0.9934

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10037.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:13.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:04:34.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.69
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:54.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4800.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:56.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3984.92
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3968.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11658.14
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:33.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11859.35
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:36.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.60
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000011383

Normal statistic for number of bits   :   0.090
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.03
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000014752

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.21e-3
p-value of test                       :    0.9967

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.39
p-value of test                       :  8.4e-3

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:11:32.56

 All tests were passed




Server wird beendet - Lösche Semaphor 177602578.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5600
p-value of test                       :  7.9e-3


-----------------------------------------------
CPU time used                    :  00:03:52.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:39.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7176
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:38.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4225
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:55.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:04.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7494
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:05.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:55.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:59.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     860
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    2.31
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:46.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.60
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.83
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.75
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:15.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:42.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.58
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.87
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.63
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.05
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.82
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.28
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  205.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.08
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:41.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1486.06
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:57.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6879.91
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:01.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.53
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.81
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5110.01
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:00.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45835
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869835
  j =  1                              :        399908337
  j =  2                              :            45821
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45809
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869809
  j =  1                              :        399908385
  j =  2                              :            45803
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:29.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:18.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:45.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:00.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 9.98e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.62e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:21.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:21.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:34.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:33.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.14
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.59
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.98
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.26
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.76
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.86
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.79
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.45
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.86
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.09
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.20
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17559.66
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.22
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.13
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.90
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.99
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.61
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.77
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.57
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.96
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.47
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.53
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.74
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.09
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.34
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.73
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.01
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.41
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.66
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.67
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.07
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.66
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.95
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.95
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4904.92
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.11
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.30
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.40
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.65
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4976.05
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.85
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.23
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.28
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :    0.51
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:26.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.39
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:25.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.65e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.69
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.15e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.85
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.57
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.21
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:05.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.48
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:07.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10025.73
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10082.90
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:46.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4837.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.45
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:50.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4023.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4015.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11836.56
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11711.41
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.32
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000022354

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.35
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000007567

Normal statistic for number of bits   :   0.060
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.43

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:06.20

 All tests were passed




Server wird beendet - Lösche Semaphor 178847762.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5452
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:53.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:39.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:04.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7131
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:04.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:55.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:04:00.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    3.70
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     819
p-value of test                       :    0.9967

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.16
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.92
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     563
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:14.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:41.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.03
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.73
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.30
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.12
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.77
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:10.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.37
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.89
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.75
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.74
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:42.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.32
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:01.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6806.06
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.86
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:02.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.90
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.77
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:35.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4966.02
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:01.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45723
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869723
  j =  1                              :        399908556
  j =  2                              :            45719
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45765
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869765
  j =  1                              :        399908474
  j =  2                              :            45757
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:28.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:17.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:44.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:58.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.25e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 5.23e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.41
p-value of test                       :  8.0e-3

-----------------------------------------------
CPU time used                    :  00:01:33.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:34.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   98.77
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.77
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.26
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.55
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.38
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.86
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:43.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.15
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.59
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.52
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17485.91
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.89
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.38
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.76
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.77
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.84
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.18
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.68
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   51.93
p-value of test                       :  1.2e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.80
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.67
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.21
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.24
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.92
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.79
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.26
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.13
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.71
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.69
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.57
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.41
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  314.60
p-value of test                       :    0.9960


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.54
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.67
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.81
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.49
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.13
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.62
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.11
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.75
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.31
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.83
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    1.93
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:24.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.25
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :   -0.98
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:24.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.45e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.59
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.28
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:07.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.62
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:08.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9954.41
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10067.02
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:45.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4670.60
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:48.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4946.55
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:51.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4040.55
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11447.72
p-value of test                       :    0.9933

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12141.63
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:30.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.60
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000017272

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.38
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000060541

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.47
p-value of test                       :    0.07

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:42.44

 All tests were passed




Server wird beendet - Lösche Semaphor 179896338.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:40.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:51.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1238
p-value of test                       :    0.9997    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334358
  j =  1                              :        599997524
  j =  2                              :             1238
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5443
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:52.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:39.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4525
p-value of test                       :  2.3e-3


-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:03.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:02.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:54.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:59.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     953
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:47.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.92
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.36
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    3.20
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:13.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:43.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.68
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.71
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.62
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.02
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:10.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.08
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.02
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.83
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  478.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:43.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1382.77
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:02.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7240.95
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:43.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.20
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:02.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.21
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.67
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:35.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4917.63
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:56.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45920
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869920
  j =  1                              :        399908165
  j =  2                              :            45910
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46024
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870024
  j =  1                              :        399907962
  j =  2                              :            46004
  j =  3                              :               10
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:28.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:17.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:44.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:58.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-3
p-value of test                       :    0.9977

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:55.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:34.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.80e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:34.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:34.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.04
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.00
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.68
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.18
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.86
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.87
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.08
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:44.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.69
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.46
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.65
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.26
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17512.23
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.72
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.72
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.39
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.01
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.18
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.03
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.68
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.17
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.87
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.24
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.49
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.20
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.58
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.30
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.42
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.55
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.15
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.40
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.11
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.37
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.35
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.41
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.06
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.78
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.85
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.64
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.32
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5036.73
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.16
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.00
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.03
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : 2.98e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:25.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.57
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :    1.14
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:23.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.78e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 4.72e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 9.21e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.98
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.14
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.40
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:04.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.20
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:08.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10093.03
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10146.90
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.42
p-value of test                       :    0.9922

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.061
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:47.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:49.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4792.79
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:51.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4123.37
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11512.69
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12069.90
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:30.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.90
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999984383

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.41
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000079639

Normal statistic for number of bits   :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.14
p-value of test                       :    0.02

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :  -0.068
p-value of test                       :    0.53

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.083
p-value of test                       :    0.53

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:38.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 10  CollisionOver, t = 14           0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 180912146.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5469
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:52.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:40.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:55.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:03.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:03.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7145
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:55.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:59.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:08.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.22
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:37.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.28
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.05
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.45
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.12
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.69
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.67
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.08
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.01
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.26
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:44.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.26
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:03.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7034.14
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:46.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.20
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.31
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:03.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.19
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.08
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:35.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5165.80
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:56.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45944
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869944
  j =  1                              :        399908117
  j =  2                              :            45934
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45749
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869749
  j =  1                              :        399908503
  j =  2                              :            45747
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:30.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :  2.2e-3

Anderson-Darling statistic = A2       :    3.54
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:16.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:44.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:59.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:33.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.45e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.37e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.78e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.52e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:37.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:38.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.89
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.71
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.79
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.95
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.73
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.13
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.75
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:43.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.23
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.78
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:29.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.39
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17150.73
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.32
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.25
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.66
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.79
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.78
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.36
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.05
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.32
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.42
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.08
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.96
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.70
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.44
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.28
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.98
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.10
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.45
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.39
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.11
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.82
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.27
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4960.07
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.85
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.32
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.60
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.19
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4718.08
p-value of test                       :    0.9979


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.78
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.30
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.85
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:24.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.02
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:26.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.28

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.20e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:46.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 7.54e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.52
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.48
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.96
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:07.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.09
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:06.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10122.17
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9985.49
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:04:09.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4768.04
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:50.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4949.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:51.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3913.14
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4036.73
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11612.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:29.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11626.37
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:31.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.01
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000130111

Normal statistic for number of bits   :    1.03
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.13
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000057799

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.58
p-value of test                       :    0.94

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   0.036
p-value of test                       :    0.49

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.45

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:23.75

 All tests were passed




Server wird beendet - Lösche Semaphor 181927954.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:39.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5344
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:55.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4241
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4544
p-value of test                       :  9.1e-4    *****


-----------------------------------------------
CPU time used                    :  00:01:59.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:58.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:06.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:04.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7162
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:55.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:00.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    2.02
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     867
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.16
p-value of test                       :    0.9978


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     340
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:11.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:42.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.90
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:54.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.86
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.40
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   37.92
p-value of test                       :  4.0e-3

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.30
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.95
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   29.93
p-value of test                       :    0.9968

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.43
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.03
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:43.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.43
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:02.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7028.79
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:43.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.20
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:03.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.14
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   92.66
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:32.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5143.81
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:07.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45850
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869850
  j =  1                              :        399908302
  j =  2                              :            45846
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46101
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870101
  j =  1                              :        399907802
  j =  2                              :            46093
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:29.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:18.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:45.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:00.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:55.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:34.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 8.30e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.23e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.78e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:33.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:37.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.47
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.10
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:48.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.09
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   51.95
p-value of test                       :  5.5e-3

-----------------------------------------------
CPU time used                    :  00:01:55.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.48
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.66
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.19
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.46
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:38.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17359.80
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.84
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.40
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.35
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.21
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.96
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   59.23
p-value of test                       :  8.7e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.50
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.48
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.09
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.59
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.19
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.43
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.49
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.39
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.13
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:50.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.25
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.69
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.13
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.27
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.26
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.10
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.24
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.87
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.03
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.36
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:40.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.55
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.83
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4927.58
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.86
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.26
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:39.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.78
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :    1.38
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:25.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.07
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:26.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :  1.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.26
p-value of test                       :    0.99

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 6.95e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:46.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 7.42e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.54
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.08
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.49
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:06.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:05.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9850.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9924.00
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -3.16
p-value of test                       :    0.9992    *****

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:46.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.01
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:49.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4713.20
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:50.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.50
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4040.79
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11907.43
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11736.54
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:29.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.21
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  7999946634

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.22
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000135841

Normal statistic for number of bits   :    1.07
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:56.31
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 16  BirthdaySpacings, t = 7         9.1e-4
 92  HammingCorr, L = 30             0.9992 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 182910994.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9937


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5388
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:01.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:44.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:54.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:03.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:12.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:28.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:31.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:04:13.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:04:47.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.90
p-value of test                       :  9.9e-3

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    2.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:12.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.9904


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:43.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.47
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.92
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.73
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.16
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.29
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.38
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.83
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.92
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  267.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.46
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:43.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1492.57
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:00.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7053.12
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:42.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.44
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.38
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:03.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.31
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   92.97
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:32.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5008.30
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:14.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45713
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869713
  j =  1                              :        399908577
  j =  2                              :            45707
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45564
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869564
  j =  1                              :        399908878
  j =  2                              :            45552
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:28.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:32.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:02.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:21.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:55.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:34.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.56e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:35.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.92
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.20
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.26
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.33
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.49
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.40
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:38.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.06
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.31
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.18
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:28.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.44
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17399.42
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.33
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.72
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.65
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.92
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.65
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.64
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.33
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.64
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.49
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.83
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.66
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.90
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.54
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.22
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  105.98
p-value of test                       :  8.7e-3


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.51
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.16
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.28
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.51
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.73
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.27
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.90
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5091.84
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.26
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.32
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.20
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.84
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5074.55
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.89
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.27
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:22.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.97
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   0.052
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:24.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 5.15e-4
p-value of test                       :    0.9995    *****

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -2.21
p-value of test                       :    0.99

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.96e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 9.11e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 8.57e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.31
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.68
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 6.38e-3
p-value of test                       :    0.9932

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  152.13
p-value of test                       :    0.9951

-----------------------------------------------
CPU time used                    :  00:02:06.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.86
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:06.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9836.52
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9885.50
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.27
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:45.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.33
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:48.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4952.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:50.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4261.93
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4123.13
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11996.69
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11448.56
p-value of test                       :    0.9932

-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.52
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999971978

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.78
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000036682

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:03.17

 All tests were passed




Server wird beendet - Lösche Semaphor 183926802.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5293
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:56.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7176
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:42.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:57.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:58.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7489
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:05.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7472
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:05.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:55.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:04:00.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.94
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     270
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.72
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:14.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:42.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.82
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.49
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.85
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.97
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.99
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.00
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.96
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:43.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1547.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:00.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7010.56
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:42.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.65
p-value of test                       :  6.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.02
p-value of test                       :  9.3e-3

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   14.80
p-value of test                       :    0.9908

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.57
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:03.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.96
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:46.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   90.81
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:34.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5080.02
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:16.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45987
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869987
  j =  1                              :        399908029
  j =  2                              :            45981
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45746
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869746
  j =  1                              :        399908510
  j =  2                              :            45742
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:29.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    3.90
p-value of test                       :  1.0e-2


-----------------------------------------------
CPU time used                    :  00:02:19.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:46.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:00.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:55.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:33.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.27e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 4.10e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.089
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:35.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:36.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.99
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  106.66
p-value of test                       :  1.5e-3

-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.07
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.06
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:48.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.04
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.55
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.23
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:45.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.69
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.04
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.11
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.74
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17527.80
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.82
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.08
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.82
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.37
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.00
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.32
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.87
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.51
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.17
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.81
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.56
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.84
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.61
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.98
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.04
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.67
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.02
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.28
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.50
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.89
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.22
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.50
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5083.66
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.00
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.32
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.04
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.36
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4763.38
p-value of test                       :    0.9918


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.24
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.45
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.52
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:23.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.10
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:24.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.77e-3
p-value of test                       :    0.9939

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.24e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 9.37e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.57e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 7.61e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.62
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.10
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.27
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:07.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:06.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9936.67
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10035.79
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:56.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4731.46
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4229.31
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4184.78
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12142.07
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:28.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12025.86
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.98
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999949994

Normal statistic for number of bits   :   -0.40
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.80
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999943535

Normal statistic for number of bits   :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.50
p-value of test                       :    0.07

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:26.75

 All tests were passed




Server wird beendet - Lösche Semaphor 184909842.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5347
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:04:00.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:43.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:45.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:00.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4430
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:02.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:12.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:12.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:09.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:13.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:50.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.06
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    2.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:14.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    3.20
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:41.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:55.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.81
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.97
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.94
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.99
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.49
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.83
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.88
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.40
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.84
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:58.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.90
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:08.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7118.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:58.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.70
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.55
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:09.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.05
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:48.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.07
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:40.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4872.75
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:28.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:08.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45888
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869888
  j =  1                              :        399908226
  j =  2                              :            45884
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45348
p-value of test                       :    0.9935


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869348
  j =  1                              :        399909305
  j =  2                              :            45346
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:31.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:20.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:54.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:11.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:56.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.14e-3
p-value of test                       :    0.9943

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:38.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 2.86e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:24.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:24.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:49.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:49.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.51
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.44
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.91
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.02
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.15
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.13
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.44
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:51.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.59
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:28.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.04
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17237.96
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.55
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.87
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.76
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.81
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.87
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.73
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.85
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.48
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.02
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.19
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.56
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.55
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.66
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.11
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.19
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.18
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.82
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.14
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.07
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.43
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.45
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.23
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.86
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.15
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.72
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  328.79
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.29
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5160.19
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.21
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.50
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.68
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :   -1.00
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:22.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.18
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:23.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.81e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.76
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.91
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.40
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:07.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.63
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:08.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9911.36
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10039.78
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:04:34.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5065.67
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:51.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4928.23
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:55.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.30
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.62
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11695.78
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:33.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11920.07
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:34.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.70
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999972686

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.39
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999828953

Normal statistic for number of bits   :   -1.35
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:09.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 9.96e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.21
p-value of test                       :    0.99

Sample variance                       :    0.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:11.71

 All tests were passed




Server wird beendet - Lösche Semaphor 185958418.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5404
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:55.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4455
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:42.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:56.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:58.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7480
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:07.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:09.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:00.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7452
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:04.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     560
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.70
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.98
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:13.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:41.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.87
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.47
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.08
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.64
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.26
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:10.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.62
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.32
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.24
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.93
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  384.58
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:00.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6957.03
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:47.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.04
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:11.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.05
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:06.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.92
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.95
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:35.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5035.20
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:05.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45974
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869974
  j =  1                              :        399908057
  j =  2                              :            45964
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45449
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869449
  j =  1                              :        399909111
  j =  2                              :            45431
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:29.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:16.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:45.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:02.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-3
p-value of test                       :    0.9985

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :  2.9e-3

Anderson-Darling statistic = A2       :    3.42
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:57.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:35.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.38e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 8.81e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-5
p-value of test                       :    0.9933

Kolmogorov-Smirnov- statistic = D-    : 3.84e-4
p-value of test                       :  2.7e-3

Anderson-Darling statistic = A2       :    3.37
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:44.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.26
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:47.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.42
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.59
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.48
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:55.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.07
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.90
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:44.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.85
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.00
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.30
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.41
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  151.16
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17730.69
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.88
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.73
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.14
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.06
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.73
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.62
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.17
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.18
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.77
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.81
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.04
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.11
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.27
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.53
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.72
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.99
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.33
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.06
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.94
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.13
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.47
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.92
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4935.75
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.74
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.11
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.17
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.54
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4848.12
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.25
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.98
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.82
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -1.85
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:23.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.32
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:23.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.4e-3

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.75
p-value of test                       :    0.04

Sample variance                       :    1.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.69e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 6.91e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9901

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.33e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.49
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.12
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:05.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.98
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:07.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9914.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10160.02
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:04:16.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4786.13
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:51.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:52.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4159.56
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3967.98
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11972.89
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:30.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11487.80
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:31.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.20
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000111160

Normal statistic for number of bits   :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.70
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000086974

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.79
p-value of test                       :    0.96

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:30.60

 All tests were passed




Server wird beendet - Lösche Semaphor 187301906.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:48.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:27.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5388
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:55.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4430
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:40.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:41.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:57.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:06.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:06.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:56.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:04:01.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     943
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:46.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.96
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    2.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.80
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.81
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:13.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:42.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.40
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.74
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.26
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.77
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.56
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.49
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.68
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.44
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  263.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  377.92
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:44.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1465.24
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:00.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7089.07
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:43.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.70
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.12
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:02.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.05
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.15
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:34.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5138.84
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:00.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45500
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869500
  j =  1                              :        399909003
  j =  2                              :            45494
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46025
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870025
  j =  1                              :        399907952
  j =  2                              :            46021
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:28.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:19.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:45.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:01.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:33.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 9.86e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9982

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.38e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:21.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:40.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:38.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.95
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.57
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.63
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.48
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.10
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.00
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.86
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.12
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17330.33
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.07
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.69
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.60
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.38
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.68
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.76
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.85
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.51
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.18
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.55
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.18
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.84
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.12
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.77
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.28
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.80
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.81
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.70
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.87
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.02
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.34
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.34
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.09
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.87
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.73
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.55
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.93
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5122.26
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.24
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.48
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.28
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:22.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.03
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :   -2.96
p-value of test                       :    0.9984



-----------------------------------------------
CPU time used                    :  00:02:20.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    2.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.24e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.61e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.60
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.42
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.26
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:05.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.39
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:05.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10155.26
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10245.00
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:33.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4934.84
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:40.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4802.37
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:34.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4027.60
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4217.13
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11573.35
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:15.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11872.25
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.24
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  8000074911

Normal statistic for number of bits   :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.00
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  7999962126

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    2.01
p-value of test                       :    0.02

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.97e-3
p-value of test                       :    0.9937

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.28
p-value of test                       :    0.01

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:00:10.73

 All tests were passed




Server wird beendet - Lösche Semaphor 188383250.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5508
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:43.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4449
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:36.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7463
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:35.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:55.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:55.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:02.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:02.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:54.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:59.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     940
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:52.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.61
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     572
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.65
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:12.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:37.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.18
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.04
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.05
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.97
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.08
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.18
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.10
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  261.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  372.02
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:50.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1466.35
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:00.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7203.57
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:50.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.41
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:15.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.15
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:46.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.43
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5019.41
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:14.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46570
p-value of test                       :  6.5e-4    *****


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870570
  j =  1                              :        399906863
  j =  2                              :            46564
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46061
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870061
  j =  1                              :        399907881
  j =  2                              :            46055
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:14.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:29.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:17.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :  3.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    3.72
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:44.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :  2.3e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    8.38
p-value of test                       :  8.2e-5    *****


-----------------------------------------------
CPU time used                    :  00:02:00.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:53.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.38e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 8.85e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 2.60e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.66
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:35.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:37.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:48.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.72
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.89
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.42
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.21
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:43.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.11
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.57
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:32.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.20
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:30.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   96.11
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17452.00
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:56.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.94
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.88
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.22
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.48
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.18
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:40.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.28
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.38
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.15
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.98
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.72
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.80
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.00
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.22
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.71
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.62
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:47.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.36
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.92
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.55
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.22
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.66
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.97
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.95
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5118.92
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.80
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.17
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.09
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.34
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.73
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.49
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.58
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:34.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.51
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:15.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.23
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:12.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:11.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:13.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 3.33e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.76e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.49
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.99
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:11.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.00
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:12.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9967.57
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10180.70
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:47.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.33
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:48.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4801.57
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:50.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.08
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3975.76
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11508.09
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11955.46
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   29.03
p-value of test                       :    0.9979


-----------------------------------------------
Total number of bits:  8000066460

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.43
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000024736

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :  -0.017
p-value of test                       :    0.51

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:30.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:17:45.14
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 44  CollisionPermut, r = 0          6.5e-4
 49  MaxOft AD, t = 32               8.2e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 168525843.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:42.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5390
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:44.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:37.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:37.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:54.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:02.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7460
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:02.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:53.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:59.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    2.17
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     972
p-value of test                       :  9.2e-3

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.65
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:10.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.02
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:38.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.24
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    5.55
p-value of test                       :    0.9977

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.10
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.68
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.50
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.80
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  466.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:43.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1501.96
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:02.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7161.83
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:41.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.03
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:19.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.99
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.83
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5164.18
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:15.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45775
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869775
  j =  1                              :        399908454
  j =  2                              :            45767
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45912
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869912
  j =  1                              :        399908181
  j =  2                              :            45902
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:30.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:17.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.94
p-value of test                       :  3.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9977


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:44.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:00.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:54.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:32.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:34.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:35.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.25
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.92
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.74
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:48.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.44
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.51
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.13
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:40.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.54
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.59
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.66
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:29.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.56
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 6.23e-3
p-value of test                       :    0.9934

Anderson-Darling statistic = A2       :    4.44
p-value of test                       :  5.6e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   94.45
p-value of test                       :    0.9919

-----------------------------------------------
CPU time used                    :  00:00:39.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 5.48e-3
p-value of test                       :    0.9942

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17762.04
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.59
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.56
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.65
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.35
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.74
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.87
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.97
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.04
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.62
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.82
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.28
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.75
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.68
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.88
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.38
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:46.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.04
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.06
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  435.33
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.16
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.53
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.36
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.05
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5134.84
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.28
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.98
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.96
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.62
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5208.20
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.21
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  257.92
p-value of test                       :  3.6e-3


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.18
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:18.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.65
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :   -1.50
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:18.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    2.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.55e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:47.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 2.32e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.55
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.52
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.65
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:08.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.81
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:12.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10051.57
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10288.61
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:04:09.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.78
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5079.71
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:49.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.52
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4045.53
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11778.52
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12024.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:30.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.39
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000011317

Normal statistic for number of bits   :   0.089
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.09
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000072232

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :  -0.081
p-value of test                       :    0.53

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:11:00.52

 All tests were passed




Server wird beendet - Lösche Semaphor 169476115.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1468
p-value of test                       :  2.8e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334588
  j =  1                              :        599997064
  j =  2                              :             1468
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1256
p-value of test                       :    0.9984

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334376
  j =  1                              :        599997488
  j =  2                              :             1256
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5383
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:46.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:37.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:37.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:54.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:02.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:02.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:53.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:00.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.03
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.99
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    3.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     551
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:12.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    2.21
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     121
p-value of test                       :    0.9916

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:47.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.26
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.46
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:11.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.58
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.31
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.42
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  193.80
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:45.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1324.52
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:00.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7034.33
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:43.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.72
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.36
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:00.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.87
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.09
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:34.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5031.28
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:21.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45878
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869878
  j =  1                              :        399908244
  j =  2                              :            45878
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46163
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870163
  j =  1                              :        399907675
  j =  2                              :            46161
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:31.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:18.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:43.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :  1.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    4.19
p-value of test                       :  7.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.9926


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:00.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:54.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:33.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.67e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.33e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:35.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:34.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.31
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.47
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.25
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:48.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.92
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.99
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.06
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.69
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.47
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.01
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.21
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17550.49
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.04
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.53
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.44
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.79
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.10
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:39.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.75
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.85
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.33
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.25
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   46.50
p-value of test                       :  1.4e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.46
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.85
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.39
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.77
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.45
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.30
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.31
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.45
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.62
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.90
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.37
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.42
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4853.24
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.74
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.52
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.36
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.17
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5165.87
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.65
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.23
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.71
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:20.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.63
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :   -2.99
p-value of test                       :    0.9986



-----------------------------------------------
CPU time used                    :  00:02:24.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.66
p-value of test                       :    0.95

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.83e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:47.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 8.36e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.77
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.00
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  159.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:08.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.46
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:08.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10186.70
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10168.46
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:57.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5015.69
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:49.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4924.88
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.96
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.21
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11798.58
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:28.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11858.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:30.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.12
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000056950

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.90
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999912725

Normal statistic for number of bits   :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:06.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 75  RandomWalk1 C (L=50, r=25)      1.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 170459155.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5522
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:45.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4226
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:37.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:36.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4472
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:55.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:57.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:04.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:05.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:01.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:04:04.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    3.20
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     965
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:46.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.93
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    2.39
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:11.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.75
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:44.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.28
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.46
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:11.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.84
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.46
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.07
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.98
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  453.96
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:56.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.85
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:08.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7049.28
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:57.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.74
p-value of test                       :  1.2e-3

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    6.36
p-value of test                       :  7.6e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.66
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.57
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:15.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.34
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.32
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:40.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4973.20
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:10.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46084
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870084
  j =  1                              :        399907837
  j =  2                              :            46074
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45853
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869853
  j =  1                              :        399908294
  j =  2                              :            45853
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:34.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:22.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:52.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:06.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:56.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:37.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 4.63e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:24.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:24.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:51.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.80
p-value of test                       :    0.9975

-----------------------------------------------
CPU time used                    :  00:01:52.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.83
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.91
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.18
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.11
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:51.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.17
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.63
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:51.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.90
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.19
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.68
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.11
p-value of test                       :    0.9908

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.46
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17453.11
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.92
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.64
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.20
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.66
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.80
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.92
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.20
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.16
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.91
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.08
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.70
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.73
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.29
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.99
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.86
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.72
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.16
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.30
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.04
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.79
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.89
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4899.55
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.90
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.70
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.46
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.87
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4916.17
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.25
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.87
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.26
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :    0.54
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:26.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.07
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:27.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.61e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.87e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.05
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.65
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.58
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:07.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.82e-3
p-value of test                       :    0.9981

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.07
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:08.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9939.79
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10080.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:04:31.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4832.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:54.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.47
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:57.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.75
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11674.16
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:35.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11731.08
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:36.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.58
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999927977

Normal statistic for number of bits   :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.37
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000117832

Normal statistic for number of bits   :    0.93
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:12:48.04

 All tests were passed




Server wird beendet - Lösche Semaphor 171311123.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5476
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:51.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:41.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:59.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:00.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:09.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:10.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7169
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:04:09.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:14.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.98
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    2.18
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:14.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.18
p-value of test                       :    0.9945

-----------------------------------------------
CPU time used                    :  00:02:42.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.51
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.41
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.09
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.74
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.35
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.23
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:29.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  527.72
p-value of test                       :  1.4e-3

-----------------------------------------------
CPU time used                    :  00:01:56.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1505.39
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:02.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6818.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:55.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.69
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.29
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:11.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.66
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:39.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5038.81
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:29.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:02.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45518
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869518
  j =  1                              :        399908968
  j =  2                              :            45510
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45665
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869665
  j =  1                              :        399908671
  j =  2                              :            45663
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.76
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:31.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:22.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:55.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:11.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:57.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 3.63e-3
p-value of test                       :    0.9961

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:38.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.04e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 7.53e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:24.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.02
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:52.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.095
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:49.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.26
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.16
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.23
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.78
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.58
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.56
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.96
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:52.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9960

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.38
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.13
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.25
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:29.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.05
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17591.37
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.64
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.06
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.08
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.18
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.29
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   56.42
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.50
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.99
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.13
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.28
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:39.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.81
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.63
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.43
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  173.19
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.86
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.72
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.33
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.10
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.26
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.47
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.24
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.69
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5029.41
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.64
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.24
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.71
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.76
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5126.54
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.74
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.21
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.47
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :    1.91
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:25.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.11
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:24.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :  -0.082
p-value of test                       :    0.53

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 5.05e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:46.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.72
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:29.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.20
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  162.77
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:18.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.63
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:21.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9858.48
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10137.07
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:04:39.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.44
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:52.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4793.70
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:54.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4036.01
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4065.19
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12018.05
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:32.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11813.48
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:35.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.18
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000065764

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.05
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000115879

Normal statistic for number of bits   :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   0.058
p-value of test                       :    0.48

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:12:56.22

 All tests were passed




Server wird beendet - Lösche Semaphor 172720147.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5479
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:54.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:40.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:42.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:01.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:12.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:12.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:57.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:04:01.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:49.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:15.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.17
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:42.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.30
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.28
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.85
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.47
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.42
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.16
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.97
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.30
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.17
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:21.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.67
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:15.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7058.42
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:28.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.63
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:01.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   13.57
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.51
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4987.42
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:55.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45699
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869699
  j =  1                              :        399908605
  j =  2                              :            45693
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46233
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870233
  j =  1                              :        399907540
  j =  2                              :            46221
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:27.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:18.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:59.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:55.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:34.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.81e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:24.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:34.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:34.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.05
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.52
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.20
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.74
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:49.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.86
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.35
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.09
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:58.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.94
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.37
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.93
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:29.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.60
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.33
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:47.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17233.81
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.43
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.52
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.46
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.44
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.49
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.31
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.30
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.19
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.57
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.17
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.42
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.78
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.14
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.58
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.40
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.92
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.11
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.57
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   84.28
p-value of test                       :    0.9998    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.50
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.31
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.28
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4901.97
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.63
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.73
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.24
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.16
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.94
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.62
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.42
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.29
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:26.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.01
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :    0.86
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:27.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   0.027
p-value of test                       :    0.49

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 6.03e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 8.34e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.21
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.02
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.04
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:09.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.33
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:11.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.5e-3

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10245.43
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.48
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.089
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:53.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9932

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.00
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4907.30
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3917.42
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.18
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11992.79
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11535.78
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.30
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999999095

Normal statistic for number of bits   : -7.15e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.90
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999997454

Normal statistic for number of bits   :  -0.020
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:41.56
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 77  RandomWalk1 R (L=1000, r=20)    0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 174129171.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5388
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:54.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4244
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:41.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:58.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:06.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7198
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:05.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:55.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7480
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:00.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     940
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    5.98
p-value of test                       :  1.0e-3

Stat. AD after spacings (mNP2-S)      :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     560
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    2.25
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.25
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    3.40
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     258
p-value of test                       :    0.9928

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:18.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.28
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:43.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.17
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   45.17
p-value of test                       :  3.9e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.02
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.43
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.63
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.23
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.89
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.98
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.51
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:43.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1472.82
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:57.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6910.16
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:42.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.22
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.70
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:02.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.08
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.44
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:35.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5319.38
p-value of test                       :  3.0e-3


-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:57.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45850
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869850
  j =  1                              :        399908303
  j =  2                              :            45844
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45816
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869816
  j =  1                              :        399908371
  j =  2                              :            45810
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:28.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:19.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:45.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:59.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:55.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:37.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:39.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.81
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.47
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.04
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.02
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.97
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.45
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.46
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:45.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.09
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.39
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.56
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.59
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:29.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.71
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17661.13
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.16
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.34
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.76
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.87
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.27
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.07
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.39
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.06
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.70
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.60
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.03
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.24
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.25
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.53
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.00
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.13
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.90
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.48
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.53
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.53
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.20
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.71
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5168.68
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  317.58
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.87
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.94
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.45
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5072.30
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.77
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.00
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.64
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:24.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.31
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :    1.66
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:25.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :  -0.027
p-value of test                       :    0.51

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 4.96e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:46.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 3.08e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.93
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.93
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.61
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:07.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.71
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:07.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9832.78
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10036.33
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:53.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4838.45
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:49.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4764.71
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:50.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3963.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3923.60
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11787.61
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11704.10
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.94
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000146701

Normal statistic for number of bits   :    1.16
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.39
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999920504

Normal statistic for number of bits   :   -0.63
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:13.18
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 28  SimpPoker, r = 0                3.9e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 175079443.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1465
p-value of test                       :  3.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334585
  j =  1                              :        599997070
  j =  2                              :             1465
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5372
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:56.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:42.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:43.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:00.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:01.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:12.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:12.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:10.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:16.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.07
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    2.32
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:48.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.94
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:15.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:43.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.10
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.50
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.40
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.76
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   93.66
p-value of test                       :  6.6e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.08
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.43
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.59
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:31.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.04
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:58.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.44
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:04.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7171.78
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:53.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.32
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.16
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:46.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.56
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:43.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4990.45
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:58.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45892
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869892
  j =  1                              :        399908222
  j =  2                              :            45880
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46140
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870140
  j =  1                              :        399907727
  j =  2                              :            46126
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:31.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:20.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:53.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:09.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:05.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:46.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.94e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:26.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:26.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:47.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:51.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.07
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   94.01
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.98
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.90
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.73
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.59
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:50.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.49
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.22
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:29.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:29.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  170.30
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17594.10
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.60
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.44
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.96
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.10
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.83
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.99
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.35
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.31
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.61
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.93
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.92
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.05
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.23
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.97
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.53
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.40
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.27
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.67
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.56
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.91
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.72
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.94
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5111.35
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.10
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.54
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.55
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.60
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4925.80
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.87
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.69
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.14
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:25.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.19
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :    1.90
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:25.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9926

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.17e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.02e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 4.68e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.67
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.22
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.64
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:06.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.48
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:06.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10071.52
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9994.48
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.38
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:04:31.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.17
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:55.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4804.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:59.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.98
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.79
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11640.87
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:36.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11543.96
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:38.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.78
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999956201

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.01
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999945068

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:49.92
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 30  CouponCollector, r = 0          6.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 176160787.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5440
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:55.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:41.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4450
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:57.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:05.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:07.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:56.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:04:00.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9950


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:49.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.14
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.77
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:17.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:44.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.17
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.80
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.19
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:11.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.41
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.95
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.78
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:44.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.79
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:00.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7089.67
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:41.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.03
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:04.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.39
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.53
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4971.31
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:54.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46114
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870114
  j =  1                              :        399907774
  j =  2                              :            46110
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46089
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870089
  j =  1                              :        399907825
  j =  2                              :            46083
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:27.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:17.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:44.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :  8.2e-4    *****

Anderson-Darling statistic = A2       :    4.33
p-value of test                       :  6.2e-3


-----------------------------------------------
CPU time used                    :  00:02:00.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :  7.4e-4    *****

Anderson-Darling statistic = A2       :    5.20
p-value of test                       :  2.4e-3

-----------------------------------------------
CPU time used                    :  00:01:17.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:36.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:22.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:22.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:43.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.21
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.54
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:49.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.45
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.04
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.42
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.22
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.73
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:45.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.07
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:28.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.56
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17482.53
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.77
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.17
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.93
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.95
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.51
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.41
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.52
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.69
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.65
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.26
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.03
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.31
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.06
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.66
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.17
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.62
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.26
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.56
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.16
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.07
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.25
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.81
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4988.25
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.07
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  162.89
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.45
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.50
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.80
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.28
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.65
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.64
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:26.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.16
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:25.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   0.087
p-value of test                       :    0.47

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   0.049
p-value of test                       :    0.48

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.92e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.13
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.47
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.51
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:06.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.81e-3
p-value of test                       :    0.9928

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  243.55
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:08.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10060.40
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10143.91
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:44.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.05
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:46.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5013.47
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:49.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3917.87
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:18.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4042.12
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11658.17
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11837.07
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.13
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000037477

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.79
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000032326

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    2.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.081
p-value of test                       :    0.53

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:46.77

 All tests were passed




Server wird beendet - Lösche Semaphor 177274899.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1465
p-value of test                       :  3.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334585
  j =  1                              :        599997070
  j =  2                              :             1465
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5426
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:54.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:40.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4442
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:57.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:05.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:07.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:58.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7171
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:04:01.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.13
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    2.01
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    2.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:47.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    3.60
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     641
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.76
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.20
p-value of test                       :    0.9904

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:14.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.17
p-value of test                       :    0.9970

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:45.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.55
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.80
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.89
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.71
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.05
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:10.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.74
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.84
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.18
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.93
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:44.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1434.27
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:00.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7147.77
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:44.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.27
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.84
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:04.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   13.35
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.15
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5083.18
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:55.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45843
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869843
  j =  1                              :        399908320
  j =  2                              :            45831
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45615
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869615
  j =  1                              :        399908775
  j =  2                              :            45605
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:28.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:17.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:44.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:59.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:56.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:37.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.77e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:21.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.96
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:41.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:43.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.56
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.58
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:55.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.81
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.15
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.21
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.76
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.30
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.93
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17470.54
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.23
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.48
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.18
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.41
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.35
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.84
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.78
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.40
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.37
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.07
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.58
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.18
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.02
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.79
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.77
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.47
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.94
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.66
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.82
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.13
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.18
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.80
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.75
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.82
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.92
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.08
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.86
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  427.21
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.56
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.66
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :   -1.43
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:25.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.33
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:25.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.94e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 7.54e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 4.68e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.30
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.70
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.77
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:07.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.11
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:07.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10036.48
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9984.57
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.052
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:53.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5069.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4767.52
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:47.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4033.82
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3960.69
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11869.49
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11941.00
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.37
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999992351

Normal statistic for number of bits   :  -0.060
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.71
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000107785

Normal statistic for number of bits   :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         : -2.98e-3
p-value of test                       :    0.50

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.65
p-value of test                       :    0.05

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:05.94

 All tests were passed




Server wird beendet - Lösche Semaphor 178323475.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5566
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:54.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4466
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:40.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4520
p-value of test                       :  2.9e-3


-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:58.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:06.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:06.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:58.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:02.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.65
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    3.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:15.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:43.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.72
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.14
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.53
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.65
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.79
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:10.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.92
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.83
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  197.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  470.49
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:44.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1379.46
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:59.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6891.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:44.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.44
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.1e-3

Anderson-Darling statistic = A2       :    4.38
p-value of test                       :  6.0e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   89.46
p-value of test                       :  8.1e-3

-----------------------------------------------
CPU time used                    :  00:03:02.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.77
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.99
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:33.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5026.36
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:58.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45727
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869727
  j =  1                              :        399908548
  j =  2                              :            45723
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45476
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869476
  j =  1                              :        399909054
  j =  2                              :            45464
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:27.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:18.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:44.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:59.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:35.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 9.00e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.54e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:36.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:38.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.65
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.29
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.02
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.78
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.64
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:56.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.67
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.09
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.66
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17300.12
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.38
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.34
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.52
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.48
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.95
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.23
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   55.77
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.47
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.71
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.76
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.94
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.62
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.00
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.76
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.46
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.45
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.75
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.54
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.72
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.83
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.51
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.66
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5096.26
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  448.81
p-value of test                       :  7.1e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.37
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.27
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.68
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5079.58
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.47
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  248.27
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.38
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :    2.52
p-value of test                       :  5.9e-3



-----------------------------------------------
CPU time used                    :  00:02:24.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.84
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:24.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 6.77e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 5.60e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.50
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.91
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.76
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:06.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.31
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:07.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10041.87
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9934.44
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:46.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4968.28
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4752.12
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.06
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12012.44
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11781.97
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.10
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000096247

Normal statistic for number of bits   :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.78
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000183955

Normal statistic for number of bits   :    1.45
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   0.099
p-value of test                       :    0.46

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:53.00

 All tests were passed




Server wird beendet - Lösche Semaphor 179372051.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5514
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:52.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:40.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:56.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4188
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:57.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:06.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7184
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:05.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:55.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:00.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    2.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:49.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    2.51
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     268
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:16.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    2.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:41.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.59
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.43
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.33
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.69
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.81
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.32
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:44.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1423.11
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:00.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7101.30
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:42.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.53
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.30
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:02.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.17
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   91.30
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:33.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5078.72
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:02.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45571
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869571
  j =  1                              :        399908865
  j =  2                              :            45557
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46211
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870211
  j =  1                              :        399907581
  j =  2                              :            46205
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:27.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  8.0e-3

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:18.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:45.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:56.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:34.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.60e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.94e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:24.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:38.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:40.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.17
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.85
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.33
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.97
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.77
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:44.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.17
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.89
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.76
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.27
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17252.69
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.69
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.73
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.81
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.74
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.18
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:38.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.52
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.71
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.38
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.26
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.27
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  194.28
p-value of test                       :  4.6e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.13
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.27
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.66
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.89
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.33
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.91
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.51
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.56
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.74
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.27
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5136.31
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.23
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.53
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.37
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.98
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5098.20
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  425.67
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.47
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:25.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.32
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:26.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.76
p-value of test                       :    0.96

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 7.35e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.97e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.09
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.43
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.19
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:07.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.26
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:08.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9893.09
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10036.21
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:47.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.04
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5035.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:49.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4033.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.28
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11608.61
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11866.10
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.32
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  8000128065

Normal statistic for number of bits   :    1.01
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.23
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000149305

Normal statistic for number of bits   :    1.18
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.57
p-value of test                       :    0.06

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:35.29

 All tests were passed




Server wird beendet - Lösche Semaphor 180387859.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5555
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:54.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4234
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:58.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:00.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:10.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:11.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:09.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:11.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.92
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     953
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:48.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.14
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.90
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.85
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:15.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:43.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.61
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   26.22
p-value of test                       :  4.6e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.67
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.21
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.70
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.81
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.24
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.75
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.27
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.63
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:54.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1369.45
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7205.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:54.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.44
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.37
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:15.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.63
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.82
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:37.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5150.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:55.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45986
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869986
  j =  1                              :        399908033
  j =  2                              :            45976
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45535
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869535
  j =  1                              :        399908933
  j =  2                              :            45529
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:31.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:19.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:51.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9966

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:05.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:06.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:46.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.21e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.87e-4
p-value of test                       :  2.5e-3

Kolmogorov-Smirnov- statistic = D-    : 8.17e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    4.23
p-value of test                       :  6.7e-3

-----------------------------------------------
CPU time used                    :  00:00:24.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:26.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:26.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:51.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:51.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.15
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.73
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:50.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.22
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   59.81
p-value of test                       :  6.5e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:50.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.97
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.96
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  102.50
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17654.04
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.66
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.17
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.06
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.02
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.14
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.09
p-value of test                       :    0.9906


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.64
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.94
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.93
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.98
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.91
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.81
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.68
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.46
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.78
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.65
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.41
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.45
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.21
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.13
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.37
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.27
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.84
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.47
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.48
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.64
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.01
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5072.40
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.58
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  237.17
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.04
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:24.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.31
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :   -1.96
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:23.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.50e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 8.88e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.82
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.55
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.16
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:07.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.19
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:07.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9961.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9820.61
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:04:21.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4987.54
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:54.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.84
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:57.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.06
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.91
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11632.54
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:32.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11896.66
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:32.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.94
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000016147

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.73
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000034270

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.91

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:57.82
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 27  SimpPoker, r = 27               4.6e-4
 65  SumCollector                    6.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 181370899.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5265
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:04:00.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:45.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:48.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:05.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:07.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:21.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:21.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:04:28.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:33.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    4.34
p-value of test                       :  6.0e-3

-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.16
p-value of test                       :    0.9981


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:14.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:43.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.55
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   43.25
p-value of test                       :  7.4e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.29
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.83
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.28
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.28
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  267.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:31.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.64
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:11.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1460.90
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:10.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7207.78
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:07.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.58
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.82
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.21
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:10.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.83
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:47.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  152.16
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:39.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5066.12
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:55.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45670
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869670
  j =  1                              :        399908660
  j =  2                              :            45670
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45345
p-value of test                       :    0.9937


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869345
  j =  1                              :        399909314
  j =  2                              :            45337
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 4.57e-3
p-value of test                       :    0.9945

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :  4.6e-3

Anderson-Darling statistic = A2       :    4.71
p-value of test                       :  4.0e-3


-----------------------------------------------
CPU time used                    :  00:02:36.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:26.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:02.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:19.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:58.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:39.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.07e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.23e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.61e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:27.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:27.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:43.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:44.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.56
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.73
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.54
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.72
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:56.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 5.26e-3
p-value of test                       :    0.9945

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.40
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.64
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.97
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  160.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17515.29
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.71
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.94
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.20
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.81
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.40
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.86
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.13
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.66
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.61
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.86
p-value of test                       :    0.9941


-----------------------------------------------
CPU time used                    :  00:00:36.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.14
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.80
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.03
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.30
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.51
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.67
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.25
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.49
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.36
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.33
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.26
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.50
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4876.52
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  425.23
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.13
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.35
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.21
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.30
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.91
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.33
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.43
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :   -1.11
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:20.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.44
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :   -1.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:20.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.14

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.6e-3

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.99
p-value of test                       :    0.02

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.52e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.81e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 6.03e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.46
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:36.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.21
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:34.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.74
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:21.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.63
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:20.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10144.26
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10069.28
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:04:18.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.01
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4835.82
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:58.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4137.18
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4248.21
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11606.68
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:35.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11869.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:38.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.66
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999951338

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:18.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.21
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999839606

Normal statistic for number of bits   :   -1.27
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.12
p-value of test                       :    0.02

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:39.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.18
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:01:40.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:14:21.09
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 28  SimpPoker, r = 0                7.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 182452243.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5402
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:58.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:43.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:45.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:00.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:01.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:11.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:12.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:03.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:04:07.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.74
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     951
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:50.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:15.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.57
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:43.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.98
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.85
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.59
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.91
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.01
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:11.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.55
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.69
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  198.97
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.06
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:50.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1461.05
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:02.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6945.17
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.00
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:09.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.94
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.62
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:36.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5154.33
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:04.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46261
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870261
  j =  1                              :        399907479
  j =  2                              :            46259
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46277
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870277
  j =  1                              :        399907447
  j =  2                              :            46275
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:33.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:20.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:47.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:05.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:56.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:37.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:43.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:39.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.32
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.40
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.70
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.30
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.74
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   48.87
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:44.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.62
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.64
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.90
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.18
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.78
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17411.32
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.46
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.54
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.12
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.70
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.97
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.64
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.99
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.70
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.11
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.49
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.31
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.41
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.10
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.51
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.99
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.49
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.54
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.04
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.85
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.66
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.76
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.41
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.69
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.90
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.19
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.72
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.02
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.32
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.82
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.23
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:34.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.21
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :   -1.12
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:18.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.36
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :   -1.31
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:18.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 8.11e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.23
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.82
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.10
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:02.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.34
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:02.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10132.17
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10071.42
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:04:02.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4727.33
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:51.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.12
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:52.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4235.71
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4162.01
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12005.48
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:30.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11868.97
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:31.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.01
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999992072

Normal statistic for number of bits   :  -0.063
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.44
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000052642

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.21
p-value of test                       :    0.9935

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   0.023
p-value of test                       :    0.49

Sample variance                       :    0.22
p-value of test                       :    0.9922

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:51.88

 All tests were passed




Server wird beendet - Lösche Semaphor 183566355.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5457
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:59.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:42.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:57.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:07.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:06.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:55.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:01.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.01
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     941
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    2.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:51.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:16.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    2.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:44.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.09
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.50
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.86
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.97
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.67
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.68
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  395.60
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:44.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1471.46
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:00.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7006.76
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:45.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.65
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:04.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.01
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:35.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5176.16
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:58.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46061
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870061
  j =  1                              :        399907882
  j =  2                              :            46053
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45874
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869874
  j =  1                              :        399908255
  j =  2                              :            45868
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:28.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 5.95e-3
p-value of test                       :    0.9929

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9903


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:18.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:44.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:59.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:57.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:35.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.00e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 6.06e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.77e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.67e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.37
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:00:22.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:36.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.88
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.19
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.76
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:49.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.40
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.27
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.55
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:39.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.48
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.17
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.19
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.59
p-value of test                       :  4.0e-4    *****

Kolmogorov-Smirnov- statistic = D-    : 3.49e-3
p-value of test                       :    0.9964

Anderson-Darling statistic = A2       :    5.11
p-value of test                       :  2.7e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   84.47
p-value of test                       :    0.9993    *****

-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17333.07
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.78
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.83
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.87
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.45
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.46
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.39
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.32
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.24
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.70
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.23
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.96
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.89
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.80
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.19
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.59
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.28
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  195.70
p-value of test                       :  3.8e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.55
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.96
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.65
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:43.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.99
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.75
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5167.30
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.20
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.30
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:34.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.05
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.32
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.85
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.29
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.82
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.78
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  :    1.15
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:20.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.25
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:21.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.65
p-value of test                       :    0.05

Sample variance                       :    2.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.92e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.09e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.43
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.73
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.76
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:03.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.79
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:03.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10065.77
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10025.77
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:49.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5020.96
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:47.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4850.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:50.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4200.87
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4244.50
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12046.45
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:29.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11934.11
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:29.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.60
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  7999921020

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.89
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999976973

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.53
p-value of test                       :    0.06

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9983

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:11.80
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 72  Savir2                          0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 184647699.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5450
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:04:01.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7162
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:43.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:57.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:59.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:06.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:06.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:56.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:00.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.18
p-value of test                       :    0.9942

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     942
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:47.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     652
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.91
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:15.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:43.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.64
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.88
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.50
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.55
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:10.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.32
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.97
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.75
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.64
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:44.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1422.12
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:00.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6936.66
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:43.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:03.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.20
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.29
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:35.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5098.18
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:59.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46023
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870023
  j =  1                              :        399907954
  j =  2                              :            46023
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46032
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870032
  j =  1                              :        399907942
  j =  2                              :            46020
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:28.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:18.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:45.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:58.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:35.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.33e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 7.91e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.39e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.065
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:35.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.57
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.05
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.70
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.81
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.57
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:41.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.40
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.32
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   10.34
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.69
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17518.60
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.49
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.31
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.95
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.06
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.02
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.86
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.92
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.40
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.03
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.44
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.99
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.30
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.36
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  174.56
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.40
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.28
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.17
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.27
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.57
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.73
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.19
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.73
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5050.24
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.86
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.19
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.44
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.41
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.91
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  329.76
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.62
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.86
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:20.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.07
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :    0.69
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:22.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    2.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.95e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.87e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 7.59e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.03
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.43
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.83
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:03.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.68
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:04.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10156.60
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9920.21
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:38.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4787.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:48.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4905.61
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:50.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4037.16
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3905.13
p-value of test                       :    0.9911

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11680.66
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11898.62
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.09
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000046189

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.46
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000010045

Normal statistic for number of bits   :   0.079
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.48
p-value of test                       :    0.07

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   0.051
p-value of test                       :    0.48

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:48.68

 All tests were passed




Server wird beendet - Lösche Semaphor 185663507.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9947


-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5432
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:04:02.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:44.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:46.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:02.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:03.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:13.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:13.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:09.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:14.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.27
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     858
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.99
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:15.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    4.28
p-value of test                       :  6.4e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     333
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.82
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:14.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:47.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.78
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.39
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.26
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.65
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.83
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.92
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.65
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.72
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.56
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  453.38
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1445.65
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:02.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7073.80
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.68
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.73
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:16.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.21
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.46
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5014.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:02.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45859
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869859
  j =  1                              :        399908288
  j =  2                              :            45847
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45383
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869383
  j =  1                              :        399909238
  j =  2                              :            45375
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:32.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:53.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:09.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:57.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:38.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.64e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.60e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.37e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:24.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.027
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.055
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:42.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.60
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:51.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.95
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.53
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.08
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.46
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.58
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:51.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.17
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.16
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.74
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17201.54
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.75
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.21
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :    9.15
p-value of test                       :    0.9984


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.24
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.55
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.18
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.75
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.47
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.84
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.50
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.22
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.68
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.56
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.27
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.81
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.10
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.90
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.86
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.71
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.33
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.45
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5126.42
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.46
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.40
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:34.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.41
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.27
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5077.28
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.10
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.20
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.58
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:21.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.89
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :   -1.42
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:21.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.18
p-value of test                       :    0.9959

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 4.92e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 8.27e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.36
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.42
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.57
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:02.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.7e-3

Anderson-Darling statistic = A2       :    4.66
p-value of test                       :  4.4e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  257.70
p-value of test                       :  3.7e-3

-----------------------------------------------
CPU time used                    :  00:02:03.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9946.21
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.09
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.034
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.098
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:04:24.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4958.93
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:58.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.92
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.62
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11898.21
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:34.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11626.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:35.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.54
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999926252

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.29
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999976628

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:27.18

 All tests were passed




Server wird beendet - Lösche Semaphor 186712083.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:38.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5314
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:58.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4158
p-value of test                       :    0.9968


-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7186
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:42.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4229
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:57.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:58.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:06.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:06.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:56.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:00.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.11
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:49.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.01
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:15.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    2.67
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:47.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.26
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.35
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.38
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.78
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:11.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.84
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.97
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.36
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.95
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.24
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:45.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1470.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7135.53
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:43.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.65
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.78
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:05.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.73
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.38
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:34.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4903.98
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:00.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46095
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870095
  j =  1                              :        399907814
  j =  2                              :            46087
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45768
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869768
  j =  1                              :        399908468
  j =  2                              :            45760
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:30.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:18.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:44.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:00.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:57.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:35.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.59e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:22.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:34.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.13
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.66
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.90
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.38
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.45
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.49
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:40.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.24
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.54
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.33
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.75
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  157.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17538.45
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:52.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.30
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.30
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.57
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.37
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.09
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.82
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.37
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.29
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.04
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.29
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.16
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.92
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.59
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.55
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.64
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.21
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.54
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.52
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.43
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.29
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.34
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5117.20
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.92
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.24
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.85
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.73
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.24
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.98
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.11
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:34.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.03
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :    2.21
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:02:22.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.70
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:21.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.31e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 7.19e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.18
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.61
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.39
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:02.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.13
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:02.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9929.88
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10105.76
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.38
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:03:38.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.56
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:47.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.41
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:50.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3995.59
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.26
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11935.45
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12111.69
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:30.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.40
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000117790

Normal statistic for number of bits   :    0.93
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.78
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999968903

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:59.52

 All tests were passed




Server wird beendet - Lösche Semaphor 187760659.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5508
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:04:01.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:43.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:46.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:01.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:11.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:12.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:07.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7447
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:04:10.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     637
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    2.69
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:16.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:45.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.99
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.96
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.45
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.73
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.78
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.74
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.67
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.24
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:52.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1483.23
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:02.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6895.96
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:53.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.63
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.06
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:12.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.74
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.34
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:37.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5031.83
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:59.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45561
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869561
  j =  1                              :        399908880
  j =  2                              :            45557
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46056
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870056
  j =  1                              :        399907889
  j =  2                              :            46054
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:28.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:16.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:41.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:54.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:48.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 2.77e-3
p-value of test                       :    0.9971

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:29.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.92e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.60e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 5.90e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.084
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:32.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:31.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   41.63
p-value of test                       :    0.9937

-----------------------------------------------
CPU time used                    :  00:00:47.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.52
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.02
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:47.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.79
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:51.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.02
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:38.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.12
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.83
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.74
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.36
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    3.41
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17084.51
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:47.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.31
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.84
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.57
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.11
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.02
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:34.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.36
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.31
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.84
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.54
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.50
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.75
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.20
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.33
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.99
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.95
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:39.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.29
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.15
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.88
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.47
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.51
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:39.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  443.89
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.66
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.89
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.32
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.55
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:32.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.83
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.53
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4988.98
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.72
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.28
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:31.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.33
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :  -0.082
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:08.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.76
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :   0.092
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:08.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9966

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.43e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 6.16e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.41e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.08
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.30
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.57
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:53.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.02
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:53.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10153.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9973.14
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:49.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.41
p-value of test                       :  7.9e-3

-----------------------------------------------
CPU time used                    :  00:03:15.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.65
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:42.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4804.40
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:45.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3999.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3966.84
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11873.88
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11688.97
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.88
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999906815

Normal statistic for number of bits   :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.38
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999988628

Normal statistic for number of bits   :  -0.090
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.73

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.80
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.62
p-value of test                       :  4.4e-3

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   02:59:43.88

 All tests were passed




Server wird beendet - Lösche Semaphor 188809235.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5414
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:43.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:37.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:35.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:54.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:55.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:02.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:02.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:54.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7162
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:59.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:50.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:13.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:37.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.72
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.95
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.16
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.89
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.72
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.59
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.74
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.44
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:17.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:47.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1505.02
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:59.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7127.31
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:43.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:02.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.63
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.73
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:36.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5057.11
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:02.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45796
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869796
  j =  1                              :        399908409
  j =  2                              :            45794
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45635
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869635
  j =  1                              :        399908736
  j =  2                              :            45623
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:14.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:29.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:19.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:46.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:00.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:53.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.39e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.62e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.053
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:34.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:35.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.19
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:48.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.07
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.55
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.47
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:48.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.83
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.92
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:40.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.11
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.74
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.66
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:32.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:32.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:10.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.47
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 8.58e-3
p-value of test                       :    0.9907

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17128.95
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.78
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.38
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.36
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.29
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.91
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.00
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.01
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.52
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.04
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.80
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.23
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.26
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.40
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.02
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.09
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:47.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.00
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.07
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.09
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.12
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.86
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:48.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  466.65
p-value of test                       :  2.4e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.50
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5051.79
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.71
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.73
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.32
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.80
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4857.26
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.92
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  254.93
p-value of test                       :  5.2e-3


-----------------------------------------------
CPU time used                    :  00:00:40.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.18
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:30.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.82
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   -1.28
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:14.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.72e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 6.36e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.62
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.17
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.66
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:08.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.23
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:13.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10058.26
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9956.34
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.038
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:51.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4852.29
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:49.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4773.26
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:50.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4141.37
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4000.25
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11790.03
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11763.74
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:30.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.89
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999911084

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.09
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999971681

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.48
p-value of test                       :    0.07

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.99
p-value of test                       :  9.2e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.84
p-value of test                       :    0.9977

Sample variance                       :    1.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.64
p-value of test                       :    0.05

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:29.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:16:00.06

 All tests were passed




Server wird beendet - Lösche Semaphor 168558612.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:01.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:04.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5482
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:43.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:37.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:36.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:54.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4228
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:55.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:03.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7497
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:02.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:53.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:59.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.87
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:10.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:34.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.10
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.18
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.12
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.32
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.67
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.28
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.08
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  261.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.91
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:50.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1395.85
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:01.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6975.63
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:49.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.14
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:02.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.09
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   86.09
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5142.67
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:03.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45784
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869784
  j =  1                              :        399908437
  j =  2                              :            45774
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46326
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870326
  j =  1                              :        399907349
  j =  2                              :            46324
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:31.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:19.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:45.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:01.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:54.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:33.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.27e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 7.11e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.050
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.096
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:34.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:34.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.29
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.90
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.80
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.82
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:48.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.70
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.17
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.04
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.32
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.63
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:30.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:29.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.95
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17335.94
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.99
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   55.33
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.87
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.52
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.89
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.75
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.74
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.95
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.94
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.95
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.30
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.48
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.49
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.31
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.79
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:47.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.34
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.68
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.69
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.37
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.35
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:46.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.91
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.13
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5048.94
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.00
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.05
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:36.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.53
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.27
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4996.93
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  425.07
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.32
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.77
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:21.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.56
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:16.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   0.087
p-value of test                       :    0.47

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.78e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 6.47e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9902

-----------------------------------------------
CPU time used                    :  00:00:47.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 2.38e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.42
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.14
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.40
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:07.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.56
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:12.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9903.86
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10188.59
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:58.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4751.77
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:49.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4978.40
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:49.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3915.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.56
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11854.69
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11805.15
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:29.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.30
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000033709

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.89
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999855929

Normal statistic for number of bits   :   -1.14
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:11:50.96

 All tests were passed




Server wird beendet - Lösche Semaphor 168984596.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:05.01

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:06.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1477
p-value of test                       :  1.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334597
  j =  1                              :        599997046
  j =  2                              :             1477
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5446
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:46.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:38.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:37.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:05.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:06.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:01.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7166
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:04:04.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     929
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    3.10
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     648
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    3.46
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    2.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:15.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:46.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.12
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.61
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.49
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.76
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:11.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.42
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:11.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.44
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.97
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.16
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.55
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  387.88
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:54.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.81
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:03.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6983.22
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:51.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.93
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.44
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:14.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.06
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  143.08
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:38.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5039.71
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:29.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:06.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45804
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869804
  j =  1                              :        399908394
  j =  2                              :            45800
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45641
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869641
  j =  1                              :        399908724
  j =  2                              :            45629
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:33.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:21.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:50.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:03.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:37.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.33e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 7.75e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:24.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:43.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.94
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.32
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.27
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.29
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.94
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.53
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.47
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:50.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.82
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.65
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.63
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   12.62
p-value of test                       :  5.5e-3

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.44
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17396.59
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.11
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.77
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.98
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.83
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.71
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.76
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.98
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.94
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.12
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.63
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.98
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.55
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.74
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.24
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.16
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.39
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.79
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  453.18
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.78
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.01
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.45
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.08
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5037.35
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.42
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.06
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.47
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.61
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5097.84
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.99
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.91
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.26
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -2.02
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:27.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.02
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :   -1.12
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:26.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.73e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 7.18e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.53
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.70
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.48
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:10.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.33
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:10.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9842.54
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10132.78
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.093
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:04:28.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4765.55
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:55.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5025.63
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4191.65
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4045.70
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11600.73
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:35.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11808.98
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:37.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.38
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999855557

Normal statistic for number of bits   :   -1.14
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.14
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000030178

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.19

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:16:21.82

 All tests were passed




Server wird beendet - Lösche Semaphor 170328084.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5524
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:48.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4434
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:39.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7156
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:38.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:03.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:03.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:55.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:01.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.43
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.26
p-value of test                       :  6.6e-3

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.91
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     649
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:16.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:45.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.12
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.05
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.19
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.06
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.10
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.43
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.75
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.38
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.40
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:45.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1475.55
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:02.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7155.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.85
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:03.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.66
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  147.21
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5042.09
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:04.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45936
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869936
  j =  1                              :        399908130
  j =  2                              :            45932
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45457
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869457
  j =  1                              :        399909087
  j =  2                              :            45455
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:28.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:18.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :  3.8e-3

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    3.41
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:45.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:54.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :  1.4e-3

Anderson-Darling statistic = A2       :    3.94
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:01:32.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 9.83e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:40.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.97
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:48.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.17
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.37
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.77
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.34
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.26
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.41
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:29.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.09
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.01
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17693.95
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.98
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.06
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.23
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.35
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.77
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.48
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.97
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.65
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.46
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.75
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.10
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.89
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.95
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.36
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.84
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.30
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.53
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.48
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.33
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.61
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.51
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.50
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.83
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.26
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.13
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.60
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4923.31
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.01
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.28
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.03
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :   -0.82
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:25.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.62
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :  -0.042
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:25.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.75e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 6.92e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.91
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.28
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.50
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:08.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:08.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10098.49
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9990.12
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:43.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5018.71
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:49.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4825.47
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.33
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.58
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11836.23
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11922.06
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.16
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999986615

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.59
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999900407

Normal statistic for number of bits   :   -0.79
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:36.11

 All tests were passed




Server wird beendet - Lösche Semaphor 171802644.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:40.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5624
p-value of test                       :  3.1e-3


-----------------------------------------------
CPU time used                    :  00:03:48.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:38.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7507
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:37.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:55.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:03.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:02.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7126
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:54.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:00.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.98
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:14.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.47
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:45.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.74
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.70
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.84
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.07
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.07
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.98
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.17
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:01.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7114.34
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.77
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:02.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.43
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:35.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4995.24
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:01.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45713
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869713
  j =  1                              :        399908578
  j =  2                              :            45705
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45857
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869857
  j =  1                              :        399908290
  j =  2                              :            45849
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:28.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:20.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:47.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:00.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:33.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.95e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:22.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:33.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.022
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:33.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.25
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:48.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.92
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.21
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.77
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.98
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.48
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:41.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.33
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.66
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.33
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:28.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.54
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17280.28
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.57
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.18
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.49
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.78
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.90
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.65
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.58
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.21
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.98
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.53
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.94
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.05
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.08
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.26
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.16
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.91
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.65
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.45
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.60
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.70
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.96
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  443.30
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.16
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.26
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.57
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.88
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.05
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.50
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.05
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.27
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.17
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :    0.54
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:24.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.86
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :   -1.02
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:25.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 7.73e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.62
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.54
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.48
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:08.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.70
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:09.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10039.23
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10121.15
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:47.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4985.07
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:50.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4907.82
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:51.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4187.72
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.15
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11981.77
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11720.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:30.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.52
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000182542

Normal statistic for number of bits   :    1.44
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.40
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999894524

Normal statistic for number of bits   :   -0.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.35

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:55.75

 All tests were passed




Server wird beendet - Lösche Semaphor 172621844.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:40.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:50.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5397
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:49.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4436
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:39.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7462
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:37.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:02.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:02.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7143
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:55.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:04:00.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.25
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    2.45
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:45.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    3.20
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     528
p-value of test                       :    0.9985

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    2.62
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:13.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.78
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:37.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:54.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.49
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.19
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.37
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.47
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.70
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.87
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.94
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.69
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:42.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.70
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:00.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7068.92
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:40.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.00
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.55
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:02.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.10
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.52
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5085.78
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:55.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45812
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869812
  j =  1                              :        399908382
  j =  2                              :            45800
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45594
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869594
  j =  1                              :        399908815
  j =  2                              :            45588
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  9.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:28.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:17.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:43.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:58.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:56.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:34.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 7.12e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 2.71e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:21.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:21.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:34.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:33.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.29
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:48.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.11
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:51.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:51.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.89
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:47.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.60
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.04
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:51.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:38.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.41
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.34
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.64
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17072.90
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.93
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.59
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.86
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.58
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.35
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.17
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.77
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.56
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.00
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.94
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.85
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.05
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.74
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.12
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.69
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.91
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.65
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.15
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.21
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.27
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.97
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5235.70
p-value of test                       :  1.0e-2


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.30
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.66
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.40
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.83
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4896.51
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.69
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.28
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.52
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :   -0.10
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:24.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.47
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:24.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 4.43e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:46.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.54e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 9.64e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.74
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    0.82
p-value of test                       :    0.9991    *****

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.71
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:08.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.79
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:08.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10185.37
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9883.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:49.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.73
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:48.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.26
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:52.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4193.54
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.91
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11541.37
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11717.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:29.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.83
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999958703

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.48
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000076984

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:28.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.77

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:41.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 87  LongestHeadRun, r = 27          0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 173572116.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5357
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:54.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:39.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7484
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:40.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:03.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:02.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:54.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:00.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.68
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    3.11
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     849
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:48.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.9908

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    3.20
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    2.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    2.78
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:14.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.27
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:45.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.66
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.80
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.17
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.70
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.58
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  271.12
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.86
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:42.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.18
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:58.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7197.19
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:41.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:01.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.84
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.89
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:33.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5184.42
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:01.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45804
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869804
  j =  1                              :        399908396
  j =  2                              :            45796
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45615
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869615
  j =  1                              :        399908773
  j =  2                              :            45609
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:28.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:18.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:45.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:58.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.98e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 2.73e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.98e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:21.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:21.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:33.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:33.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.92
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.31
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.93
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.67
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.30
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:51.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.89
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.09
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:39.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.63
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.96
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:29.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.64
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.92
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.39
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9984

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17428.04
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   16.39
p-value of test                       :    0.9979


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.46
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.05
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.15
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.75
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   17.86
p-value of test                       :    0.9951


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.31
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.31
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.04
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.63
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.08
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.78
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.05
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  183.96
p-value of test                       :  3.9e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.08
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.06
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.42
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.52
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.86
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.94
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.05
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.62
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4765.83
p-value of test                       :    0.9912


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  427.85
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.84
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.86
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.48
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.66
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.47
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.48
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.74
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:24.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.83
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :    1.33
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:23.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 5.26e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.01
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.53
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.70
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:07.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.74
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:09.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10169.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9933.89
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.046
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:50.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4991.58
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:49.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4788.85
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:50.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.47
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3968.91
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11914.02
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:29.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11770.28
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:30.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.88
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000043219

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.61
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999868865

Normal statistic for number of bits   :   -1.04
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    1.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    1.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:11.25

 All tests were passed




Server wird beendet - Lösche Semaphor 174587924.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  8.7e-3


-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1245
p-value of test                       :    0.9994    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334365
  j =  1                              :        599997510
  j =  2                              :             1245
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5430
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:54.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:40.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:38.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4446
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:55.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:03.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7444
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:02.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:53.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:59.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.56
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    3.57
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    2.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:12.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:42.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.07
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.99
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.40
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.53
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.72
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.86
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.65
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.08
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  474.92
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:44.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1560.17
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:00.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7090.41
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.01
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.06
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:02.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.12
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.84
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:34.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5013.85
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:54.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46045
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870045
  j =  1                              :        399907916
  j =  2                              :            46033
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45948
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869948
  j =  1                              :        399908109
  j =  2                              :            45938
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:28.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:16.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:44.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:58.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:56.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:36.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 4.98e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.28e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.021
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:34.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:34.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.53
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:48.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.27
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.47
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:49.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.55
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.58
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:38.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   62.39
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.22
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.27
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.55
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17131.27
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.03
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.35
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.43
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.48
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.02
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.10
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.84
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.00
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.65
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.25
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.67
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.71
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.40
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.38
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.67
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.56
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.64
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  432.45
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.25
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.24
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.68
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.16
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.91
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.54
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.80
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.00
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.30
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.40
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.76
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.05
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.09
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:23.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.75
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :   -1.71
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:23.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.72
p-value of test                       :    0.04

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 4.44e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 4.47e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.71
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.61
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.24
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:05.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.37
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:07.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9837.88
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9899.75
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:50.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.51
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:49.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5007.47
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:50.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.84
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4023.89
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11800.03
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:30.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11827.33
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.85
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999912371

Normal statistic for number of bits   :   -0.69
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.59
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000039640

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.72

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:37.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           0.9994 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 175538196.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5335
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:57.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:39.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:55.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:04.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:02.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:54.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:58.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:47.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.78
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    2.42
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:12.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:42.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.44
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.29
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.48
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.14
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.94
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.54
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.02
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:20.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.09
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.73
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:43.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1389.08
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:00.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7127.37
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:43.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.34
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:03.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.30
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.33
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:35.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5026.21
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:13.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:53.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45469
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869469
  j =  1                              :        399909063
  j =  2                              :            45467
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45862
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869862
  j =  1                              :        399908285
  j =  2                              :            45844
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:28.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:17.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:43.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.60e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:56.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:36.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 3.56e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.76e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.061
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:21.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.41
p-value of test                       :    0.9919

-----------------------------------------------
CPU time used                    :  00:01:34.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:34.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.43
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.19
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.11
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:49.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.06
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.63
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:39.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.79
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.50
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.55
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17793.90
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.75
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.93
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.70
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.54
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.94
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.74
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.95
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.67
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.80
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.73
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.74
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.97
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.60
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.40
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.85
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.70
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.95
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.66
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.51
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.19
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.21
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.21
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5112.93
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.63
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.63
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.84
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.59
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5171.69
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.48
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.26
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.10
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:22.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.07
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :   -1.60
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:22.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   0.043
p-value of test                       :    0.48

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.74e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 7.11e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 7.72e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.11
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.77
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.02
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:05.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.51
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:06.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10190.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9981.22
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.13
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.040
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.46
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:03:52.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4911.74
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4799.19
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:51.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4019.57
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.16
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11939.64
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11821.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.58
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999956828

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.12
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999983810

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.72

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   0.025
p-value of test                       :    0.49

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:38.98

 All tests were passed




Server wird beendet - Lösche Semaphor 176488468.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9916


-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:59.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4463
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:42.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:40.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:57.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:04.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:03.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:55.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:59.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.94
p-value of test                       :  9.5e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    5.67
p-value of test                       :  1.4e-3

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:12.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:41.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.36
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.13
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.99
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.72
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.06
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.27
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.28
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.64
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:44.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1321.97
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:02.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7076.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:43.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9985

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.49
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.42
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:03.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.26
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  145.76
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:34.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5111.61
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:59.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45867
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869867
  j =  1                              :        399908271
  j =  2                              :            45857
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45833
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869833
  j =  1                              :        399908336
  j =  2                              :            45829
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:29.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:18.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:44.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:00.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:56.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:36.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 4.80e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 6.96e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.35
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:33.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.70
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.34
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.26
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.42
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.66
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.13
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:51.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.35
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:38.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.55
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.18
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.28
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.99
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17542.50
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.08
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.50
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.15
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.87
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.93
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.66
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.23
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.83
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.97
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.43
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.01
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.19
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.55
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.13
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.21
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.87
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.00
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.75
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.72
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.03
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.86
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  444.15
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.26
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.97
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.79
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.16
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.42
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.01
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.00
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.20
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.71
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :    0.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:22.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.57
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:21.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.90e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 2.71e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.78
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.54
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.29
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:07.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.01
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:07.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10044.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10062.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:59.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4946.91
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:50.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4987.25
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4157.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4069.81
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11724.12
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11981.66
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:31.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.60
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000041635

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.07
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000024799

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    3.34
p-value of test                       :  4.3e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.32
p-value of test                       :    0.01

Sample variance                       :    2.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:09.17

 All tests were passed




Server wird beendet - Lösche Semaphor 177471508.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5398
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:04:02.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:43.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7520
p-value of test                       :  9.6e-3


-----------------------------------------------
CPU time used                    :  00:02:43.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:58.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:57.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:04.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:05.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:56.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:57.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.99
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.37
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    3.74
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:13.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.90
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:41.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.68
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.23
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.77
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.84
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.98
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.81
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.84
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.45
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  475.85
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1522.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:01.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6989.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:48.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.15
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.29
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:08.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.30
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:48.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.20
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5199.65
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:57.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45894
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869894
  j =  1                              :        399908213
  j =  2                              :            45892
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45601
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869601
  j =  1                              :        399908802
  j =  2                              :            45593
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:30.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:18.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:06.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:35.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.15e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.15e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:24.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:42.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:41.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.77
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.75
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   97.07
p-value of test                       :  9.6e-3

-----------------------------------------------
CPU time used                    :  00:00:55.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.93
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.80
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.16
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.56
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:46.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.49
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.43
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.35
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.05
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17236.30
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.80
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.14
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.64
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.89
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.92
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.68
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.17
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.74
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.15
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.76
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.11
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.41
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.92
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.21
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.00
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.47
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  194.28
p-value of test                       :  4.7e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.00
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.54
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.64
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.36
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.40
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5103.57
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.92
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.81
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.23
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.11
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5157.52
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.68
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.33
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.61
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:23.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.75
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:22.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   0.060
p-value of test                       :    0.48

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.56e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.31
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.29
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.41
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:05.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.66
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:06.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10045.52
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10034.52
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.70
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:04:22.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4846.35
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:54.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5035.53
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:54.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4324.26
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4157.70
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12156.66
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:33.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11902.69
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:31.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.58
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999870098

Normal statistic for number of bits   :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.13
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000185338

Normal statistic for number of bits   :    1.47
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.38
p-value of test                       :  8.6e-3

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :  -0.024
p-value of test                       :    0.51

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:28.12

 All tests were passed




Server wird beendet - Lösche Semaphor 178520084.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5497
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:57.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:40.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4445
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:57.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:04.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7153
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:04.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:53.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:59.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.27
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:45.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.35
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:12.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.13
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:40.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.43
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.68
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.78
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.67
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.56
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  195.69
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.31
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:44.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.94
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:00.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6987.80
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.90
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:02.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.11
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.36
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:32.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5264.54
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:00.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45967
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869967
  j =  1                              :        399908070
  j =  2                              :            45959
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45643
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869643
  j =  1                              :        399908717
  j =  2                              :            45637
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:28.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:17.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:46.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:00.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:56.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.27e-3
p-value of test                       :    0.9917

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:36.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:37.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:37.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.90
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.80
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.11
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.96
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.85
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.36
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.09
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.22
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.84
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.21
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17163.22
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.30
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.57
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.45
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.83
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.89
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.07
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.86
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.13
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.13
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.79
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.63
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.25
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.64
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.19
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.82
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.40
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.45
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  580.45
p-value of test                       :  7.3e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.23
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  116.14
p-value of test                       :  1.3e-3


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.27
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.76
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5155.67
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.43
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.75
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.25
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.48
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.41
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.87
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.70
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.14
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:23.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.67
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:22.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :  -0.060
p-value of test                       :    0.52

Sample variance                       :    2.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.93e-3
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.31
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.88
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.25
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:06.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.80
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:08.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10054.06
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10079.08
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.081
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:45.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.62
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:48.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.48
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:51.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4021.26
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4090.30
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11897.90
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12130.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:30.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.86
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000048148

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.62
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000072559

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:10.23

 All tests were passed




Server wird beendet - Lösche Semaphor 179568660.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9910


-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5439
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:58.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:40.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:57.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7452
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:04.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:03.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:53.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:59.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:47.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    2.69
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.90
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:07.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:32.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.60
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.85
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    5.84
p-value of test                       :    0.9968

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.49
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.01
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.97
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.84
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.01
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  475.31
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:44.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1465.01
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:01.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7121.45
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.96
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.35
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:03.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.88
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.68
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:33.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4940.57
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:59.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45662
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869662
  j =  1                              :        399908678
  j =  2                              :            45658
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45658
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869658
  j =  1                              :        399908688
  j =  2                              :            45650
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:28.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:17.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:44.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:00.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:56.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9909

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:36.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.41e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:21.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:35.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.70
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.46
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.21
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.81
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.73
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.90
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:38.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9962

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.82
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.42
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.96
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17515.56
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.26
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.30
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.23
p-value of test                       :    0.9918


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.42
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.27
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.56
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.11
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.48
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.52
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.55
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.63
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.83
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.43
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.01
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.12
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.13
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.95
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.24
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.94
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.71
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:43.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.11
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.57
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5104.45
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.14
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.09
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.80
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.62
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4921.93
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.57
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.83
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.66
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :   0.016
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:22.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.39
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:22.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.91
p-value of test                       :    0.97

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 2.96e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.28e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.82
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.33
p-value of test                       :    0.9952

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  245.55
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:05.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.17
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:07.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9956.75
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10139.42
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.096
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:50.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4843.01
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:48.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:50.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4136.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.72
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12087.03
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11632.10
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:29.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.78
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000060655

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.02
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000126232

Normal statistic for number of bits   :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.84
p-value of test                       :    0.97

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:41.26

 All tests were passed




Server wird beendet - Lösche Semaphor 180551700.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:39.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5370
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:00.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:43.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:57.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:59.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:07.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:05.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:55.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:58.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:46.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:11.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.91
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.44
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.63
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.00
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.83
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.18
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.75
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.91
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  371.60
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1381.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:03.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7208.95
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.48
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   41.57
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:06.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.23
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.94
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:36.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4963.25
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:12.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:04.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46038
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870038
  j =  1                              :        399907926
  j =  2                              :            46034
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45886
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869886
  j =  1                              :        399908229
  j =  2                              :            45884
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:29.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:17.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:44.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:01.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :  5.7e-3

Anderson-Darling statistic = A2       :    4.92
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.53e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.16e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 5.54e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -9.48e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:45.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.034
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:45.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.61
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.46
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.62
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.52
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.90
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.23
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:43.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.24
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.82
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.42
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17298.18
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.54
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.09
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.19
p-value of test                       :    0.9920


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.42
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.09
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.40
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.46
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.93
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.80
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.58
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.56
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.86
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.38
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.74
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.29
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.94
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.45
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.17
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.66
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.31
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.71
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.52
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.36
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.79
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.60
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.55
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.84
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.62
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.22
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.52
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.45
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:21.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.24
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :  -0.028
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:23.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.10

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 3.02e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.84e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 6.88e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.65
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.91
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.03
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:06.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.19
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:06.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9854.61
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10045.60
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.36
p-value of test                       :    0.9908

-----------------------------------------------
CPU time used                    :  00:04:18.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4838.14
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:50.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5018.57
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:52.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.03
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3989.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11579.52
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:29.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11641.77
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:30.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.73
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000057820

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.69
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000042799

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:56.29

 All tests were passed




Server wird beendet - Lösche Semaphor 181600276.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1269
p-value of test                       :    0.9952

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334389
  j =  1                              :        599997462
  j =  2                              :             1269
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5393
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:00.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:43.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:43.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:57.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:58.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:04.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:04.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:54.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:01.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.11
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     568
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.85
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    2.24
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    2.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:12.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:40.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.96
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.88
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.45
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.83
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.92
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.58
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.28
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.01
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:43.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.25
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:01.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7112.87
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:44.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.35
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.39
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:02.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.71
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   90.58
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:33.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4922.90
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:03.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46148
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870148
  j =  1                              :        399907707
  j =  2                              :            46142
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46002
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870002
  j =  1                              :        399907997
  j =  2                              :            46000
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:28.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:20.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  7.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:44.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:58.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:56.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.92
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:01:18.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:36.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.80e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 2.03e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 8.54e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:34.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:35.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.16
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:48.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   98.70
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.88
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.22
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.47
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.65
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.23
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:39.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.43
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.09
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17131.78
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.50
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.04
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.41
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.34
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.26
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.78
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.18
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.83
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.96
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.94
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:37.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.00
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.31
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.77
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.82
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.15
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.92
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.92
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.09
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.02
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.18
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.60
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.32
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5126.50
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.00
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.81
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.63
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.58
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.55
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.24
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.10
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.75
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :   -1.06
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:22.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.90
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :   -0.60
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:23.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.13

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.72

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.89e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 8.89e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 4.90e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   22.03
p-value of test                       :  4.9e-3

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.63
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.25
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:06.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.55e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  241.74
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:06.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10003.82
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.18e-3
p-value of test                       :    0.9912

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10200.20
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:55.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4743.84
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:49.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.07
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.43
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4160.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11825.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11833.59
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.85
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000104737

Normal statistic for number of bits   :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.70
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000149719

Normal statistic for number of bits   :    1.18
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.77e-3
p-value of test                       :    0.9961

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.58
p-value of test                       :  4.9e-3

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:02.81

 All tests were passed




Server wird beendet - Lösche Semaphor 182681620.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:00.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:43.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:44.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:57.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:05.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:05.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:56.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7508
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:59.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    2.13
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     865
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:46.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.17
p-value of test                       :    0.9957

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.16
p-value of test                       :    0.9974

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:13.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.13
p-value of test                       :    0.9995    *****

-----------------------------------------------
CPU time used                    :  00:02:40.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.27
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.61
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.72
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.42
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.11
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.44
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:44.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:00.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7120.76
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.96
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.0e-3

Anderson-Darling statistic = A2       :    3.45
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   87.93
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:03:01.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.86
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:32.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4998.07
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:03.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45854
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869854
  j =  1                              :        399908293
  j =  2                              :            45852
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45656
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869656
  j =  1                              :        399908688
  j =  2                              :            45656
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  8.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    3.50
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:27.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:17.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:45.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:58.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:34.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 6.76e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.40e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:33.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.030
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.18
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:48.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.12
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.20
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.39
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.47
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.07
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:38.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.96
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.97
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.96
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.33
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9909

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17467.56
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.07
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.44
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.05
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.90
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.34
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.66
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.85
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.41
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.20
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.64
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.33
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.58
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  551.73
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  180.27
p-value of test                       :  6.6e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.05
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.81
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.77
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.29
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.30
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.57
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.79
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.90
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4978.28
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  431.12
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.36
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.94
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.87
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4912.41
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.81
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.74
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.15
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :   -0.79
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:22.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.19
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:22.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.07e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 5.72e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 6.72e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.67
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.61
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.06
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:05.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.45
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:06.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9959.42
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10075.91
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.022
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:45.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4841.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:48.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5034.64
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:50.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4243.47
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3982.03
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11473.49
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:28.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11645.24
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:30.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.63
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000027313

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.11
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000015802

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:45.81
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs mNP2S, t = 16        0.9995 
 53  SampleMean, r = 0               0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 183730196.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  1.7e-3


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5473
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:06.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:44.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7467
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:46.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:01.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:01.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:12.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:12.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:09.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7176
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:10.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    3.29
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.76
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:13.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:43.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.39
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.92
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.85
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.65
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.43
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  267.15
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.20
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:54.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1503.92
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:06.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7110.99
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.04
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.00
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:17.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.19
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.39
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:40.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4882.48
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:02.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45755
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869755
  j =  1                              :        399908492
  j =  2                              :            45751
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45861
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869861
  j =  1                              :        399908283
  j =  2                              :            45851
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:32.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:21.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:53.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:07.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:56.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:38.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.11e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 3.19e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.69e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:24.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:49.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:49.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  101.03
p-value of test                       :  4.6e-3

-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.35
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:51.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.86
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.96
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:51.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.03
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.11
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.16
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.15
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  163.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17263.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.74
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.97
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.45
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.93
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.41
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.11
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.94
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.19
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.76
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.23
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.69
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.30
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.50
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.26
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   39.70
p-value of test                       :    0.9996    *****


-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.53
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.99
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.93
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.11
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.91
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.18
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.14
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.25
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  425.58
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.19
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.36
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.90
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4831.61
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.75
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.77
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.22
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :   -2.13
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:24.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.59
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :    1.30
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:25.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 4.26e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.84e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.58
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.37
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.52
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:06.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.51
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:06.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9949.14
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10018.21
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:11.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:04:30.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.43
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:55.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4727.48
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:58.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3892.93
p-value of test                       :    0.9939

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.65
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12037.53
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:35.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12107.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:36.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.08
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999999236

Normal statistic for number of bits   : -6.04e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.43
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000011710

Normal statistic for number of bits   :   0.093
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 2.11e-3
p-value of test                       :    0.9979

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.64
p-value of test                       :    0.95

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:20.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 C (L=1000, r=0)     0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 184778772.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1265
p-value of test                       :    0.9966

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334385
  j =  1                              :        599997470
  j =  2                              :             1265
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5467
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:59.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:44.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:58.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:06.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7115
p-value of test                       :    0.9914


-----------------------------------------------
CPU time used                    :  00:03:05.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:56.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:00.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.00
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:48.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:13.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:40.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.98
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.61
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.19
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.69
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.87
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.48
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.14
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.39
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  192.10
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.96
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:43.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1395.11
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:00.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7047.35
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:42.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.03
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.42
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:03.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.46
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.50
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:33.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5080.57
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:04.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46007
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870007
  j =  1                              :        399907991
  j =  2                              :            45997
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45965
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869965
  j =  1                              :        399908074
  j =  2                              :            45957
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 8.23e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:29.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:18.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:59.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:55.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:33.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.98e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 2.03e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.056
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:36.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.29
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.65
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:51.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.53
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.68
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.67
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.12
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.96
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:37.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.52
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.71
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.15
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.63
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.11
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17588.25
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.20
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.41
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.13
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.33
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.68
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.24
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.36
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.65
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.08
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.33
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.88
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.47
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.78
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.79
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.48
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.59
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.10
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.95
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.77
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.14
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.70
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.83
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5093.87
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.61
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.53
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.23
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.76
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.87
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.08
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  159.21
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.55
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :   -1.05
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:24.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.53
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:23.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.61e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 6.23e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.54e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 7.65e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.25
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.03
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.20
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:05.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.85
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:08.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.46
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10266.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.48
p-value of test                       :  6.6e-3

-----------------------------------------------
CPU time used                    :  00:03:43.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.08
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:49.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4949.16
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:50.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.93
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4214.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11797.63
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12020.34
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:29.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.92
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999959762

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.73
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000031060

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.86
p-value of test                       :    0.03

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:08.14

 All tests were passed




Server wird beendet - Lösche Semaphor 185892884.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997143
  j =  2                              :             1427
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5471
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:59.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4461
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:43.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:44.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:01.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:08.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:09.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7138
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:04:02.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:05.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    2.06
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    2.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:48.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.42
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:15.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:43.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.18
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.58
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.03
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.83
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   82.99
p-value of test                       :  6.8e-3

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.57
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.37
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  483.79
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1317.79
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:05.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7118.26
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:49.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.91
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.51
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:09.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.60
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.24
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:37.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5002.89
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:13.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:07.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46136
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870136
  j =  1                              :        399907730
  j =  2                              :            46132
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46288
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870288
  j =  1                              :        399907428
  j =  2                              :            46280
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:30.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:19.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  6.6e-3

Anderson-Darling statistic = A2       :    3.84
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:49.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:06.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.71e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 7.57e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.65
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:43.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:45.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.23
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.66
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.16
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.99
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.80
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:46.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.29
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.68
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:29.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:29.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.05
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  102.67
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:39.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17255.88
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.48
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.48
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.79
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.77
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.40
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.77
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.53
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.82
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.53
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.49
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.90
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.06
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.24
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.57
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.01
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.76
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.01
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  555.90
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.75
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.07
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.88
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.05
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4940.02
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.55
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.12
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.71
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.26
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5119.55
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.31
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.85
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.44
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:22.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.37
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   -1.60
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:22.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.97e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 9.53e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.23e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.53
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.73
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:06.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:06.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9934.03
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10045.81
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:04:25.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4946.08
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:52.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4771.84
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:54.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4174.04
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4049.02
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11835.44
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:31.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11995.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:32.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.45
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999995555

Normal statistic for number of bits   :  -0.035
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.97
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999961070

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:40.71

 All tests were passed




Server wird beendet - Lösche Semaphor 186875924.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:38.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5495
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:57.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4443
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:41.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:56.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:58.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:05.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:05.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7177
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:56.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:00.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:13.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.83
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    2.93
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:44.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.79
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.32
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.11
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.38
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.23
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.30
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.61
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  193.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:45.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:01.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6926.42
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.41
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.75
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:04.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.14
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:46.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.62
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:33.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5070.18
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:59.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45727
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869727
  j =  1                              :        399908550
  j =  2                              :            45719
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45751
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869751
  j =  1                              :        399908500
  j =  2                              :            45747
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:29.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:20.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:45.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:59.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:55.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:33.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.55e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 8.02e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:24.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 8.70e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:36.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.054
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:35.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.99
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:48.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.98
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.31
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.83
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.31
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.08
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:40.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.63
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:28.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.33
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.66
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17299.34
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.63
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.75
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.32
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.52
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.20
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.85
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.79
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.84
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.26
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.70
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.09
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.82
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.42
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  195.61
p-value of test                       :  6.2e-4    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.50
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.39
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.24
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.22
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.59
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.20
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.38
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.97
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.04
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.11
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.91
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.54
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.62
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5069.44
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  434.12
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.79
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.10
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :    1.91
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:22.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.81
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:22.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:10.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.78e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.93e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.59
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.87
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.25
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:05.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.44
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10013.96
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10131.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : 1.35e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:55.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:39.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4846.47
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.67
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:50.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.95
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4006.76
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12070.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:29.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11744.98
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.57
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000049381

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.89
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000049666

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.50
p-value of test                       :    0.07

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    1.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:37.46
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 R (L=1000, r=0)     6.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 188121108.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5541
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:44.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:37.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:37.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:57.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4228
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:58.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:07.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7135
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:08.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:04:06.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:11.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     572
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:12.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:10.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:48.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.10
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.02
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.76
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.02
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.96
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.46
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  198.30
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:30.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.20
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:57.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1514.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:08.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7069.82
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.08
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.96
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:14.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.11
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.55
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:43.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5239.56
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:32.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  6.0e-3


-----------------------------------------------
CPU time used                    :  00:03:11.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46006
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870006
  j =  1                              :        399907990
  j =  2                              :            46002
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46085
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870085
  j =  1                              :        399907836
  j =  2                              :            46073
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:31.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:17.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:46.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:03.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:38.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.87e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:24.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:45.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.91
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.56
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.53
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.18
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.31
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:54.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:30.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.87
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17384.38
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.16
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.96
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.24
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.38
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.83
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.05
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.86
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.58
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.98
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.09
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:40.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.29
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.87
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.43
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.49
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.34
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:47.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.67
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.10
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.47
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.57
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.02
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:46.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.44
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.46
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4848.17
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.51
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.21
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.58
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.12
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5286.87
p-value of test                       :  2.4e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.35
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.67
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.30
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:29.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.17
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :    1.06
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:25.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.50
p-value of test                       :    0.93

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.97e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 7.50e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.69
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.27
p-value of test                       :    0.9959

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:08.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:08.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9969.60
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9877.90
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.085
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:04:31.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4889.20
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:07.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4802.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:17.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3952.68
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:34.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.66
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:38.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12141.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:40.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11816.81
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:44.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.20
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000008932

Normal statistic for number of bits   :   0.071
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.03
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999970505

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.53
p-value of test                       :    0.06

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:12.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:22:34.67

 All tests were passed




Server wird beendet - Lösche Semaphor 168591381.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:47.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5385
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:49.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:39.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:38.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:55.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:56.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:04.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7151
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:04.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7483
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:54.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7454
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:04.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:50.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    2.19
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     541
p-value of test                       :    0.9923

Stat. AD (mNP2)                       :    1.97
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:18.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.72
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.52
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:46.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.70
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.12
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.18
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.76
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.91
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.26
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.47
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.75
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  472.05
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:43.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.27
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:00.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6845.98
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.10
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.57
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:03.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.82
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   90.51
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4964.10
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:58.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45698
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869698
  j =  1                              :        399908607
  j =  2                              :            45692
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46258
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870258
  j =  1                              :        399907487
  j =  2                              :            46252
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:24.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:15.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:44.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:57.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:55.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
p-value of test                       :    0.9998    *****

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:33.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.69
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.18
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.19
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.61
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.71
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.34
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:42.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.56
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17315.85
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.83
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.29
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.31
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.40
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.21
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.69
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.95
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.41
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.62
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.41
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.95
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.61
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.54
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.79
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.75
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:46.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.15
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.49
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  438.32
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.82
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.43
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.93
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.17
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.85
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.03
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.64
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.11
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.12
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.88
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  331.70
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.99
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.06
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : 2.98e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:27.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.20
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :  -0.019
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:27.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:47.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.93e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.35
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.42
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.18
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:09.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.32
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:08.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.51
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10323.11
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9788.66
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:57.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4948.37
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:50.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4772.00
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:51.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4200.84
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.39
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11660.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11559.19
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.68
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999938021

Normal statistic for number of bits   :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.76
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000011368

Normal statistic for number of bits   :   0.090
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:04.70

 All tests were passed




Server wird beendet - Lösche Semaphor 169934869.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5548
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:51.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:39.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:39.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4454
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:56.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7159
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:04.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:55.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:02.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.46
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:50.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     645
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.08
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.71
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    2.46
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:18.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:46.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.25
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.40
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.95
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.03
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.28
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.50
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.66
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  474.91
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:41.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1493.88
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:56.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7198.86
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.18
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.80
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:05.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.38
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.41
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:35.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4951.08
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:05.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45832
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869832
  j =  1                              :        399908336
  j =  2                              :            45832
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45881
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869881
  j =  1                              :        399908243
  j =  2                              :            45871
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:25.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:15.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:44.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:01.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:54.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:32.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 3.60e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 7.52e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:34.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:34.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.78
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:47.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.76
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.58
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.62
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.57
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:40.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.32
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.68
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.25
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:29.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.16
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.75
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17600.26
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.35
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.61
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.25
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.04
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.43
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.70
p-value of test                       :    0.9923


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.24
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.56
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.06
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.89
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.90
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.16
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.87
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.06
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.60
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.93
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.71
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.10
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.74
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.32
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.22
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.50
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5197.68
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.24
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.37
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.74
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.57
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5061.08
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.83
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.72
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.14
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :    1.20
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:23.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.64
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :    0.72
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:25.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :  -0.082
p-value of test                       :    0.53

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.99e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 6.43e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:46.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.45
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.41
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.96
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:08.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.38
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:08.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10127.25
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9962.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:47.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4771.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:50.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5007.94
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:51.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4022.83
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4137.62
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11674.43
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:29.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11682.62
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:30.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.21
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000177013

Normal statistic for number of bits   :    1.40
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.18
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000099244

Normal statistic for number of bits   :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:43.62

 All tests were passed




Server wird beendet - Lösche Semaphor 170950677.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5497
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:48.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:38.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7477
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:38.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4228
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:56.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:03.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7106
p-value of test                       :    0.9936


-----------------------------------------------
CPU time used                    :  00:03:03.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:55.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:04:01.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     862
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:50.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    2.07
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:16.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.96
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.76
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     128
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:46.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.98
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.24
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.68
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.14
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.32
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:10.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.13
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.22
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.47
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:45.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1375.92
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:02.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7025.00
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.28
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:03.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.07
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.55
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:36.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4945.70
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:10.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46131
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870131
  j =  1                              :        399907742
  j =  2                              :            46123
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45766
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869766
  j =  1                              :        399908471
  j =  2                              :            45760
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:27.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:17.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:45.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:01.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:54.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:32.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.99e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 3.95e-4
p-value of test                       :  1.9e-3

Anderson-Darling statistic = A2       :    4.33
p-value of test                       :  6.0e-3

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:33.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:33.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.16
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.10
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.96
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.34
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.20
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.29
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.75
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.37
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:30.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.25
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:10.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.52
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17479.59
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.51
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.84
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.94
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.57
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.04
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.22
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.19
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.77
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.87
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.46
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.63
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.40
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.98
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.22
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.25
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.08
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.52
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.14
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.58
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.12
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.26
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.11
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4934.67
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.01
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.83
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.03
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.65
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4934.06
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  306.71
p-value of test                       :    0.9970


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.53
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.40
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :   -1.33
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:23.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.25
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :  -0.078
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:25.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:11.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.40e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 5.96e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:47.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.14e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.44
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.27
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.20
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:08.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.14
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:08.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10189.45
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9753.02
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:42.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4703.00
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:49.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.14
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:50.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.06
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4239.77
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11442.69
p-value of test                       :    0.9939

-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11953.58
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.58
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999928856

Normal statistic for number of bits   :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.80
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999891938

Normal statistic for number of bits   :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.29
p-value of test                       :    0.99

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    2.25
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:40.18

 All tests were passed




Server wird beendet - Lösche Semaphor 171835413.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:43.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:54.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5358
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:49.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:39.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:39.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4197
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:57.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:58.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:07.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:07.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:06.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:10.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:49.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.10
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.21
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.65
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    2.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:15.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.96
p-value of test                       :  9.9e-3

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:45.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.98
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.05
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.68
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.87
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.95
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.51
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  202.48
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:29.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.68
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:56.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1422.76
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:01.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6998.06
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:55.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.67
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.89
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:17.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.31
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.48
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5058.09
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:13.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46064
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870064
  j =  1                              :        399907876
  j =  2                              :            46056
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45675
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869675
  j =  1                              :        399908651
  j =  2                              :            45673
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:32.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 6.90e-4
p-value of test                       :    0.9993    *****

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:20.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:50.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:07.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:38.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.97e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:24.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:24.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.62
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.56
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.88
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.28
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.52
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.47
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.72
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:50.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.95
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   20.83
p-value of test                       :    0.9947

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.93
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:28.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.09
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:29.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  157.25
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  8.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17099.64
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.85
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.97
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.03
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.28
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.67
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.57
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.18
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.08
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.98
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.48
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.24
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.40
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.92
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.05
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.81
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.31
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.47
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.83
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.23
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.56
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.93
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.36
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.67
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.94
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.95
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:37.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.74
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.08
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5061.16
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  431.49
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.34
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.25
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:26.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.91
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :    1.08
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:26.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.23

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 3.65e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 6.54e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.39
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.73
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.07
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:05.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.28
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:09.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9999.25
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10125.91
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:04:33.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4961.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4979.60
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:58.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4147.52
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4130.93
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12006.40
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:35.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11864.35
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:37.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.20
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999816317

Normal statistic for number of bits   :   -1.45
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.51
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000040645

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.65
p-value of test                       :    0.05

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:03.65

 All tests were passed




Server wird beendet - Lösche Semaphor 172654613.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1274
p-value of test                       :    0.9929

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334394
  j =  1                              :        599997452
  j =  2                              :             1274
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5371
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:50.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:40.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:39.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:56.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:57.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:07.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:06.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7450
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:01.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:05.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.44
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.71
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:14.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.65
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:43.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.66
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.91
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.30
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.91
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.90
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.93
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.09
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.86
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.92
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.74
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:51.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1365.07
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:00.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6998.08
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:50.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.68e-3
p-value of test                       :    0.9921

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.82
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:09.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.38
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.70
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:39.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5123.29
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:05.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45724
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869724
  j =  1                              :        399908558
  j =  2                              :            45712
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45846
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869846
  j =  1                              :        399908313
  j =  2                              :            45836
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:25.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:30.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:18.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:45.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:03.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:55.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:35.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.28e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 3.83e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.43e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.049
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:40.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:43.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.85
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.01
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.18
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.72
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.37
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.42
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:29.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.84
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:30.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.53
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  159.16
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:41.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17221.97
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.45
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.38
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.40
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.65
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.74
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.08
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.49
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.41
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.99
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.61
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.50
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.37
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.54
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.79
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.77
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.95
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.32
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.16
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.73
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.09
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.94
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4991.99
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.39
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.90
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.50
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.46
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.72
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.35
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.05
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.57
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:27.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.71
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:28.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    5.00
p-value of test                       :  3.0e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.92
p-value of test                       :    0.9983

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 9.52e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:46.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.22e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.90
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.43
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:07.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.92
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:08.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9810.14
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9923.70
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.051
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:04:23.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4814.39
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:52.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4817.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:54.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4148.93
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11648.42
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:30.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11775.19
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.27
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000093991

Normal statistic for number of bits   :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.15
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999906314

Normal statistic for number of bits   :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:33.38

 All tests were passed




Server wird beendet - Lösche Semaphor 173965333.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5463
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:53.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:41.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4241
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:58.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:06.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:06.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:56.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:01.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.53
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:47.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.72
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:16.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.78
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:44.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.72
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.23
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.47
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.60
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   84.94
p-value of test                       :  4.6e-3

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.36
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.75
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:43.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:59.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6993.71
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.12
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:02.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.05
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.48
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:34.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4992.52
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:57.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46452
p-value of test                       :  3.8e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870452
  j =  1                              :        399907096
  j =  2                              :            46452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45596
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869596
  j =  1                              :        399908811
  j =  2                              :            45590
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:27.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:18.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:59.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:55.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:35.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 7.41e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 5.07e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:39.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.20
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.65
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.28
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.73
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.83
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.63
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:44.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.62
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.65
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:30.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.97
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:09.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.24
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17261.71
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.58
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.71
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   54.85
p-value of test                       :  5.1e-4    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.64
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.41
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.58
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.40
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.11
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.17
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.46
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.32
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.34
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.24
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.02
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  101.59
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.05
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  193.37
p-value of test                       :  5.3e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.65
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.94
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.83
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.97
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  461.52
p-value of test                       :  4.0e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5106.36
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.50
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.78
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.17
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.39
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5180.87
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.09
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.52
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.98
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:25.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.83
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   -1.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:25.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.35

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.28e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.45e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.68
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.14
p-value of test                       :    0.9972

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.19
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:08.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.07
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:08.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9879.31
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9913.04
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:56.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 6.51e-3
p-value of test                       :    0.9931

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4717.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:48.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4741.93
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:50.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4272.89
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4283.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12035.80
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11728.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   33.95
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  7999951815

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.09
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999887930

Normal statistic for number of bits   :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    2.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:32.42
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 J (L=50, r=0)       5.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 175046677.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5338
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:52.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:39.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:40.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4446
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:57.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:05.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7494
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:05.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:55.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:01.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     943
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    2.37
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:15.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.93
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:41.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.91
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.66
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.65
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.02
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.49
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:11.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.32
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.97
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.32
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.09
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:44.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1429.81
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:00.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7161.25
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:44.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.83
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:02.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.54
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  144.46
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:35.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5117.86
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:58.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45647
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869647
  j =  1                              :        399908712
  j =  2                              :            45635
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45724
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869724
  j =  1                              :        399908555
  j =  2                              :            45718
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:28.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:19.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:45.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:00.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:55.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:34.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.59e-4
p-value of test                       :  5.7e-3

Kolmogorov-Smirnov- statistic = D-    : 3.16e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.17
p-value of test                       :  7.2e-3

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:22.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:40.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:41.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.74
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.30
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.76
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.81
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.21
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:45.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.70
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.83
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.13
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:29.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.25
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:29.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.98
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17581.76
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.11
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.86
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.43
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.72
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.24
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.88
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.44
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.45
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.86
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.67
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.39
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.80
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.82
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.62
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.72
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.27
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.56
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.25
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.15
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.77
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.75
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.65
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4926.50
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.50
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.58
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.04
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.97
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.92
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.05
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.24
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.21
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :    1.61
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:26.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.43
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:25.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.73e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.40e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.74
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.99
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 5.73e-3
p-value of test                       :    0.9940

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  160.34
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:08.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.04
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:07.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9949.29
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10183.59
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:52.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4800.49
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.26
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:50.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4141.58
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4234.74
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11680.67
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11853.27
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.47
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000049837

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.22
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000048961

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.15

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    1.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:12.22

 All tests were passed




Server wird beendet - Lösche Semaphor 176095253.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1263
p-value of test                       :    0.9971

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334383
  j =  1                              :        599997474
  j =  2                              :             1263
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5526
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:51.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:39.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:39.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:57.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:04.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7167
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:04.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:55.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:01.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.95
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.06
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    2.33
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.13
p-value of test                       :    0.9996    *****

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     325
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:13.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:43.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.92
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.96
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.72
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.24
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.53
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.25
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.83
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.14
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.88
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.78
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:43.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.28
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7047.25
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:44.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.38
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.05
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:02.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.63
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.24
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:35.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4955.10
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:55.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45905
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869905
  j =  1                              :        399908197
  j =  2                              :            45891
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45621
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869621
  j =  1                              :        399908763
  j =  2                              :            45611
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:27.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:18.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:45.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:01.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:55.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:35.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.82e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.26e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.23e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:36.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:38.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.08
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.35
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.06
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.71
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.79
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.91
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:45.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.99
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.87
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.99
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:28.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  1.9e-3

Anderson-Darling statistic = A2       :    3.55
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  167.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 7.70e-4
p-value of test                       :    0.9992    *****

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17008.97
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.85
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.68
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.38
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.78
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.82
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.82
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.17
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.28
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.03
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.05
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.77
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.54
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.21
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.41
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.77
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.55
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.67
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.50
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.28
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.03
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.42
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.09
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.96
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.26
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.96
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.41
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.28
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5036.09
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.46
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  240.81
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.76
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :   -2.39
p-value of test                       :    0.9915



-----------------------------------------------
CPU time used                    :  00:02:26.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.05
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:25.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.63
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.11
p-value of test                       :    0.98

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.90e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 5.28e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.03
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.99
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.23
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:08.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.90
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:08.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9903.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10067.11
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:51.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5051.72
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.98
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:49.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.00
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4148.93
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11644.60
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11882.23
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:29.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.81
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000115579

Normal statistic for number of bits   :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.14
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999903830

Normal statistic for number of bits   :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.20
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.88
p-value of test                       :    0.97

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:10.75
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP, t = 9           0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 177111061.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1487
p-value of test                       :  5.4e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334607
  j =  1                              :        599997026
  j =  2                              :             1487
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5427
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:50.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:39.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:39.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:57.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:04.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:04.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:54.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:00.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.59
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:46.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:14.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     173
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:39.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.42
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.12
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.30
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.43
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  271.46
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.34
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:43.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.58
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:01.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7202.00
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:45.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.66
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.52
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:02.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.56
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.38
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:35.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5107.77
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:57.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45543
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869543
  j =  1                              :        399908920
  j =  2                              :            45531
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46094
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870094
  j =  1                              :        399907814
  j =  2                              :            46090
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:27.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:17.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:59.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:55.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    3.54
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:34.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.92e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.26e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:34.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:35.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.89
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:48.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.31
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.46
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.31
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.10
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.98
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.93
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:44.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.00
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:11.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.16
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.8e-3

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17765.23
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.24
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.49
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.46
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.76
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.10
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.49
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.21
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.23
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   54.21
p-value of test                       :  4.0e-4    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.66
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.03
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.10
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.44
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.54
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.16
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.85
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.76
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  569.94
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.02
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.29
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.83
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.48
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4927.06
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.42
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.43
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.49
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.95
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4903.89
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.10
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.26
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.85
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:25.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.97
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:25.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.09e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 4.17e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:46.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.65e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.39
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.80
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:08.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.71
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:09.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9927.25
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9844.20
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:48.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5064.32
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:48.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4868.41
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:49.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4275.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4157.68
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11804.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11773.91
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:30.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.50
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000008836

Normal statistic for number of bits   :   0.070
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.45
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999879095

Normal statistic for number of bits   :   -0.96
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:48.55
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           5.4e-4
 75  RandomWalk1 R (L=50, r=25)      4.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 178094101.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:42.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5444
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:56.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:42.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:45.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:03.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:05.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:18.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:17.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:23.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:28.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    2.72
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     966
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:49.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.87
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:17.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:46.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.22
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.26
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.26
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.35
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.66
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.53
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.11
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.39
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:33.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.07
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:05.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1543.31
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:58.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7143.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:58.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.54
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:15.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.85
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.17
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4938.28
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:01.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45704
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869704
  j =  1                              :        399908594
  j =  2                              :            45700
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46069
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870069
  j =  1                              :        399907864
  j =  2                              :            46065
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:32.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:25.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :  1.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    4.54
p-value of test                       :  4.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9963


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:54.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:18.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:57.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-3
p-value of test                       :    0.9988

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:39.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:24.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:26.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:26.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.017
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:44.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:46.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.18
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.12
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.79
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.16
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.62
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:53.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.37
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.40
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.58
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:29.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.07
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17620.43
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.88
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.68
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.93
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.56
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.79
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.06
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.77
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.74
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.15
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   35.63
p-value of test                       :  5.1e-3


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.37
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.88
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  420.68
p-value of test                       :    0.9958


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.62
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.97
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.10
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.92
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.23
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.48
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.69
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.19
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.41
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4926.22
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.46
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.33
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.12
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.78
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4988.53
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  331.61
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.08
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.02
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :    1.16
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:23.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.13
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:24.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.76
p-value of test                       :    0.04

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 8.25e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.59e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.06
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:34.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.14
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:31.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.22
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:19.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.20
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:17.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9807.65
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9886.63
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:04:16.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.24
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4889.66
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:56.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.56
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.21
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11705.32
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:33.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11945.64
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:34.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.24
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999903143

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.73
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000070855

Normal statistic for number of bits   :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:38.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:41.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:15:17.69

 All tests were passed




Server wird beendet - Lösche Semaphor 179109909.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5486
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:58.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:42.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4236
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:58.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:06.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:06.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:57.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:02.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:50.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:18.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:47.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.21
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.84
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.71
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.19
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.23
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:41.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.26
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  263.88
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  379.60
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:42.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1392.51
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:00.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7006.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.32
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:59.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.02
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.30
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5088.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:12.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:11.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45734
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869734
  j =  1                              :        399908536
  j =  2                              :            45726
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45532
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869532
  j =  1                              :        399908945
  j =  2                              :            45514
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:31.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:18.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:44.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:58.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:57.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:37.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.43e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:22.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.077
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:22.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:40.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:44.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.67
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.14
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.44
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:49.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.35
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.49
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.24
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:44.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.91
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.24
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:28.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.49
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.98
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:38.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17557.11
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.27
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.10
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.82
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.87
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.29
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.48
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.30
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.37
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.82
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.67
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.03
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.99
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.04
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.66
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.72
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.05
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.96
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.89
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.76
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.05
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.77
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.42
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5107.33
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.40
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  154.45
p-value of test                       :    0.9927


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.82
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.56
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.03
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.94
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.09
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.55
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:22.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.14
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:23.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 7.53e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 4.26e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.62
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.21
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:04.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.67
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:03.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9980.76
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10016.01
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.069
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:33.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.50
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:45.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4982.30
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:49.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4221.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.80
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11812.76
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11811.08
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.01
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999897740

Normal statistic for number of bits   :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.53
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000172780

Normal statistic for number of bits   :    1.37
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.5e-3

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -1.79
p-value of test                       :    0.96

Sample variance                       :    0.21
p-value of test                       :    0.9927

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    0.20
p-value of test                       :    0.9940

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:46.45

 All tests were passed




Server wird beendet - Lösche Semaphor 180453397.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:48.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5465
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:58.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:42.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:43.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:58.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:59.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:09.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:10.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:04:06.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7188
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:12.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.20
p-value of test                       :  7.0e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:49.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:16.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.22
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:46.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.29
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.06
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.21
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.01
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.51
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.63
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.34
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.26
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.84
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1400.54
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:03.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7059.61
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:50.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.30
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:09.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.49
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.39
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:38.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5074.91
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:57.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45850
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869850
  j =  1                              :        399908301
  j =  2                              :            45848
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45732
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869732
  j =  1                              :        399908539
  j =  2                              :            45726
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:31.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:20.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:08.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:37.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.10e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.94e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.076
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:47.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.06
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.05
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.12
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.30
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.55
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.93
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.30
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.24
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.90
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.15
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:40.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17303.89
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.66
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.15
p-value of test                       :    0.9917


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.12
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.63
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.30
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.81
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.23
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.54
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.85
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.71
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.09
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.06
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  446.68
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.62
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   46.36
p-value of test                       :    0.9951


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.09
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.37
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.64
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.18
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.67
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.72
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.75
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4841.68
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  323.43
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.46
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.05
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.25
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4858.30
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.38
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.78
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.91
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:23.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   27.55
p-value of test                       :  6.4e-3


-----------------------------------------------
Normal statistic for number of jumps  :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:22.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:10.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.17e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.71e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 9.00e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.69
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.68
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.05
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:03.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.54
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:03.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10018.40
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9771.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:04:07.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.53
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:51.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4979.52
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:51.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4197.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.47
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11913.50
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:30.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11891.52
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.26
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999893408

Normal statistic for number of bits   :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.50
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000029863

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.57
p-value of test                       :    0.06

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:30.80

 All tests were passed




Server wird beendet - Lösche Semaphor 181501973.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5377
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:57.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:42.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:59.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:59.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:09.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:10.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:05.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:04:12.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:51.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.93
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:17.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:48.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.00
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.88
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.45
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.62
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.37
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.83
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:29.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.97
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:29.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1462.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:01.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7148.72
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:49.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.00
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:21.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.81
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.72
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4970.75
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:57.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45977
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869977
  j =  1                              :        399908048
  j =  2                              :            45973
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45911
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869911
  j =  1                              :        399908186
  j =  2                              :            45895
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:33.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:21.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:49.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:06.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:57.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.10e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:24.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.047
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:46.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.03
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.98
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.79
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.00
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.33
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:47.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.48
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.05
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.86
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.66
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17510.97
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.70
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.98
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.31
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.72
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.47
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.94
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.44
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.56
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.99
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.55
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.77
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.68
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.72
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.62
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.40
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.29
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.28
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.21
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.85
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.14
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.04
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.09
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5155.69
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.93
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.63
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.97
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.42
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4835.70
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.12
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.02
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.25
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :   -0.98
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:21.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.28
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:24.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.36e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 5.42e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.93
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.54
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.98
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:01.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.70
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:02.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9822.00
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10230.07
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:04:06.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9955

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.74
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:51.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.49
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:51.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.13
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.09
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11948.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:29.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.20
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:30.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.80
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000010678

Normal statistic for number of bits   :   0.084
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   33.84
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  8000014323

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :  8.1e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    4.97
p-value of test                       :  3.2e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.88
p-value of test                       :    0.9980

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.057
p-value of test                       :    0.48

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.23

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:18.36

 All tests were passed




Server wird beendet - Lösche Semaphor 182550549.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997113
  j =  2                              :             1442
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5287
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:56.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7174
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:41.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:56.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:58.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:06.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:07.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:58.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:03.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.94
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.08
p-value of test                       :  2.7e-3

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:50.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    3.45
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     633
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    2.76
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    3.21
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:17.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     174
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:43.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.24
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.02
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.13
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.00
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:11.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.76
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.11
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.72
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.39
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  478.72
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:43.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1414.54
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:00.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7196.67
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:43.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.32
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.88
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:03.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.78
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.41
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:33.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5029.94
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:02.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45880
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869880
  j =  1                              :        399908242
  j =  2                              :            45876
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45886
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869886
  j =  1                              :        399908231
  j =  2                              :            45880
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:29.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:18.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:44.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:02.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:58.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 7.75e-3
p-value of test                       :    0.9910

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:37.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.64e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.45e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:24.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.090
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:22.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:37.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.071
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:36.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.79
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.44
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.44
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.08
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.66
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.95
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:42.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.66
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.42
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.97
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17463.59
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.00
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.96
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.54
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.76
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.87
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.40
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.32
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.04
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.47
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.24
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:37.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.43
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.21
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.92
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.72
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.87
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.62
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.07
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.50
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.99
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.90
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.98
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.38
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.42
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.21
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.73
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.43
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.08
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.44
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  428.12
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  238.73
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.58
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :    1.40
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.35
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:21.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.77

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.92e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.35
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.56
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.90
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:04.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.84
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:06.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10083.95
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10049.14
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:32.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4816.23
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:46.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5044.00
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:49.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4042.24
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:18.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4013.94
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11582.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12111.20
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.52
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999956984

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.23
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999917960

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:19.85

 All tests were passed




Server wird beendet - Lösche Semaphor 183533589.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5417
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:56.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:42.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:57.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:58.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:07.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7476
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:07.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:58.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:01.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.91
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:49.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     331
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    3.69
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:14.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:47.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.16
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.91
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.07
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.57
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.56
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.27
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.53
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.07
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.14
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.24
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:43.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1471.67
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:00.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6976.48
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:43.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.44
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.41
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:03.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.15
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.70
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:35.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5017.44
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:59.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45959
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869959
  j =  1                              :        399908086
  j =  2                              :            45951
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46172
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870172
  j =  1                              :        399907660
  j =  2                              :            46164
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 3.18e-3
p-value of test                       :    0.9964

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :  5.0e-3

Anderson-Darling statistic = A2       :    4.15
p-value of test                       :  7.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  2.5e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:29.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:18.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:00.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:58.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:37.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.81e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.38e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.066
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.019
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:21.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:38.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:39.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.10
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.83
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.23
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.14
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.30
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.93
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:43.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.65
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.98
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.03
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  160.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17758.13
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.35
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.62
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.24
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.71
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.91
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.29
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.16
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.89
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.71
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.79
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.62
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.04
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.85
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.86
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.27
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.19
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.09
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  422.33
p-value of test                       :    0.9950


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.37
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.43
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.11
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.13
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5082.79
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.81
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.79
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.03
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.72
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.48
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.12
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.22
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.53
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:22.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.77
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:21.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 8.31e-4
p-value of test                       :    0.9992    *****

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.88
p-value of test                       :    0.97

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 4.13e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 5.13e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.08
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.07
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.30
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:04.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.08
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:05.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9782.13
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9811.10
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:36.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5020.83
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:46.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:50.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.36
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4237.75
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11596.94
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11740.18
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.40
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999977357

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.63
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000028969

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:11.85

 All tests were passed




Server wird beendet - Lösche Semaphor 184582165.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5348
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:56.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7110
p-value of test                       :    0.9926


-----------------------------------------------
CPU time used                    :  00:02:42.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:57.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:58.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:06.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7495
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:06.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:57.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:01.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:49.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.12
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    2.35
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:16.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.94
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    2.59
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:44.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.68
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.42
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.01
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.66
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.36
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.57
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.72
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.73
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.32
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:41.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1358.87
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:59.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6975.83
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:39.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.57
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   88.59
p-value of test                       :  9.6e-3

-----------------------------------------------
CPU time used                    :  00:03:02.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.52
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  150.26
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:32.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5106.52
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:00.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45837
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869837
  j =  1                              :        399908328
  j =  2                              :            45833
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46224
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870224
  j =  1                              :        399907558
  j =  2                              :            46212
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:28.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:19.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:45.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:59.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:57.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:36.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-5
p-value of test                       :    0.9932

Kolmogorov-Smirnov- statistic = D-    : 2.33e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.066
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:21.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:35.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:33.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.23
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.64
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.92
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:50.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.87
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.39
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.18
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.33e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   62.62
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.47
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:28.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.63
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:29.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.27
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17437.32
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.39
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.28
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.68
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.82
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.91
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.06
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.75
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.06
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.07
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.49
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.03
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.15
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.71
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.24
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.66
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.74
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.55
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.27
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.95
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.44
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.32
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.04
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.59
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.89
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.80
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:36.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.05
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.37
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4810.94
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.41
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.04
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.60
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :   -1.73
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:23.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.88
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :    1.49
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:23.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    1.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.63e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 4.43e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.66
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.05
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.62
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:04.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.38
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:06.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10283.79
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10200.88
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : -9.71e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:37.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4964.48
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:48.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4970.32
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:49.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3978.89
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.36
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11779.51
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11829.68
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.41
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999987071

Normal statistic for number of bits   :   -0.10
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.92
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000076999

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.18
p-value of test                       :    0.01

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:00.30

 All tests were passed




Server wird beendet - Lösche Semaphor 185630741.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:50.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5318
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:55.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:42.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:58.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:59.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:09.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:09.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:04:05.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:09.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     952
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:50.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     643
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:16.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.25
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.69
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    3.34
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:44.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.55
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.43
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.67
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.93
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.35
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:12.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.10
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.89
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.96
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.91
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.47
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:48.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1387.78
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:02.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7262.27
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.09
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.76
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:08.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.81
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.91
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:37.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5016.90
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:09.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45951
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869951
  j =  1                              :        399908102
  j =  2                              :            45943
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46188
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870188
  j =  1                              :        399907627
  j =  2                              :            46182
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:32.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:17.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:47.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:02.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:36.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 8.02e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 7.95e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:44.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:43.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.80
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.05
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.06
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.84
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.72
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.40
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-3
p-value of test                       :    0.9981

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   65.58
p-value of test                       :  6.6e-3

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.92
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.39
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:39.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17468.88
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.13
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.87
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.31
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.34
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.17
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.66
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.03
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.32
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.30
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.04
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.28
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.43
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.11
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.30
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.20
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.98
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.03
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.57
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.44
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.68
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.70
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.88
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5078.07
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.31
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.56
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.68
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.18
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.26
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.84
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.84
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   -1.12
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:24.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.22
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :  -0.078
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:23.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    2.40
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.58e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.21e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.16
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.24
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.19
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:04.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.51
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:05.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9776.08
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10099.87
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:04:03.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4927.52
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:51.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.14
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:52.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4057.07
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4285.31
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11660.35
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:29.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11844.77
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.45
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  7999965774

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.84
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999939386

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:50.70

 All tests were passed




Server wird beendet - Lösche Semaphor 186646549.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5429
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:55.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:42.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4447
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:58.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:06.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:08.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:57.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:02.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.54
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     858
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:49.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:16.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:45.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.77
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.92
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.81
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.44
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.07
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.90
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  354.88
p-value of test                       :    0.9978

-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1483.08
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:00.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7001.79
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:40.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.88
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:04.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.14
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.55
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4953.63
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:02.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45964
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869964
  j =  1                              :        399908077
  j =  2                              :            45954
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45299
p-value of test                       :    0.9967


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869299
  j =  1                              :        399909403
  j =  2                              :            45297
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:28.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:19.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:00.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:57.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:35.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.23e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.58e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:21.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:37.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:38.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.32
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.74
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.10
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.55
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.43
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:43.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9948

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.88
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.92
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  161.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17446.02
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.39
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.44
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.55
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.19
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.40
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.91
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.45
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.89
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.21
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.93
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.06
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.36
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.27
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.56
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.35
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.32
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.85
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.90
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.00
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.53
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.77
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.85
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.09
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.89
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.68
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.88
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.42
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5089.48
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.70
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.04
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.00
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:24.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.84
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:24.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 5.09e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.39e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.52
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.52
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.94
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:05.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.52
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:05.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10047.35
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9953.50
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:36.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4824.26
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:46.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4915.10
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:50.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.85
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3990.25
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11817.26
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11617.57
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.33
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999871442

Normal statistic for number of bits   :   -1.02
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.02
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999890006

Normal statistic for number of bits   :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.81
p-value of test                       :    0.03

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.26

Sample variance                       :    1.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:37.65

 All tests were passed




Server wird beendet - Lösche Semaphor 187695125.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:50.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5379
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:56.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:42.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4498
p-value of test                       :  7.6e-3


-----------------------------------------------
CPU time used                    :  00:01:57.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:58.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:06.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:06.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:57.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:04:02.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:49.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:16.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:49.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.72
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.13
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.54
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.75
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.95
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.58
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:43.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1344.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:01.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6894.72
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.33
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.86
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:04.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.33
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.58
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:35.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5199.26
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:59.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45880
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869880
  j =  1                              :        399908247
  j =  2                              :            45866
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46231
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870231
  j =  1                              :        399907540
  j =  2                              :            46227
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:28.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9981


-----------------------------------------------
CPU time used                    :  00:02:18.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:45.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-3
p-value of test                       :    0.9988

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:59.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:01.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.08e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.67e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 8.88e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:21.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:37.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.018
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:36.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.09
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:47.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.71
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.61
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:48.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.18
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.00
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.23
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.63
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.10
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    5.64
p-value of test                       :  1.5e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   84.15
p-value of test                       :    0.9994    *****

-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17670.61
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:49.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.09
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.11
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.78
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.68
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.96
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.10
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.41
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.18
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.78
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.40
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:34.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.40
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.68
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  558.50
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.69
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.36
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :   95.58
p-value of test                       :    0.9996    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.92
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.15
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.72
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.41
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.13
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.21
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5183.60
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.80
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  155.72
p-value of test                       :    0.9911


-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.82
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.69
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4954.91
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.93
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.23
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   27.48
p-value of test                       :  6.6e-3


-----------------------------------------------
Normal statistic for number of jumps  :    1.76
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:11.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.05
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :    0.82
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:11.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    2.32
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 7.96e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.45e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:40.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.93
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.39
p-value of test                       :    0.9943

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.44
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:53.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.35
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:54.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10271.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10167.43
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:50.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:21.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4798.96
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:36.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4839.24
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3934.81
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:11.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4150.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11682.79
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11727.41
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.50
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999902465

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.06
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999995573

Normal statistic for number of bits   :  -0.035
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:14.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   02:58:03.22
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 72  Savir2                          0.9994 
 77  RandomWalk1 H (L=1000, r=20)    0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 188743701.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5316
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:44.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4430
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:38.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:37.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4437
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:57.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:58.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:08.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:09.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:04:08.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:12.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    2.38
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    2.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:45.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    2.88
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     550
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9915

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:11.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.18
p-value of test                       :    0.9946

-----------------------------------------------
CPU time used                    :  00:02:47.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.29
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   35.38
p-value of test                       :  8.5e-3

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.46
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.74
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.24
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.08
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.59
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:32.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.38
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:58.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1445.34
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:10.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7029.40
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:55.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.97
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.86
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:13.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.32
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.12
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:45.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5197.26
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:10.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45965
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869965
  j =  1                              :        399908076
  j =  2                              :            45953
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45879
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869879
  j =  1                              :        399908243
  j =  2                              :            45877
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:31.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:18.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:08.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:56.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:39.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.68e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.83e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.30e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:25.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:25.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:50.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:51.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.02
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.34
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.09
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.93
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.21
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:52.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.93
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.24
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.51
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:29.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.18
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17355.59
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.81
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.67
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.16
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.08
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.79
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:39.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.26
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.90
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.97
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.37
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.87
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:39.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.17
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.48
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.46
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.53
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.14
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.84
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.95
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.76
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.73
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.68
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.25
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.16
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4913.74
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.61
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.34
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.02
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.56
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4884.87
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.36
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.14
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.41
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:24.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.43
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:24.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.27e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 6.76e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:46.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.28
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.52
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.36
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:07.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.22
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:07.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9923.19
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9900.21
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.24
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:04:36.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4867.27
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:53.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4781.82
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:57.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3970.18
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.20
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11695.07
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:35.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11796.12
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:35.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.59
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999940916

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.30
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000024490

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    0.14
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.01
p-value of test                       :    0.98

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:13.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:21:43.78

 All tests were passed




Server wird beendet - Lösche Semaphor 168624150.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:46.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1484
p-value of test                       :  7.2e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334604
  j =  1                              :        599997032
  j =  2                              :             1484
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5404
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:49.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:39.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7122
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:39.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:57.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:04.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:02.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:56.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:03.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.94
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:50.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:15.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:17.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:42.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.25
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.69
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.55
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.00
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.22
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.10
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.85
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.39
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.01
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.32
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:43.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.62
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:00.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7134.72
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:48.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.16
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:04.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.64
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.31
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:33.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5124.71
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:57.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46001
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870001
  j =  1                              :        399908002
  j =  2                              :            45993
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46097
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870097
  j =  1                              :        399907809
  j =  2                              :            46091
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:24.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:16.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 3.48e-3
p-value of test                       :    0.9963

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:00.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:54.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:33.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 4.52e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:22.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:32.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:32.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.53
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.64
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.24
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.96
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:55.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.72
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:43.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.00
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.49
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.12
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17785.83
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.64
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.74
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.35
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.84
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.43
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.64
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.98
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.67
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.90
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.98
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:39.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.15
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.86
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.45
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.65
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.76
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.94
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.51
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.83
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.18
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.20
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.84
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.70
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5093.77
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.49
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.41
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.41
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.52
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4896.61
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.89
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.57
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:37.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.97
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:27.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.82
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:26.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.94e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:47.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.41e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 6.95e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.35
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.76
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.07
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:09.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.17
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:08.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10030.45
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9985.98
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.020
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:47.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4730.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:49.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.17e-3
p-value of test                       :    0.9923

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5109.80
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:51.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4147.80
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12182.08
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11978.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.27
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999926351

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.04
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999849488

Normal statistic for number of bits   :   -1.19
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9988

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:53.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           7.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 169967638.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:48.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5437
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:50.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:39.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7462
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:38.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4451
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:55.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:04.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:03.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:54.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:04:01.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     867
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    2.11
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:50.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.86
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9910

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:17.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:47.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.81
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.23
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.14
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.93
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.94
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.10
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.22
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.18
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.10
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:43.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1411.20
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:58.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6863.27
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:46.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.27
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:11.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.17
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:05.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.54
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.09
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:37.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5012.23
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:12.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46008
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870008
  j =  1                              :        399907988
  j =  2                              :            46000
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45553
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869553
  j =  1                              :        399908899
  j =  2                              :            45543
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:14.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:24.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:15.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:44.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:01.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:54.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.92e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 3.15e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.77
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:34.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:33.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:51.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.23
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.20
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.28
p-value of test                       :    0.9958

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.22
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.17
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:40.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.01
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.92
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.74
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17592.39
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.22
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.83
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.68
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.86
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.05
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.41
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.40
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.15
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.70
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.09
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.43
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.20
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.31
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.00
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.07
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.08
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.89
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.78
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.58
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  110.29
p-value of test                       :  4.0e-3


-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.39
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.96
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.51
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.69
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.93
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.55
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.24
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4880.36
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.97
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.41
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.73
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:24.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.58
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:26.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 9.23e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:47.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 9.18e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.16
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.82
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.62
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:07.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.36
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:08.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  8.2e-3

Kolmogorov-Smirnov- statistic = D-    : 7.20e-3
p-value of test                       :    0.9923

Anderson-Darling statistic = A2       :    3.93
p-value of test                       :  9.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9616.74
p-value of test                       :    0.9969

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10147.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:42.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4905.53
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:50.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4769.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:51.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.29
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4078.30
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11751.94
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11786.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:29.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.24
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999960284

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.02
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999896699

Normal statistic for number of bits   :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   0.044
p-value of test                       :    0.48

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    1.85
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:08.64

 All tests were passed




Server wird beendet - Lösche Semaphor 170983446.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5346
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:49.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:39.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:58.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:58.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7065
p-value of test                       :    0.9985


-----------------------------------------------
CPU time used                    :  00:03:07.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:07.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:07.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7577
p-value of test                       :  1.3e-3


-----------------------------------------------
CPU time used                    :  00:04:12.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     847
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.06
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    4.25
p-value of test                       :  6.6e-3

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:15.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.10
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.06
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:46.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.12
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.54
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.59
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.76
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:11.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.26
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.29
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.52
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.41
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.07
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:29.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.27
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:56.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.01
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:02.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7069.81
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:56.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.24
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.62
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:17.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.15
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:46.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.40
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:40.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5162.37
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:02.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45817
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869817
  j =  1                              :        399908369
  j =  2                              :            45811
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46334
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870334
  j =  1                              :        399907334
  j =  2                              :            46330
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:31.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:17.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:48.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:04.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:56.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    3.29
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:38.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.85e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 9.22e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.90e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:24.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:45.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.85
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.37
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:50.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.69
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.65
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   52.55
p-value of test                       :  4.7e-3

-----------------------------------------------
CPU time used                    :  00:01:50.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.83
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.22
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.35
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:29.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:29.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.56e-3
p-value of test                       :    0.9963

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.19
p-value of test                       :  7.4e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  183.23
p-value of test                       :  1.5e-3

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17563.85
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.20
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.54
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.64
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.93
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.69
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:38.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.22
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.55
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.34
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.85
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.40
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.49
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.10
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.07
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  184.14
p-value of test                       :  3.8e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.44
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.80
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.02
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.74
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.03
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.35
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  446.59
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.17
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5078.28
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.06
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.74
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.17
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.98
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.75
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.75
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.97
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.19
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:27.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.40
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :   -1.79
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:25.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.60e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.27
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.92
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.86
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:07.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.49
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:06.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9982.31
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10200.62
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.085
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:04:28.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4731.90
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:55.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5001.91
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:58.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.65
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4136.38
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11708.40
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:33.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11734.35
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:34.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.67
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999909578

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.40
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999978002

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.91
p-value of test                       :    0.97

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.71
p-value of test                       :    0.96

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:12.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:11:43.82

 All tests were passed




Server wird beendet - Lösche Semaphor 171868182.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5397
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:51.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:39.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:40.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:57.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:58.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:06.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:07.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:04:01.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:06.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    9.90
p-value of test                       :  1.6e-5    *****

-----------------------------------------------
CPU time used                    :  00:01:49.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.23
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:15.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:42.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.00
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.61
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.22
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.05
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.60
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.53
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  388.45
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:52.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.48
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:00.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6962.28
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:52.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.51
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.20
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:09.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.09
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.96
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:37.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5093.40
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:55.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45957
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869957
  j =  1                              :        399908087
  j =  2                              :            45955
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45837
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869837
  j =  1                              :        399908327
  j =  2                              :            45835
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:28.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:17.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:45.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:02.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:36.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:44.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.65
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.56
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.48
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.27
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.04
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.85
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:48.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.03
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.76
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.50
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.65
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17215.24
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.80
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.69
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.29
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.47
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.04
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.32
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.25
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.43
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.41
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.01
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.87
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.56
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.87
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.90
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.75
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.40
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.86
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.05
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.32
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.95
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.64
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.84
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5153.21
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.04
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.30
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.73
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.86
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.03
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.33
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.96
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.59
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:23.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.28
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:25.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    0.16
p-value of test                       :    0.9975

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 7.62e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 9.55e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.72
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.40
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.35
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:08.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.70
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:07.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.03
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9903.92
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.56
p-value of test                       :    0.9947

-----------------------------------------------
CPU time used                    :  00:04:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4851.57
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:55.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4793.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:54.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4259.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4271.14
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11669.37
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:30.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11725.36
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:30.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.60
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999997145

Normal statistic for number of bits   :  -0.023
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.65
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000033571

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.88

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:59.81
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP2S, t = 3         1.6e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 173015062.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9955


-----------------------------------------------
CPU time used                    :  00:00:52.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5430
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:56.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:51.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4413
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:01.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:11.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:30.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:32.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7184
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:13.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:04:50.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.90
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:14.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     263
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:16.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:44.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.91
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.25
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.09
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.46
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.72
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.22
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.51
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.13
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.31
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:39.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.81
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:00.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6888.29
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:45.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.26
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.26
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:01.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.96
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.88
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:34.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5033.76
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:56.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45992
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869992
  j =  1                              :        399908021
  j =  2                              :            45982
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45635
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869635
  j =  1                              :        399908731
  j =  2                              :            45633
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :  4.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.96
p-value of test                       :  9.2e-3


-----------------------------------------------
CPU time used                    :  00:02:31.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:24.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:55.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:10.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:55.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.55e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 8.23e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.05e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.79e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -5.32e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:37.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.33
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.12
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.15
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.26
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.09
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.50
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.38
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.14
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.54
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:30.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.07
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17856.31
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:00:54.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.77
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.85
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.84
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.37
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.40
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.47
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.90
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.67
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.82
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.13
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.57
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.66
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  445.63
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.86
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.62
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.42
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.17
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.25
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.32
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.52
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.87
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.79
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.53
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.35
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.83
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:51.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.19
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  311.28
p-value of test                       :    0.9973


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5147.54
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.07
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.36
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.11
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:27.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.42
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :    1.37
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:28.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :  1.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.06
p-value of test                       :    0.98

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.54e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 6.09e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.23
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.48
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.32
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:07.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.53
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:08.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9966.29
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10172.13
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:04:00.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4820.51
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:47.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4781.98
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:48.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.90
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.49
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11676.66
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11890.93
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:28.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.46
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999968336

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.06
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000002134

Normal statistic for number of bits   :   0.017
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:05.96

 All tests were passed




Server wird beendet - Lösche Semaphor 174096406.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1269
p-value of test                       :    0.9952

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334389
  j =  1                              :        599997462
  j =  2                              :             1269
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5382
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:53.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:40.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:56.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:57.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:06.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7484
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:06.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:55.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:00.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     561
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    2.67
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    2.14
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     265
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:17.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.12
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:45.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.88
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.23
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.76
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.44
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.03
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.18
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.84
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  181.53
p-value of test                       :    0.9939

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.74
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.94
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:54.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7243.15
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.51
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:11.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.62
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:01.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.94
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.05
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:35.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5063.94
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:00.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45877
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869877
  j =  1                              :        399908250
  j =  2                              :            45869
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45474
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869474
  j =  1                              :        399909058
  j =  2                              :            45462
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:28.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:18.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:45.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:00.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:35.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.54e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.72e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 9.22e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:39.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:38.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.88
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.11
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.13
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:49.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.83
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.70
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.64
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:29.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.32
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17476.56
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.24
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.96
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.36
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.35
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.50
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.17
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.78
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.27
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.16
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.14
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.98
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.75
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.82
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.64
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.70
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.39
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.93
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.98
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.10
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.84
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:43.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.28
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.10
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5058.98
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  435.40
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.62
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.96
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4981.47
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.58
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.79
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.00
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :   -0.90
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:26.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.61
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:26.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    2.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.78e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 7.37e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:46.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.49e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 7.23e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.64
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.62
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.20
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:08.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.26
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:07.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.57
p-value of test                       :  6.8e-4    *****

Anderson-Darling statistic = A2       :    4.58
p-value of test                       :  4.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10354.56
p-value of test                       :  6.5e-3

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10247.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:04:05.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.49
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:49.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4928.96
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4040.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4251.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11554.42
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11750.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:29.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.97
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999997970

Normal statistic for number of bits   :  -0.016
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.70
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000049525

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:28.48

 All tests were passed




Server wird beendet - Lösche Semaphor 175013910.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:40.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5470
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:52.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:56.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:57.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:05.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:04.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:56.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:04:02.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.98
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.22
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.35
p-value of test                       :  6.2e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.85
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:14.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.83
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    3.29
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:44.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.63
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.87
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.76
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.68
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.17
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  189.13
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.29
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:42.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1514.36
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:00.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7106.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:40.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.48
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:02.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.51
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   85.36
p-value of test                       :    0.9914


-----------------------------------------------
CPU time used                    :  00:01:35.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4981.83
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:00.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45798
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869798
  j =  1                              :        399908407
  j =  2                              :            45792
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45746
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869746
  j =  1                              :        399908510
  j =  2                              :            45742
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:27.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9966

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:17.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:45.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:59.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:55.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9935

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:33.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.01e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.30
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:21.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:34.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.18
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.76
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.49
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.57
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.89
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:45.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.85
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.29
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.83
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:28.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9932

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.32
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17569.24
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.61
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.80
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.93
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.09
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.57
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.08
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.88
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.46
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.10
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.95
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.20
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.59
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.70
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.22
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.58
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.61
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.61
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.22
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.09
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.56
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  442.06
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.46
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5025.66
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.52
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.98
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.56
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.07
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4863.32
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.38
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.80
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :   -0.98
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:25.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.41
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :    1.27
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:26.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.74e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.65e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.59
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.94
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.56
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:08.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.79
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:09.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9929.33
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.55
p-value of test                       :  1.2e-3

Anderson-Darling statistic = A2       :    5.03
p-value of test                       :  2.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10367.91
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:46.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4811.62
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:48.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4980.85
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:49.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.08
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3978.99
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11713.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11968.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:29.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.53
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999992630

Normal statistic for number of bits   :  -0.058
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.58
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999964139

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:10.92

 All tests were passed




Server wird beendet - Lösche Semaphor 176062486.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:41.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:51.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5355
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:51.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:39.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:39.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:57.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:04.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:04.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:55.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:01.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.89
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     859
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    2.53
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:14.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.42
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:43.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.58
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.92
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.61
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.56
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.26
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.27
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.14
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:41.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.97
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:00.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7266.70
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:40.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.17
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.51
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:02.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.29
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.28
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:35.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4858.60
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:57.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45797
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869797
  j =  1                              :        399908411
  j =  2                              :            45787
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45722
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869722
  j =  1                              :        399908560
  j =  2                              :            45714
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:27.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:17.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:45.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:00.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:54.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:33.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 6.60e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 7.64e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.03
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:21.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:36.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:36.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.90
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:49.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.33
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.78
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.29
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.47
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   14.89
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.00
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.70
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.62
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.57
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.05
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17420.53
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.05
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.43
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.16
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.10
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.84
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.29
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.30
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.07
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.96
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.89
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.56
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.92
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  561.92
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.72
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.43
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.17
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.80
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.22
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.68
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   50.92
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.89
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  325.35
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5153.05
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.77
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.26
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.21
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.50
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4794.88
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.89
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.57
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.73
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:24.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.35
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:24.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   0.049
p-value of test                       :    0.48

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 5.51e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.36e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.90
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.59
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.55
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:09.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.58
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:08.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9872.63
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9939.63
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:49.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.7e-3

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5064.18
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:48.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.47
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:49.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4123.31
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3967.43
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11877.75
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:28.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11937.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:29.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.75
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999975677

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.05
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999890351

Normal statistic for number of bits   :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.39
p-value of test                       :  8.4e-3

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:27.93

 All tests were passed




Server wird beendet - Lösche Semaphor 177012758.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:51.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5452
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:51.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:38.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7463
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:04.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:05.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7465
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:54.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:59.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.88
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:13.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.67
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.91
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:42.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   18.65
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.37
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.83
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.34
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.74
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.44
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.61
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.00
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.48
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.89
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:42.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1429.09
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:00.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7115.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.45
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.51
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:02.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.59
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:34.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5036.66
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:59.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46238
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870238
  j =  1                              :        399907526
  j =  2                              :            46234
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46132
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870132
  j =  1                              :        399907741
  j =  2                              :            46122
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:27.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:18.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:45.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:58.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:55.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:33.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 8.92e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 8.06e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.49
p-value of test                       :    0.9936

-----------------------------------------------
CPU time used                    :  00:00:21.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:35.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:35.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.93
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:48.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.59
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.11
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.58
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.35
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.01
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:42.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.77
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.37
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:29.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:29.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.92
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.92
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17025.34
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.89
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.32
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.33
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.77
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.72
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.33
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.53
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.13
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.44
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.40
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.22
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.55
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.39
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.55
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.65
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:46.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.07
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.38
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.77
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  170.76
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.84
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.22
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.47
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5128.55
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.47
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.90
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:36.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.47
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.15
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5062.85
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.99
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.31
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.82
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:26.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.46
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:25.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   0.065
p-value of test                       :    0.47

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 6.63e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.99e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.94
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.02
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.73
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:08.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.80
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:10.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9963.74
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9840.39
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.081
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:46.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4784.55
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5042.76
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:49.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4224.01
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11698.78
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11896.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:30.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.97
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999994061

Normal statistic for number of bits   :  -0.047
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.56
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000016876

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.12

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:33.25

 All tests were passed




Server wird beendet - Lösche Semaphor 177963030.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:51.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:39.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:39.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:57.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:06.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:07.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:58.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:03.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.83
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:49.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:15.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.69
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:42.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.64
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.83
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.99
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.32
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.55
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.90
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  393.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:49.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1438.27
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:58.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6998.49
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:48.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.78
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:10.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.43
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.03
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4941.49
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:09.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45787
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869787
  j =  1                              :        399908426
  j =  2                              :            45787
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46030
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870030
  j =  1                              :        399907946
  j =  2                              :            46018
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:30.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:18.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:46.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.27
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  6.6e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:04.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:36.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.22e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.064
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:43.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.021
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:44.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.01
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.52
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.30
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.75
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.64
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.91
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.05
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:46.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.97
p-value of test                       :  9.5e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.54
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.22
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:29.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.85
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:39.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17552.88
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.65
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.78
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.76
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.93
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.92
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:39.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.43
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.84
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.41
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.15
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.74
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.25
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.91
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.25
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.86
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.40
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.94
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.31
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.66
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.00
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.19
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.48
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4960.86
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.75
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.45
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:36.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.35
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.01
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4806.72
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.79
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.14
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.94
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :   -0.11
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:23.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.34
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :   -1.51
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:25.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.99e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:47.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.68e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 8.23e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.18
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   20.99
p-value of test                       :  7.2e-3

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:08.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.46
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:08.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10038.64
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10022.52
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:04:23.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4970.25
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:54.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.09
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:54.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.98
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.30
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11804.46
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:32.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12056.57
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:32.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.22
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000081361

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   83.39
p-value of test                       :  6.3e-3


-----------------------------------------------
Total number of bits:  8000088690

Normal statistic for number of bits   :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   0.033
p-value of test                       :    0.49

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.12

Sample variance                       :    1.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:09.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:10.03

 All tests were passed




Server wird beendet - Lösche Semaphor 178978838.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5454
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:54.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:41.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:00.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:00.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:08.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:10.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:07.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:08.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.75
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:47.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.81
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.91
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     662
p-value of test                       :  6.6e-3

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:14.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:44.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.63
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.81
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.72
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.27
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.78
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.73
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.33
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.00
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.54
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1535.68
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:00.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7014.19
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:42.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.26
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.41
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:02.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.72
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.77
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:35.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5005.73
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:00.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45984
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869984
  j =  1                              :        399908035
  j =  2                              :            45978
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45774
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869774
  j =  1                              :        399908456
  j =  2                              :            45766
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:27.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:18.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:44.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:00.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:55.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:34.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 8.16e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:21.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:35.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:37.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.58
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:48.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.35
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.73
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.50
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.22
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.98
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:42.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.15
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.04
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.18
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17418.80
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.58
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.55
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.51
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.33
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.63
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.12
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.55
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.09
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.77
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.42
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.30
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.69
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.26
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.48
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.44
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.17
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.58
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.80
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.23
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.27
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.05
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.79
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5121.48
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.71
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.18
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.06
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.06
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4986.96
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.51
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.43
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:36.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.41
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :   -1.81
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:25.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.87
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:27.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.86e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 9.34e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.17e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 9.10e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.06
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.72
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.23
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:06.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.00
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:07.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9946.74
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9937

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10023.36
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.35
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:46.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.62
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  2.1e-3

Kolmogorov-Smirnov- statistic = D-    : 6.72e-3
p-value of test                       :    0.9929

Anderson-Darling statistic = A2       :    4.20
p-value of test                       :  7.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4625.23
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:01:51.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4014.32
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4173.53
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12078.11
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11840.87
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:29.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.71
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999925262

Normal statistic for number of bits   :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   31.73
p-value of test                       :    0.9933


-----------------------------------------------
Total number of bits:  8000127048

Normal statistic for number of bits   :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.55
p-value of test                       :    0.94

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:28.28

 All tests were passed




Server wird beendet - Lösche Semaphor 180224022.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5510
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:52.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:40.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4439
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:57.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:58.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:05.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:06.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:59.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:04.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.83
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    1.80
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:15.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:43.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.22
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.98
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.76
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.13
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.38
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.52
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.05
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.33
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:51.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.06
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:00.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7255.08
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:51.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.89
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:09.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.95
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   93.11
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:37.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5032.73
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:57.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45885
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869885
  j =  1                              :        399908235
  j =  2                              :            45875
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45640
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869640
  j =  1                              :        399908726
  j =  2                              :            45628
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:29.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    3.43
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:17.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:46.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:02.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:56.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:36.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.28e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 3.94e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:44.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.99
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.78
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.90
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.01
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.90
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.29
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:48.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.34
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.28
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.49
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17409.39
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.13
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.71
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.93
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.52
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.68
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.91
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.59
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.80
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.47
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.28
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.66
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.54
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  420.43
p-value of test                       :    0.9959


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.90
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.53
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.36
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.71
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.04
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.10
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.91
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.56
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.10
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5068.21
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.28
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.58
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.29
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.51
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5023.50
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.45
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.85
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.36
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:26.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.10
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:26.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.91e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.17
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.47
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.57
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:07.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.45
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:07.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9734.58
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9929.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:04:21.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5031.56
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:54.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5023.18
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3952.97
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.42
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11917.45
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:31.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11691.55
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.62
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999914081

Normal statistic for number of bits   :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.34
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000193972

Normal statistic for number of bits   :    1.53
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.57
p-value of test                       :    0.94

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:27.46

 All tests were passed




Server wird beendet - Lösche Semaphor 181174294.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:50.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1223
p-value of test                       : 1 -  5.3e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334343
  j =  1                              :        599997554
  j =  2                              :             1223
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5392
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:53.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:39.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:40.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:57.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:05.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:04.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:56.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:01.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     951
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    3.34
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    3.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:49.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.90
p-value of test                       :  3.3e-3

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:14.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:43.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.42
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.73
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.51
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.75
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.67
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.26
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.90
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:16.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.68
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:42.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1453.77
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:00.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6832.44
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:43.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.71
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.55
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:02.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.88
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.20
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:33.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5126.35
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:58.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45959
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869959
  j =  1                              :        399908084
  j =  2                              :            45955
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46118
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870118
  j =  1                              :        399907767
  j =  2                              :            46112
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:26.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:17.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.9999    *****

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:45.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :  3.4e-3

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:57.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:55.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:34.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-5
p-value of test                       :    0.9908

Kolmogorov-Smirnov- statistic = D-    : 3.90e-4
p-value of test                       :  2.3e-3

Anderson-Darling statistic = A2       :    4.63
p-value of test                       :  4.3e-3

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:34.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.64
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.57
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.80
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.98
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:48.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.14
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.45
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:43.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.90
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.11
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.96
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.80
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  157.28
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17270.77
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.99
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.85
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.21
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.04
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.96
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.03
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.82
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.67
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.15
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.60
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.77
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.55
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.50
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.36
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.16
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.05
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.49
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  574.73
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.23
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.29
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.73
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.43
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4938.79
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.73
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.00
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.21
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.26
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.48
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.26
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.86
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.92
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:24.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.45
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:26.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.51e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.10
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.06
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.35
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:08.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.22
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:07.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10217.99
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10105.54
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:55.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:44.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5044.62
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.36
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:50.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4152.09
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4214.43
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11906.99
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11713.26
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:30.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.35
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000049792

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.27
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999930893

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.35

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:28.18
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  4  CollisionOver, t = 2           1 -  5.3e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 182288406.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:41.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5481
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:54.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:40.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:57.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:59.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:08.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:08.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7453
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:03.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:04:08.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    2.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:51.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.98
p-value of test                       :  3.0e-3

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:17.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    2.75
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:48.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.64
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.74
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.01
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:10.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.61
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.63
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.38
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.89
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.14
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:52.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.15
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:00.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7081.83
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:53.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:16.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.95
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:14.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.67
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.49
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:37.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5081.73
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:17.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45612
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869612
  j =  1                              :        399908780
  j =  2                              :            45604
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45718
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869718
  j =  1                              :        399908568
  j =  2                              :            45710
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:30.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:19.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:48.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:05.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:56.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:36.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.46e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.36e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:46.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:45.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.90
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.10
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.85
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.57
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.51
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.82
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:48.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.17
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   21.38
p-value of test                       :  8.8e-5    *****

-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:28.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17708.09
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.61
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.31
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.14
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.23
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.66
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:38.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.31
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.02
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.54
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.09
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.40
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.93
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.32
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.23
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.96
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  101.56
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.62
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.61
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.39
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.03
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.20
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.51
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.08
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.04
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.75
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.35
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.63
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.47
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.89
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.90
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.14
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.36
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:25.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.26
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:26.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.85e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.47e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 7.10e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.92
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.20
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:05.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.09
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:06.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10221.10
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9809.46
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:04:27.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.54
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:56.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.33
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:58.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.20
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11705.08
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:33.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11800.03
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:33.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.46
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999903611

Normal statistic for number of bits   :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   30.41
p-value of test                       :    0.9960


-----------------------------------------------
Total number of bits:  7999803330

Normal statistic for number of bits   :   -1.55
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 9.47e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.76
p-value of test                       :    0.96

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:14.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   0.062
p-value of test                       :    0.48

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:32.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 68  MatrixRank, L=1000, r=0         8.8e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 183304214.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:40.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:50.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5381
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:54.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4445
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:41.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4432
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:58.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:06.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:07.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7096
p-value of test                       :    0.9954


-----------------------------------------------
CPU time used                    :  00:04:02.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7186
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:05.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     941
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    2.94
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:15.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:44.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.51
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.68
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.20
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.80
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.01
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.62
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.13
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.41
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  261.74
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.07
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:47.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.63
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:01.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6926.74
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   48.78
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   41.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:08.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.88
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.13
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:35.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5021.30
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:03.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45449
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869449
  j =  1                              :        399909105
  j =  2                              :            45443
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45763
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869763
  j =  1                              :        399908477
  j =  2                              :            45757
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:29.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:17.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:45.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:01.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:56.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :  3.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:36.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 2.23e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:26.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:37.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:39.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.42
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.68
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.01
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.58
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.76
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.12
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.56
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.90
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.03
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.65
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.62
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.69
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17290.81
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.89
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.80
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.94
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.12
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.54
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   12.36
p-value of test                       : 1 -  8.2e-5    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.95
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.60
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.80
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.48
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.61
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.75
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.48
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.11
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.48
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.04
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.15
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.66
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.50
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  328.80
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.93
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5173.12
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.91
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.27
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.99
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.85
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.12
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.20
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.75
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.36
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:25.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.82
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:24.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  1.7e-3

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    4.43
p-value of test                       :  5.7e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.05
p-value of test                       :    0.98

Sample variance                       :   0.093
p-value of test                       :    0.9997    *****

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.58e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:46.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 6.39e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.49
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.36
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.45
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:06.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.18
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:07.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10077.44
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9708.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:04:07.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.05
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:50.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4755.57
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:53.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.50
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.40
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11877.45
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:30.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11836.05
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:31.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.82
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000128929

Normal statistic for number of bits   :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.68
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000063361

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:10.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:11.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:51.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 75  RandomWalk1 H (L=50, r=25)     1 -  8.2e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 184385558.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5535
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:08.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4444
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:58.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4455
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:17.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:17.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:40.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:41.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:05:06.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:05:06.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.73
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:13.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:14.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.92
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:44.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.95
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.45
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.16
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.15
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.62
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.45
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.07
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:43.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1356.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:01.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6989.53
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:41.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.66
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.21
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:01.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.72
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.47
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:33.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4945.93
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:12.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:02.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45417
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869417
  j =  1                              :        399909171
  j =  2                              :            45407
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45544
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869544
  j =  1                              :        399908914
  j =  2                              :            45540
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :  4.4e-3

Anderson-Darling statistic = A2       :    3.49
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9974


-----------------------------------------------
CPU time used                    :  00:02:28.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:18.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 5.27e-3
p-value of test                       :    0.9942

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:45.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.73
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  9.0e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:59.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:36.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.02e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.47e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 5.22e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:37.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:37.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.76
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.57
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.34
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.75
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.82
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.32
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.19
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:44.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.69
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:11.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:10.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.66
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.23
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:39.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17352.93
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.61
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.20
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.07
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.34
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.75
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.27
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.67
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.84
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.39
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.37
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.78
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.91
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.59
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.03
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.71
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.10
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.93
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.25
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.35
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.44
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.20
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.43
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.27
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.43
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.89
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:36.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.82
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.04
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5048.42
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.60
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.00
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.46
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :    0.69
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:24.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.41
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:25.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :  -0.076
p-value of test                       :    0.53

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.05e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.26e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 9.59e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.24
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.23
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:06.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.38
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:06.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10119.46
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9699.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:45.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.87
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:47.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.14
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:49.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4195.84
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4123.71
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11774.44
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11689.19
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.98
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000001972

Normal statistic for number of bits   :   0.016
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.47
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  8000018193

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:27.70

 All tests were passed




Server wird beendet - Lösche Semaphor 185368598.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5499
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:57.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4458
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:45.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:00.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:02.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:13.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:13.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:08.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:04:14.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.88
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.75
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    2.11
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     266
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    2.01
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:15.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:40.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.82
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.45
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.11
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.55
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.67
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.75
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.37
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.56
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:56.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:07.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6943.69
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:57.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.95
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:16.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.35
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:46.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.44
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5006.87
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:00.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45638
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869638
  j =  1                              :        399908726
  j =  2                              :            45634
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45636
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869636
  j =  1                              :        399908736
  j =  2                              :            45620
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:32.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:21.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:53.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:07.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  7.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:56.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:37.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 6.01e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.75e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:24.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:24.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:48.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:51.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.95
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.49
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.98
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.79
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:50.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.48
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.86
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:51.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.1e-3

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.10
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.84
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.64
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.21
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17039.64
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.32
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.74
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.03
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.76
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.22
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.56
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.67
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.13
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.11
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.21
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.04
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.29
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.97
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.05
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.93
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.89
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.07
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.43
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.35
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.72
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.16
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.22
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4936.02
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.83
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.06
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.42
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.75
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5096.41
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.67
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.32
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.31
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:25.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.93
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :   0.034
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:26.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 6.35e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:46.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 4.72e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.43
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.56
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.55
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:06.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.08
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:08.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9883.71
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9905.64
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.051
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.09
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.061
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:04:27.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4825.74
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4668.77
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:59.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4200.77
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4061.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11658.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:35.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11828.39
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:37.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.93
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000006688

Normal statistic for number of bits   :   0.053
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.40
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000069478

Normal statistic for number of bits   :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   0.098
p-value of test                       :    0.46

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.79
p-value of test                       :    0.96

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.60
p-value of test                       :    0.05

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:11:13.73

 All tests were passed




Server wird beendet - Lösche Semaphor 186417174.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:39.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5381
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:56.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:41.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:40.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:58.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:06.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:06.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:55.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:04:02.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.86
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:50.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    2.45
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     663
p-value of test                       :  5.9e-3

Stat. AD (mNP2)                       :    1.93
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    2.07
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     267
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:18.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:45.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.48
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.43
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.12
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.62
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.80
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:11.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.03
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.64
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.05
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.81
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  496.42
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1410.33
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:02.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7235.19
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.47
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:02.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.87
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  143.49
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:32.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4817.71
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:05.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45856
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869856
  j =  1                              :        399908293
  j =  2                              :            45846
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46441
p-value of test                       :  4.5e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870441
  j =  1                              :        399907119
  j =  2                              :            46439
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:29.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:18.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:46.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 4.92e-3
p-value of test                       :    0.9946

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:00.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:56.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:36.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.04e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.97e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:41.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.87
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.89
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.78
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.95
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:49.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.78
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.95
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.46
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.49
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.67
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17622.47
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.56
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.45
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.39
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.59
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.99
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.24
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.22
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.58
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.15
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.09
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.50
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.14
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.09
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.54
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.38
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.38
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.68
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.76
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.14
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.64
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.40
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.41
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5014.17
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.23
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.51
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.92
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.05
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5050.80
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.99
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.31
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.53
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:23.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.21
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :   -1.61
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:24.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 7.70e-3
p-value of test                       :    0.9918

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.72
p-value of test                       :    0.96

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.57e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.90e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 8.98e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.93
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.16
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.64
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:08.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.13
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:09.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9972.61
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10139.71
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:38.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4728.42
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:47.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4796.06
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:49.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.59
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.32
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11937.97
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11885.68
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.71
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999977135

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   32.97
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  7999994016

Normal statistic for number of bits   :  -0.047
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:27.09

 All tests were passed




Server wird beendet - Lösche Semaphor 187531286.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:50.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1258
p-value of test                       :    0.9981

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334378
  j =  1                              :        599997484
  j =  2                              :             1258
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5544
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:55.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7145
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:40.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:05.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:05.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7480
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:57.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:01.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:49.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:15.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:16.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.84
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.00
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     173
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:42.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.73
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.42
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.59
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.34
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.35
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.35
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.96
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  494.70
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:43.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1481.50
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:01.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6926.05
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:42.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.76
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.79
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:03.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.94
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.65
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:34.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5103.82
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:01.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46148
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870148
  j =  1                              :        399907710
  j =  2                              :            46136
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45484
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869484
  j =  1                              :        399909033
  j =  2                              :            45482
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:29.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:18.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :  3.4e-3

Kolmogorov-Smirnov- statistic = D-    : 8.21e-3
p-value of test                       :    0.9904

Anderson-Darling statistic = A2       :    5.32
p-value of test                       :  2.1e-3


-----------------------------------------------
CPU time used                    :  00:01:45.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:59.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :  6.3e-4    *****

Anderson-Darling statistic = A2       :    3.89
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:34.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : -1.79e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:36.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.041
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:37.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.70
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.25
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:48.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.13
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.99
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.68
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.63
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.28
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17353.50
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.04
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.14
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.88
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.20
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.39
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.75
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.69
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.86
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.81
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.12
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.35
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.63
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.92
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  167.21
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.42
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:42.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.14
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.51
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.48
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.43
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.06
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.99
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.52
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4909.28
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.03
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.84
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:33.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.12
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.72
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5084.14
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.32
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.94
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:32.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.90
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:13.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.57
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  :    2.07
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:13.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    0.22
p-value of test                       :    0.9922

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-3
p-value of test                       :    0.9980

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    2.22
p-value of test                       :    0.01

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.98e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:40.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.95
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.58
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.10
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:54.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:55.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9966.21
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10148.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:22.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5000.38
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:39.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5018.06
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.24
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:13.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.72
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11590.15
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11715.86
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.80
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000055006

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   33.48
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  8000020893

Normal statistic for number of bits   :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:15.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.21e-3
p-value of test                       :    0.9912

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.51e-3
p-value of test                       :    0.9931

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.90
p-value of test                       :    0.03

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -2.10
p-value of test                       :    0.98

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   02:58:34.50

 All tests were passed




Server wird beendet - Lösche Semaphor 188579862.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1274
p-value of test                       :    0.9929

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334394
  j =  1                              :        599997452
  j =  2                              :             1274
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5414
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:43.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:37.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:36.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:55.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:55.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:02.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:02.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:53.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:59.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.71
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:51.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    3.88
p-value of test                       :  1.0e-2

-----------------------------------------------
CPU time used                    :  00:02:11.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:38.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.53
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.33
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.58
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.05
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.38
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.66
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.53
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.40
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.12
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:42.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.60
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:00.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6885.13
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:44.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.60
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   38.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:03.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.57
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.65
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:38.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4939.88
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:15.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:02.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45573
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869573
  j =  1                              :        399908858
  j =  2                              :            45565
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46170
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870170
  j =  1                              :        399907665
  j =  2                              :            46160
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:29.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 2.25e-3
p-value of test                       :    0.9976

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:20.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:46.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:00.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:52.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:31.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.53e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.28e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 5.03e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:36.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:37.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.31
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.33
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.89
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.67
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:47.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.36
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.64
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.99
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:40.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.78
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.75
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:30.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:17.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.42
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17553.88
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.05
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.06
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.31
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.83
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.15
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.18
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.53
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.00
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.15
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.22
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.36
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.96
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.20
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.54
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  101.10
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:46.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.66
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.14
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.66
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.98
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.70
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  328.63
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.15
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4863.05
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.83
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.74
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:34.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.04
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.02
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5094.75
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.48
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.54
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:32.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.45
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:12.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.61
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :    1.35
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:14.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 3.74e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:47.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.14e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.04
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.89
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:14.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.99
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:08.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9959.56
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10168.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:04:15.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4967.14
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:49.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4976.69
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:50.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.24
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4172.14
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11678.78
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11847.03
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:31.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.70
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000102463

Normal statistic for number of bits   :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.85
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999957863

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:16:42.00

 All tests were passed




Server wird beendet - Lösche Semaphor 168656919.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1227
p-value of test                       : 1 -  8.4e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334347
  j =  1                              :        599997546
  j =  2                              :             1227
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5489
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:45.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:38.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:37.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:54.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7457
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:02.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:02.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:54.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:04:00.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.45
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.90
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     845
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.83
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     636
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.17
p-value of test                       :    0.9965

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:09.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.07
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:43.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.00
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.88
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.37
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.54
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.44
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.27
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.61
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  477.61
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:44.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.50
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:59.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7027.67
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:45.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.69
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.43
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:02.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.70
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.29
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5120.35
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:05.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45950
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869950
  j =  1                              :        399908101
  j =  2                              :            45948
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45815
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869815
  j =  1                              :        399908374
  j =  2                              :            45807
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:30.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.34
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:17.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:01.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:54.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:32.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.82e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:34.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.03
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:33.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.23
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:48.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.41
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.77
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.98
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:48.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.86
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.07
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.71
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:41.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.5e-3

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.14
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.63
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.037
p-value of test                       :    0.9981

-----------------------------------------------
CPU time used                    :  00:01:28.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.88
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17724.76
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.43
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.20
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.03
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.34
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.61
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:39.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.32
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.92
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.57
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.79
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   33.81
p-value of test                       :  8.9e-3


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.05
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.20
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.36
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.94
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.68
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.30
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.77
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.57
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.11
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.38
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.29
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.38
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5109.24
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.03
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.61
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:34.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.54
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.43
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.24
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.86
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.92
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:33.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.17
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:16.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.73
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:21.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.67e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:48.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.00e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 8.35e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.59
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.87
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.03
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:09.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:11.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9907.35
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9880.78
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:04:03.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.65
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:49.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4830.44
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:49.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3899.03
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4296.92
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12042.62
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11698.16
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:29.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.81
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000096523

Normal statistic for number of bits   :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.22
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000016588

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    2.25
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:39.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 10  CollisionOver, t = 14          1 -  8.4e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 169705495.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5460
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:46.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4247
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:37.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:36.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:55.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:02.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:02.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:53.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:59.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:46.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.90
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:13.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.88
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    2.92
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    2.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:42.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.19
p-value of test                       :    0.9911

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.03
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.89
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.79
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:11.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.08
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.43
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.60
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.11
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:43.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1423.79
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:59.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7066.37
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:42.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:15.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.38
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:00.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.79
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.89
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:34.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4979.69
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  5.6e-3


-----------------------------------------------
CPU time used                    :  00:03:03.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45590
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869590
  j =  1                              :        399908823
  j =  2                              :            45584
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45990
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869990
  j =  1                              :        399908023
  j =  2                              :            45984
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:32.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:19.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:45.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:02.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:33.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.64e-4
p-value of test                       :  4.9e-3

Kolmogorov-Smirnov- statistic = D-    : 5.31e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    4.03
p-value of test                       :  8.4e-3

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:33.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.69
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:48.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.15
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.11
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.64
p-value of test                       :    0.9914

-----------------------------------------------
CPU time used                    :  00:00:48.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:44.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.12
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.32
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.96
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.17
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17328.14
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.96
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.07
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.32
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.38
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.58
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.04
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.61
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.57
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.49
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.88
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.18
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.48
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.89
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.48
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.68
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.28
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.98
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.37
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.38
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.36
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.17
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5125.87
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.93
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.18
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.52
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.66
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.83
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.88
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.09
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:20.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.27
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :    0.19
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:26.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   0.049
p-value of test                       :    0.48

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:47.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.80e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 8.63e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:46.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.56
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.64
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:08.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.24
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:08.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10100.52
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10067.80
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:04:00.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.87
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4770.30
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:50.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.94
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.36
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11908.39
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11574.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:29.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.68
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999913673

Normal statistic for number of bits   :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   82.58
p-value of test                       :  7.4e-3


-----------------------------------------------
Total number of bits:  7999909344

Normal statistic for number of bits   :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :  -0.090
p-value of test                       :    0.54

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:30.55

 All tests were passed




Server wird beendet - Lösche Semaphor 170491927.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:38.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:50.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5419
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:44.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:37.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:36.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:55.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:55.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:01.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:02.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7172
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:53.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:59.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.87
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    2.30
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     827
p-value of test                       :    0.9927

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:46.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.67
p-value of test                       :  4.2e-3

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.58
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    5.11
p-value of test                       :  2.5e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     253
p-value of test                       :    0.9970

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    2.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:14.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.68
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:44.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.28
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.65
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.81
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.26
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.09
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.49
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.42
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.64
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.59
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.38
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1493.56
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:01.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7026.73
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:41.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.35
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:04.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.66
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.40
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5125.06
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:01.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45820
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869820
  j =  1                              :        399908364
  j =  2                              :            45812
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45919
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869919
  j =  1                              :        399908163
  j =  2                              :            45917
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:31.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:19.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:45.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:00.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:56.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:33.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 9.77e-6
p-value of test                       :    0.9962

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 2.04e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.34
p-value of test                       :  9.7e-3

-----------------------------------------------
CPU time used                    :  00:00:21.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:34.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:34.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:47.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.97
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:48.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.36
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.13
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:37.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.85
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.36
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.15
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17555.83
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.40
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.05
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.64
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.09
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.85
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.49
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.79
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.75
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.32
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.25
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:37.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.46
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.07
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.82
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.22
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.68
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.07
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.71
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.01
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.17
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.54
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.97
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.34
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4902.09
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.28
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.15
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.99
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.38
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.15
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.46
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.15
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.61
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:22.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.88
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  :    2.55
p-value of test                       :  5.4e-3



-----------------------------------------------
CPU time used                    :  00:02:25.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 7.97e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.16e-4
p-value of test                       :    0.9983

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.18
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.96
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.80
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:07.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.56
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:08.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10070.85
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9689.64
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:54.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.09
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:50.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4954.13
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:51.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.27
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4036.26
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11935.75
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11728.91
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:30.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.03
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999965159

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.33
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999986258

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-3
p-value of test                       :    0.9980

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.23
p-value of test                       :    0.01

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:10.61

 All tests were passed




Server wird beendet - Lösche Semaphor 171343895.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5469
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:50.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:39.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:36.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:54.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4203
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:54.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:00.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:01.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:52.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:59.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     946
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:46.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:11.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:41.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.00
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.04
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.57
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.68
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.59
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.43
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.67
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.82
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  453.93
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:42.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.46
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:01.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6682.48
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:01:41.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.58
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.45
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:03.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.45
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.02
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:33.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4917.70
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:00.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45552
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869552
  j =  1                              :        399908901
  j =  2                              :            45542
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45672
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869672
  j =  1                              :        399908661
  j =  2                              :            45662
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:29.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:18.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:45.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:57.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:36.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.51e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 3.68e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:22.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:35.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:35.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.49
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.61
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.98
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:47.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.52
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.56
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.22
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:37.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.27
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.57
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.80
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.10
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.09
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17575.89
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.72
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.67
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.04
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.75
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.96
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.96
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.68
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.14
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.17
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.70
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.00
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.27
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.71
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.32
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.86
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.41
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.89
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  436.99
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.63
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.90
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.38
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.22
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4992.43
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.03
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.38
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  441.23
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.20
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5126.91
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.01
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.83
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.06
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:22.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.47
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :   0.048
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:23.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.08

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.32e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 7.42e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.62e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 4.10e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.71
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.49
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.41
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:07.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:07.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9870.53
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10133.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.045
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:55.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4887.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:51.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.09
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:50.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.82
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.83
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11908.03
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:28.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11922.02
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.26
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000000952

Normal statistic for number of bits   : 7.53e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.11
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999957407

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    2.54
p-value of test                       :  6.4e-3

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.021
p-value of test                       :    0.51

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.61
p-value of test                       :  2.3e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    6.08
p-value of test                       :  9.6e-4    *****

Tests on the sum of all N observations
Standardized normal statistic         :   -3.09
p-value of test                       :    0.9990    *****

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:17.52
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 37  Gap, r = 20                     0.9991 
 105  AutoCor, d=1, r=27              0.9990 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 172228631.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5380
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:57.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7192
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:40.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:56.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:56.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7457
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:03.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:02.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:53.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:58.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.74
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    3.19
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     540
p-value of test                       :    0.9931

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    2.51
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:14.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    2.22
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     173
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:43.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.52
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.89
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.22
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.87
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   30.11
p-value of test                       :    0.9965

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.73
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.14
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  283.15
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  394.71
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:44.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1587.50
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:02:01.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7022.30
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:41.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.76
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.22
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:03.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.42
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.13
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:33.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5115.10
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:57.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45860
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869860
  j =  1                              :        399908286
  j =  2                              :            45848
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45556
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869556
  j =  1                              :        399908889
  j =  2                              :            45554
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:31.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 2.13e-3
p-value of test                       :    0.9977

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:27.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:55.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:10.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 4.83e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:21.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:22.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:37.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.86
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.65
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.53
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.34
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.56
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.73
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:38.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.78
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.10
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.97
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.37
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:39.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17298.77
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.65
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.46
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.94
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.83
p-value of test                       :    0.9902


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.39
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.89
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.65
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.41
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.62
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.62
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.47
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.34
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.01
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.44
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.50
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.97
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.52
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.27
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.55
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.24
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.46
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.37
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5167.13
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.69
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.17
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.60
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.61
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4892.11
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.74
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.13
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.05
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :    1.34
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:23.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.69
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:23.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.25e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 7.01e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.62e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.04
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.36
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.26
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:05.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.22
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:05.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10096.49
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10170.31
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.016
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:50.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4679.85
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:50.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4846.24
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4224.62
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4097.05
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11814.95
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:28.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11781.36
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:29.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.79
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  7999879077

Normal statistic for number of bits   :   -0.96
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.50
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000028684

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.063
p-value of test                       :    0.53

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:29.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    2.43
p-value of test                       :  9.3e-3

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:34.06

 All tests were passed




Server wird beendet - Lösche Semaphor 173244439.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:50.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1475
p-value of test                       :  1.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334595
  j =  1                              :        599997050
  j =  2                              :             1475
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1274
p-value of test                       :    0.9929

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334394
  j =  1                              :        599997452
  j =  2                              :             1274
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5399
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:00.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:43.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:42.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:57.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7126
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:06.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:05.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:53.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7175
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:57.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:52.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:16.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:46.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.77
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.38
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.58
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.67
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.94
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.09
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.25
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:43.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1405.07
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:59.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7182.00
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:41.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.76
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.18
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:01.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.68
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.69
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:33.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5187.31
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:01.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45429
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869429
  j =  1                              :        399909144
  j =  2                              :            45425
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45651
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869651
  j =  1                              :        399908702
  j =  2                              :            45643
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:29.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:16.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:43.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:57.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:55.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:34.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 6.97e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.33e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 2.72e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:21.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:35.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:36.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.57
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.67
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.34
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.49
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.48
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.96
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:51.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   56.53
p-value of test                       :  1.6e-3

-----------------------------------------------
CPU time used                    :  00:01:37.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.94
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.14
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.74
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:39.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17317.63
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:52.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.68
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.80
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.10
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.10
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.65
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.12
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.29
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.22
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.77
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.09
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.01
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.10
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.85
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.48
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.94
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.89
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.90
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.16
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.93
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.76
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.99
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.78
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5046.05
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.18
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.93
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.85
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.80
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4901.47
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.34
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.11
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:34.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.48
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:21.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.56
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:22.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.75e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.12e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.26
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.15
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.25
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:06.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.89
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:06.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9894.96
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9821.69
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:43.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.97
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:58.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:01.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4271.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:29.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4170.10
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:29.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11947.56
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:39.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11908.92
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:37.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.25
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999794765

Normal statistic for number of bits   :   -1.62
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.10
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000091030

Normal statistic for number of bits   :    0.72
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-3
p-value of test                       :    0.9989

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.79
p-value of test                       :    0.04

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:43.03

 All tests were passed




Server wird beendet - Lösche Semaphor 174227479.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:40.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5459
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:04:05.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:45.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:48.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:02.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:02.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7483
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:13.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:11.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:03.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:04:03.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.80
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:50.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    3.92
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:01:15.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:16.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:44.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.18
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.40
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.55
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.99
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.59
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.91
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.33
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:54.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1389.81
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:06.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7216.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:56.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.64
p-value of test                       :  8.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.71
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.45
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:17.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.51
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:46.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.82
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:39.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5010.93
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:56.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45719
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869719
  j =  1                              :        399908564
  j =  2                              :            45715
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46167
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870167
  j =  1                              :        399907668
  j =  2                              :            46163
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:31.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:20.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:51.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:08.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:37.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.08e-4
p-value of test                       :  1.3e-3

Kolmogorov-Smirnov- statistic = D-    : 7.97e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    3.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:24.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:50.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:52.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.92
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:50.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.24
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.29
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.45
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.75
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:52.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.27
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.33
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  157.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.47
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17898.24
p-value of test                       :  6.4e-3



-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.02
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.03
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.68
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.89
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.86
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.85
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.23
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.22
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.71
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.87
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:36.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.25
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.33
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.76
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.60
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.96
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.12
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.93
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  595.71
p-value of test                       :  2.0e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.94
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.98
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.15
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.65
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5276.90
p-value of test                       :  3.2e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  328.76
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.11
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.08
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.59
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4790.77
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.19
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.35
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.55
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :   -1.13
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:21.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.89
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:22.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.68e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.88e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 8.09e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.01
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.61
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.96
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:05.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.00
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:07.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10167.12
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9955.01
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:11.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:04:34.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.3e-3

Kolmogorov-Smirnov- statistic = D-    : 7.58e-3
p-value of test                       :    0.9919

Anderson-Darling statistic = A2       :    4.17
p-value of test                       :  7.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4610.95
p-value of test                       :    0.9980

-----------------------------------------------
CPU time used                    :  00:01:54.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4821.46
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:57.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3997.48
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11809.17
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11826.29
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:36.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.99
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000178708

Normal statistic for number of bits   :    1.41
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.29
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000027553

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.79
p-value of test                       :    0.04

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:55.31

 All tests were passed




Server wird beendet - Lösche Semaphor 175276055.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5341
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:00.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7175
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:42.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:57.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:05.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:05.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:57.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:00.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     940
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:46.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.85
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     336
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:12.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    2.42
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     174
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:39.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   21.38
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:00:54.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.61
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.22
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.71
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.67
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.38
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.71
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.86
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.64
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  383.96
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1550.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:05.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7075.49
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.79
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   84.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:09.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.08
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.21
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5104.89
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:55.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45495
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869495
  j =  1                              :        399909014
  j =  2                              :            45487
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45832
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869832
  j =  1                              :        399908339
  j =  2                              :            45826
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:30.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:18.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9979

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:06.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:56.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:36.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 9.26e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.065
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:37.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:38.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.34
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:50.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.76
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.82
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.40
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:45.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.81
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.86
p-value of test                       :    0.9913

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.25
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.14
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.86
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17322.64
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.97
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.23
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.20
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.02
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.43
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.53
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.37
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.81
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.38
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.10
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.63
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.88
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.83
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.95
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.71
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.87
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.93
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.57
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.91
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.71
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:43.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.93
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  323.80
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.15
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.43
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.32
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.10
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.41
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5078.75
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.05
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.83
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.24
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:22.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.65
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :   -0.96
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:22.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.48e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.16e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.90
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.34
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:07.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.25
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:08.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9967.87
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9992.84
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : 9.05e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:04:24.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4963.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:53.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:55.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4229.09
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4136.50
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11985.56
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:32.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11843.10
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:31.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.33
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999832613

Normal statistic for number of bits   :   -1.32
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.07
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000094771

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.95e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.26
p-value of test                       :    0.01

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.65
p-value of test                       :    0.95

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:26.02

 All tests were passed




Server wird beendet - Lösche Semaphor 176455703.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1461
p-value of test                       :  4.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334581
  j =  1                              :        599997078
  j =  2                              :             1461
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5428
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:56.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:42.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:00.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:00.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:10.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7147
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:09.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7461
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:04.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:04:08.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     865
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:49.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:13.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:42.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.11
p-value of test                       :    0.9929

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.22
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.76
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.32
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.64
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:12.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.62
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.31
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:29.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.47
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:57.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.71
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:04.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7064.18
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.42
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.12e-4
p-value of test                       :    0.9995    *****

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.6e-3

Anderson-Darling statistic = A2       :    4.67
p-value of test                       :  4.4e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :  101.07
p-value of test                       :  7.2e-4    *****

-----------------------------------------------
CPU time used                    :  00:03:18.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.80
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:46.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.36
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:42.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4959.44
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:01.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45724
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869724
  j =  1                              :        399908555
  j =  2                              :            45718
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45725
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869725
  j =  1                              :        399908552
  j =  2                              :            45721
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:32.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:21.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:54.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:13.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:56.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:38.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.05e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.63e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.43e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 7.54e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:24.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:24.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:24.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:42.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.39
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.24
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.54
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.69
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.69
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.58
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.48
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:51.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.16
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.33
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.63
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.67
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17748.62
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.50
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.66
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.27
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.80
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.47
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.65
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.88
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.03
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.54
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.56
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.72
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.40
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  560.16
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.14
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.55
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.00
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.52
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.21
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.29
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.95
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:43.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.67
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.04
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.64
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.97
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.67
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.18
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.98
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4878.73
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.84
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  238.68
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.78
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -1.13
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:26.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.22
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :   0.052
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:27.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.88e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 8.55e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.12e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 5.92e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.77
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.49
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:08.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.18
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9926.78
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10067.05
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:12.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:04:37.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.71
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:54.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.42
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:57.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4304.34
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4296.34
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11802.30
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:34.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11789.45
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:35.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.14
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999919496

Normal statistic for number of bits   :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.73
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000040498

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:30.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 39  Run, r = 15                     7.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 177537047.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:50.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1472
p-value of test                       :  2.0e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334592
  j =  1                              :        599997056
  j =  2                              :             1472
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5456
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:52.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:39.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:55.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:04.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:04.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:54.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:00.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    3.18
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.67
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    2.62
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     565
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.57
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     267
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:15.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:43.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.02
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.97
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.84
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.09
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.50
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.49
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.54
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.92
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.54
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1521.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:59.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7139.46
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.74
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.87
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:01.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.58
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.34
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:35.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5014.29
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:01.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45715
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869715
  j =  1                              :        399908571
  j =  2                              :            45713
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45782
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869782
  j =  1                              :        399908439
  j =  2                              :            45776
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9932

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:29.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:19.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:46.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:59.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:55.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:33.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.74e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:34.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:34.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.00
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.36
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.45
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.96
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.32
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.15
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:38.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.95
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.94
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.13
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.96
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.15
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.9999    *****

Anderson-Darling statistic = A2       :    3.83
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16878.71
p-value of test                       :    0.9986



-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.33
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.58
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.65
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.29
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.99
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.41
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.59
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.96
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.98
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.90
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.16
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.52
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.20
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.53
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.04
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.61
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.17
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.93
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.87
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.23
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.00
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.51
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.54
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.68
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.80
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.62
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.88
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5148.29
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.94
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.77
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.81
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :    0.14
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:24.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.19
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :    1.20
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:27.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.26

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.87
p-value of test                       :    0.97

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.29e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 8.27e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.01
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.92
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.67
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:09.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.42
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:06.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9920.17
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.31e-3
p-value of test                       :    0.9933

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10248.51
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:55.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.03
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:49.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.38
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4675.45
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:50.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4216.18
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.73
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11613.87
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11631.36
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:30.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.23
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000043180

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.00
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999884066

Normal statistic for number of bits   :   -0.92
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    2.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:32.37

 All tests were passed




Server wird beendet - Lösche Semaphor 178782231.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5274
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:53.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:39.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:39.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:55.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:56.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:03.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:03.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:54.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:59.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    2.10
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     846
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    4.89
p-value of test                       :  3.2e-3

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    2.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:14.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:42.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.99
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.08
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.60
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.88
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.73
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.14
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.44
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.20
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:42.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.23
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:00.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7071.38
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:40.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.02
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.90
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:02.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.32
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.17
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:34.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4865.66
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:01.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45830
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869830
  j =  1                              :        399908341
  j =  2                              :            45828
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46002
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870002
  j =  1                              :        399908000
  j =  2                              :            45994
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:28.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:17.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:44.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:40.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.93e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:33.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.054
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:34.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.07
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:48.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.60
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.15
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.92
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:48.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.70
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.64
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.57
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:38.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.76
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.04
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.77
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.54
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17579.70
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.23
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.01
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.84
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.12
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.10
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.08
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.33
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.07
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.50
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.79
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.93
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  107.40
p-value of test                       :    0.9930


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.67
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  177.54
p-value of test                       :  9.6e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.17
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.67
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.87
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.17
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.79
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.73
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.03
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.37
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.20
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.91
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.66
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.26
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.75
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.97
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  437.76
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.21
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.00
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:24.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.32
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :  -0.095
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:25.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.77

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9992    *****

Tests on the sum of all N observations
Standardized normal statistic         :   0.092
p-value of test                       :    0.46

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.18e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 4.68e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.72
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.14
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.25
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:06.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.95
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:07.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9810.90
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10276.68
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:50.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4706.99
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:49.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5015.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:50.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4237.79
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3987.00
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11735.36
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:29.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11755.28
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:30.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.58
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999962189

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.57
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000165469

Normal statistic for number of bits   :    1.31
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   0.020
p-value of test                       :    0.49

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:25.05

 All tests were passed




Server wird beendet - Lösche Semaphor 179830807.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:39.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5437
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:54.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:39.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:39.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:56.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:03.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:02.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:55.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7175
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:00.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    2.54
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:13.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     174
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.19
p-value of test                       :    0.9932

-----------------------------------------------
CPU time used                    :  00:02:41.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.85
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.97
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.44
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.61
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.32
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.88
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.42
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.79
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:00.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6981.62
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.74
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.08
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:02.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.27
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.88
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:35.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4989.46
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:56.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45967
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869967
  j =  1                              :        399908067
  j =  2                              :            45965
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45854
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869854
  j =  1                              :        399908295
  j =  2                              :            45848
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:29.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:17.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:44.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:59.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:34.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.19e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.95e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.58e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 2.06e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:21.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:33.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.71
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.65
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.28
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.56
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:38.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.61
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:17.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.17
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 8.02e-3
p-value of test                       :    0.9914

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.3e-3

Anderson-Darling statistic = A2       :    3.56
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17884.66
p-value of test                       :  7.8e-3



-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.16
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.16
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.87
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.49
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.05
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.13
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.83
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.04
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.19
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.29
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.79
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.15
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.06
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.58
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.83
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.79
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.91
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.39
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.65
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.01
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.34
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.57
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4919.52
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.87
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.69
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.97
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.93
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.11
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.91
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.84
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.23
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -0.90
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:25.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.72
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:26.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :  -0.022
p-value of test                       :    0.51

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.46e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 2.45e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.35
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.48
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.54
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:06.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.76
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:05.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10104.83
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10216.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:46.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4844.10
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:49.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.96
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:51.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.46
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.44
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11520.76
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12120.14
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:29.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.15
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000073192

Normal statistic for number of bits   :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   85.50
p-value of test                       :  4.1e-3


-----------------------------------------------
Total number of bits:  8000076270

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:57.37

 All tests were passed




Server wird beendet - Lösche Semaphor 180846615.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5533
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:56.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:43.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:00.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:01.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:10.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7144
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:11.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:09.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7487
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:13.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:49.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:14.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:40.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.51
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.19
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.38
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.05
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.25
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.98
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.76
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.71
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.00
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.13
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:59.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1466.81
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:08.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7169.08
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:58.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.90
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:16.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.65
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:46.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.27
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:40.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5024.83
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:02.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45992
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869992
  j =  1                              :        399908020
  j =  2                              :            45984
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45885
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869885
  j =  1                              :        399908230
  j =  2                              :            45885
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:31.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:21.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:12.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :  5.2e-3

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:56.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:38.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.70e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:24.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:46.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.02
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.20
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.68
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.77
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.20
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.78
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:50.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.47
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.40
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.51
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:30.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.80
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17308.41
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.37
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.99
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.34
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.55
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.95
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.02
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.20
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.18
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.12
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.47
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.37
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.48
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.07
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.26
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.92
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.25
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.07
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.92
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.80
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.63
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:46.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.80
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.64
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4767.53
p-value of test                       :    0.9907


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.67
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.51
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.82
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.96
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5132.75
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.69
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.49
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.43
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :    2.12
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:25.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.31
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :    1.40
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:23.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 6.22e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.06e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.82
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.17
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.21
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:06.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.74
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:08.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9959.20
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10080.80
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:04:37.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4717.99
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:52.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4983.82
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.09
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.25
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12118.66
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:33.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11805.44
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:35.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.80
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999929102

Normal statistic for number of bits   :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:12.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.57
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000009349

Normal statistic for number of bits   :   0.074
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.57
p-value of test                       :  7.2e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    5.33
p-value of test                       :  2.1e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.67
p-value of test                       :    0.9963

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.24

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:11:18.27

 All tests were passed




Server wird beendet - Lösche Semaphor 181862423.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1493
p-value of test                       :  3.1e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334613
  j =  1                              :        599997014
  j =  2                              :             1493
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5402
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:53.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7482
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:39.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:57.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:05.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:05.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:56.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:04:01.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.80
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9927

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    3.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:17.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:45.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.72
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.10
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.19
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.66
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.30
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.34
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.38
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  274.39
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.06
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:44.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1550.61
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:00.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6984.07
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.11
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.11
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:02.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.59
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.73
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:34.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5247.64
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:59.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46180
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870180
  j =  1                              :        399907643
  j =  2                              :            46174
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46189
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870189
  j =  1                              :        399907630
  j =  2                              :            46173
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:28.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:19.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:45.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:59.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 9.86e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:32.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.91e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.40
p-value of test                       :  8.3e-3

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:21.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:36.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.71
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.57
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.19
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.17
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.52
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.04
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.48
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:44.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.41
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.27
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.05
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:29.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.65
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17357.78
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.61
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.48
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.62
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.45
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.29
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:38.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.44
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.30
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.80
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.44
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.03
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.68
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.65
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.42
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.11
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.92
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.10
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.72
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  565.52
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.68
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.61
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.87
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.33
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4886.98
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.76
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.60
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.48
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.31
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5101.09
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.50
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.58
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.49
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :   -1.08
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:26.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.59
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :    0.29
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:25.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.44e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.42e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.88
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.45
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.73
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:06.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.04
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:06.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10014.61
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10077.27
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:44.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4972.87
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5016.07
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:50.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4348.78
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4007.18
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11794.52
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11644.70
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:30.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.68
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999996293

Normal statistic for number of bits   :  -0.029
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.97
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000031795

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:07.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  3  CollisionOver, t = 2            3.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 183336983.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:40.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:51.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5353
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:54.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:40.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:56.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4233
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:04.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:04.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:55.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:59.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:15.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.97
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    2.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:45.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.03
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.46
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.76
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.29
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.57
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.32
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.49
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:44.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1423.50
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:01.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6923.69
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:45.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.00
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.27
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:02.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.99
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:35.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4990.19
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:59.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46132
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870132
  j =  1                              :        399907741
  j =  2                              :            46122
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45910
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869910
  j =  1                              :        399908183
  j =  2                              :            45904
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:28.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:19.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:44.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:01.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.55e-3
p-value of test                       :    0.9950

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:36.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.25e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 8.12e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:21.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:37.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:37.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.52
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.08
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.32
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.84
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.67
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.77
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:45.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.6e-3

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.14
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.82
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17616.22
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.75
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.06
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.08
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.48
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.67
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.14
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.31
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.45
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.92
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.45
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.32
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.57
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.21
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.61
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.22
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.41
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.08
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.39
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.69
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.60
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.62
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4875.35
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.72
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.28
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.20
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.67
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4945.18
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  439.25
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.60
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.56
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :   -1.57
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:24.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.90
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :    1.10
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:25.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.40e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 8.25e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.71
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.12
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:04.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:07.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9991.35
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9955.14
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.34
p-value of test                       :  9.7e-3

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:04:01.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4887.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:49.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4790.22
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:51.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.76
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.91
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11744.04
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:29.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11920.28
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:29.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.19
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000149548

Normal statistic for number of bits   :    1.18
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.48
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000097783

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :  -0.086
p-value of test                       :    0.53

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:04.04

 All tests were passed




Server wird beendet - Lösche Semaphor 184287255.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:39.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5397
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:55.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4239
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:42.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:57.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:58.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:06.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:07.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:04:00.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:04:05.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     940
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:53.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:20.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:50.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.02
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.26
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.57
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.06
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:10.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.26
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.35
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.15
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.55
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.14
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:47.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1357.24
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:59.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6984.05
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.64
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:08.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.45
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.10
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5174.66
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:58.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45432
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869432
  j =  1                              :        399909142
  j =  2                              :            45420
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45683
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869683
  j =  1                              :        399908635
  j =  2                              :            45681
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:29.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:17.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:03.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:36.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 6.73e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:37.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:37.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:17.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.18
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.27
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.96
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.38
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:44.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.55
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  1.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.61
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.01
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:09.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.49
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:40.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17488.50
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.46
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.61
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.29
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.98
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.11
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.02
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.79
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.57
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.12
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.36
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.77
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.19
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.17
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  103.75
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.20
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.59
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.83
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.06
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.45
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.27
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.74
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.49
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4927.10
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  318.64
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.49
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.61
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.35
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5068.34
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.46
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.44
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.15
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :    1.12
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:24.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.56
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:24.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 6.95e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.79e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.58
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.62
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.12
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:06.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.65
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:06.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10058.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9960.08
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.44
p-value of test                       :  7.3e-3

-----------------------------------------------
CPU time used                    :  00:04:11.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4952.90
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:52.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.50
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:55.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4246.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.93
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11752.61
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:30.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11562.49
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:31.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.49
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999942095

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.81
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000076204

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:13.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:18.18

 All tests were passed




Server wird beendet - Lösche Semaphor 185270295.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:48.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5487
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:55.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:59.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4413
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:58.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7181
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:09.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:08.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:04:02.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:04.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.26
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    2.44
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     845
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:53.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    2.68
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     556
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:15.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:40.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.10
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.79
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.20
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.26
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.15
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.32
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.63
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.33
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1413.17
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:01.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7189.80
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   41.41
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:07.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.78
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.35
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:36.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5029.77
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:59.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46018
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870018
  j =  1                              :        399907966
  j =  2                              :            46014
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46127
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870127
  j =  1                              :        399907748
  j =  2                              :            46123
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:29.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:18.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:45.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:02.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.048
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:38.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:38.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.27
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:49.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.91
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:54.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.86
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.46
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.92
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.82
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.74
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.38
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.62
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:28.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   98.35
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17556.04
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.08
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.39
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.94
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.33
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.69
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.09
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.90
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.92
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.62
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.95
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.61
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.24
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.29
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.78
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.98
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.23
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.39
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.51
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.70
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.93
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.74
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.70
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5073.10
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.91
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.70
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.66
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.97
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.74
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.74
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.39
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.57
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:22.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.00
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :    1.30
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:22.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.62
p-value of test                       :    0.05

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 8.75e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.40e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 8.51e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.98
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.18
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.44
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:07.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.99e-3
p-value of test                       :    0.9926

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:08.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9884.90
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9791.70
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:04:14.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5022.12
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:51.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.18
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:53.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4141.31
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4172.80
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11811.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:29.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11727.38
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:30.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.66
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000111142

Normal statistic for number of bits   :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.22
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000028009

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :  1.0e-3    *****

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    5.46
p-value of test                       :  1.9e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -3.01
p-value of test                       :    0.9987

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:26.40

 All tests were passed




Server wird beendet - Lösche Semaphor 186318871.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5339
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:55.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:58.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:58.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:06.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:07.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:56.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:01.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.74
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.79
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:46.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.71
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:15.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     129
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:44.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.14
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.97
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.77
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.62
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.05
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.67
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.48
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.46
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.60
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:43.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.86
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:00.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6956.53
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9927

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.40
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:04.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.22
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.70
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:33.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5074.48
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:55.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46059
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870059
  j =  1                              :        399907883
  j =  2                              :            46057
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46006
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870006
  j =  1                              :        399907993
  j =  2                              :            45996
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 3.40e-3
p-value of test                       :    0.9961

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:27.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9930

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  6.6e-3

Anderson-Darling statistic = A2       :    3.27
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:17.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9970


-----------------------------------------------
CPU time used                    :  00:01:45.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:59.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:56.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:38.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 9.08e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:24.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:21.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.045
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:34.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:34.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.74
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.67
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.36
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.61
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.71
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.36
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:41.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    3.97
p-value of test                       :  9.4e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   96.53
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17448.17
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.88
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.56
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.71
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.88
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.16
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.28
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.62
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   43.28
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.59
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.00
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.48
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.09
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.96
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.58
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.56
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.03
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.04
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.29
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.49
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.64
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.50
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4941.00
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.18
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.82
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.76
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.14
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5166.44
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.54
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.66
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.82
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:23.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.95
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:25.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.10
p-value of test                       :    0.98

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.88e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.50e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.35
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.93
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.67
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:08.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.51
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:06.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9949.82
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10021.30
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.095
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:46.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:47.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4911.68
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:50.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.94
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4032.16
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11784.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11826.80
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.51
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000062038

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   84.83
p-value of test                       :  4.7e-3


-----------------------------------------------
Total number of bits:  8000066949

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   0.031
p-value of test                       :    0.49

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.051
p-value of test                       :    0.48

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:07.89

 All tests were passed




Server wird beendet - Lösche Semaphor 187400215.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:03.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5605
p-value of test                       :  6.6e-3


-----------------------------------------------
CPU time used                    :  00:03:57.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:42.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:43.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4219
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:01.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:02.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:13.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:13.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:07.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:04:09.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    4.05
p-value of test                       :  8.3e-3

-----------------------------------------------
CPU time used                    :  00:01:47.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     635
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:15.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.85
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    1.76
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     173
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:42.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.73
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.75
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.26
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:11.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.43
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.21
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.52
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.35
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.43
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:54.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1503.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:02.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7047.08
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.52
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.56
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:17.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.77
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  152.42
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:39.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4939.54
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:55.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45581
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869581
  j =  1                              :        399908839
  j =  2                              :            45579
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46077
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870077
  j =  1                              :        399907848
  j =  2                              :            46073
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:32.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:21.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:50.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:11.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:56.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:38.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.47e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 8.87e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:24.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.062
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:24.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:38.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:40.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.11
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.81
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.61
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.39
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.80
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.91
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:52.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.59
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.23
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:40.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17307.45
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.73
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.21
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.26
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.35
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.36
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.44
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.99
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.98
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.76
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.82
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.66
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.55
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  445.67
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.76
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.36
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.04
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.94
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.17
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.38
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.25
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.35
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5107.72
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.03
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.35
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.45
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.88
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4869.68
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.73
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.12
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.34
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    1.24
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:21.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.41
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:20.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.10

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.76e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.83e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.17
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.45
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:57.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.82
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:57.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10127.29
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:55.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10208.63
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:54.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.97
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:46.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4755.78
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:49.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4019.41
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.90
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11807.61
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11768.41
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.59
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999905222

Normal statistic for number of bits   :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.90
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999931289

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         : 9.64e-3
p-value of test                       :    0.50

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:34.00

 All tests were passed




Server wird beendet - Lösche Semaphor 188448791.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5402
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:43.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:36.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:35.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:54.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:55.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:02.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:02.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:54.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:59.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:50.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.06
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:11.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:34.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.43
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.88
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.30
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.47
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.46
p-value of test                       :    0.9939

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.83
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.13
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.70
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1492.17
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:01.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6908.94
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.63
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.03
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.31
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:02.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.20
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:46.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.38
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:36.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5037.85
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:12.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46106
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870106
  j =  1                              :        399907791
  j =  2                              :            46100
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46060
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870060
  j =  1                              :        399907885
  j =  2                              :            46050
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:14.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:28.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:17.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:45.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :  2.4e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    5.33
p-value of test                       :  2.1e-3


-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:52.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:15.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.77e-3
p-value of test                       :    0.9923

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:33.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.41e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.58
p-value of test                       :  4.9e-3

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:36.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.023
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:37.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.69
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:48.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.94
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.39
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:55.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.85
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:49.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.80
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.54
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.93
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:43.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.35
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.95
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:32.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.11
p-value of test                       :    0.9911

-----------------------------------------------
CPU time used                    :  00:01:31.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.36
p-value of test                       :  9.3e-3

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17129.51
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.80
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.63
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.14
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.06
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.67
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:40.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.41
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.50
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.52
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.11
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.89
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:40.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.71
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.28
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.46
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.44
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:49.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.52
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  194.27
p-value of test                       :  4.7e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.12
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.80
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.02
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:48.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.76
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.74
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.12
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.20
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.07
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.74
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.84
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.70
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.97
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.58
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.91
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :  -0.060
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:19.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.21
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:13.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.51e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 9.12e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 5.07e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.25
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.05
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.95
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:10.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.63
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:12.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9830.02
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
p-value of test                       :    0.9929

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9700.10
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:51.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4838.95
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.93
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.68
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.80
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12168.48
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:28.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11793.95
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   28.72
p-value of test                       :    0.9981


-----------------------------------------------
Total number of bits:  7999968942

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   33.11
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  7999913289

Normal statistic for number of bits   :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:16:41.05

 All tests were passed




Server wird beendet - Lösche Semaphor 168689688.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5430
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:43.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:36.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:36.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:54.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:55.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7465
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:02.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:02.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:53.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:59.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.08
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:48.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:12.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:39.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.65
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.91
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.45
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.91
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.62
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.29
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.15
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.16
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.88
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1446.75
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:00.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7078.20
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:44.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.87
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.01
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:02.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.60
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.36
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:35.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5041.13
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  9.9e-3


-----------------------------------------------
CPU time used                    :  00:03:15.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46158
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870158
  j =  1                              :        399907689
  j =  2                              :            46148
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46271
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870271
  j =  1                              :        399907460
  j =  2                              :            46267
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:14.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:31.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  7.9e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    5.74
p-value of test                       :  1.3e-3


-----------------------------------------------
CPU time used                    :  00:02:18.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:45.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 2.87e-3
p-value of test                       :    0.9970

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:53.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:33.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 6.26e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.01
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:22.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:34.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:35.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:47.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.83
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.63
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.29
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:48.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.43
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.75
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:39.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  4.1e-3

Anderson-Darling statistic = A2       :    4.70
p-value of test                       :  4.2e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   66.32
p-value of test                       :  5.5e-3

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.39
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:30.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.99
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:30.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.96
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17539.40
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:55.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.87
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.57
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.03
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.94
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.87
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.99
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.24
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.34
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.86
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.33
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:39.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.34
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.79
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.70
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.42
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   47.08
p-value of test                       :    0.9938


-----------------------------------------------
CPU time used                    :  00:00:47.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.37
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  108.64
p-value of test                       :    0.9910


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.31
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.95
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.78
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:47.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.69
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.05
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4924.09
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.62
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.00
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.53
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.35
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5050.43
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.58
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.95
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.84
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:24.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.69
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:18.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.86e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 7.92e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.17
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:29.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.40
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.64
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:06.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.31
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:11.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10028.47
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9997.28
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:59.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5068.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:48.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4755.14
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:49.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4197.74
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.63
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11689.51
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12025.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.94
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999820064

Normal statistic for number of bits   :   -1.42
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.60
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999934781

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:08.51

 All tests were passed




Server wird beendet - Lösche Semaphor 169246744.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5409
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:43.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:37.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:36.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:55.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4441
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:55.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:02.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:02.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:53.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:59.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.63
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.92
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:49.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.17
p-value of test                       :    0.9958

Test on the Nm values of W_{n,i}(mNP1):    2.31
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    2.03
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:14.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:39.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.56
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    4.97
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.74
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.94
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.01
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.17
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.03
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.03
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:41.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1407.83
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:59.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6900.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 9.15e-3
p-value of test                       :    0.9905

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.18
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.43
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:59.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   92.95
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:34.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4937.58
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:13.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46353
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870353
  j =  1                              :        399907299
  j =  2                              :            46343
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45817
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869817
  j =  1                              :        399908371
  j =  2                              :            45807
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 7.50e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:33.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:19.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.92
p-value of test                       :  9.8e-3


-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:59.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:55.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:33.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.75e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:22.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:34.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.67
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.12
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.59
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   16.78
p-value of test                       :    0.9983

-----------------------------------------------
CPU time used                    :  00:00:48.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.07
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.39
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:44.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.27
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.08
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.18
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17342.22
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.63
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.60
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.99
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.91
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.57
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.55
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.13
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.93
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.19
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.38
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.56
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.36
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.55
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.84
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.12
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.54
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.37
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.98
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.27
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.04
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.38
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.94
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4874.35
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.59
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.16
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  446.59
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.86
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5098.57
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.95
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.76
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.63
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :    0.51
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:24.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.21
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:22.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :  -0.038
p-value of test                       :    0.52

Sample variance                       :    2.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.96e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :  8.6e-3

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 7.64e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.12
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:29.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.97
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:07.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.32
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:10.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9812.95
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10162.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -3.46
p-value of test                       :    0.9997    *****

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:54.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 5.44e-3
p-value of test                       :    0.9943

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4703.55
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:49.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4934.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:50.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4184.93
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4288.39
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.25
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12013.17
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:30.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.38
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  8000042520

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.21
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000014074

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:25.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 92  HammingCorr, L = 30             0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 170229784.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:39.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1461
p-value of test                       :  4.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334581
  j =  1                              :        599997078
  j =  2                              :             1461
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5449
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:46.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:37.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:37.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:56.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:58.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:07.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:07.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:04:06.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:10.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.41
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:49.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.57
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    3.62
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     272
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:14.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:40.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.97
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.86
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.96
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.64
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.32
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.09
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.27
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.20
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.81
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.63
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:57.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.81
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:09.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6899.39
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:00.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.61
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:15.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.57
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.24
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4878.31
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:21.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46009
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870009
  j =  1                              :        399907985
  j =  2                              :            46003
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45818
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869818
  j =  1                              :        399908372
  j =  2                              :            45802
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:33.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :  6.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9901


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:53.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:10.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:57.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:39.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.09e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:25.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:46.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:46.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.90
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.37
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.92
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:52.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.38
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    3.46
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.03
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:29.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.14
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:29.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.86
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17158.76
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.30
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.79
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.76
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.07
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.29
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.04
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.63
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.89
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.84
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.09
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.99
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.76
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.05
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.04
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.24
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.12
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.18
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.36
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.23
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.01
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.22
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.86
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.95
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.63
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.47
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5135.42
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  328.37
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  146.29
p-value of test                       :    0.9984


-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   28.21
p-value of test                       :  5.1e-3


-----------------------------------------------
Normal statistic for number of jumps  :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:25.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.11
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -0.37
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:24.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.55
p-value of test                       :    0.94

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 4.74e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.29e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 6.53e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.71
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.73
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  8.0e-3

Anderson-Darling statistic = A2       :    3.31
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:07.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.66
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:09.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10037.37
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9725.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:04:37.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.31
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:52.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4808.24
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4170.35
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4129.48
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11672.57
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:33.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11906.92
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:35.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.19
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999946919

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.84
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999910436

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:09.30

 All tests were passed




Server wird beendet - Lösche Semaphor 171180038.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5512
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:49.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:39.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:38.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:56.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:02.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:04.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:54.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:01.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     939
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    3.39
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:14.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:43.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.72
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.80
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.96
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.05
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.85
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.97
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  268.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.06
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:43.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.43
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:00.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6843.54
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:40.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.41
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:03.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.49
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.17
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:35.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5111.77
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:18.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45910
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869910
  j =  1                              :        399908183
  j =  2                              :            45904
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45802
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869802
  j =  1                              :        399908398
  j =  2                              :            45798
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:28.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :  1.5e-3

Kolmogorov-Smirnov- statistic = D-    : 1.46e-3
p-value of test                       :    0.9985

Anderson-Darling statistic = A2       :    5.94
p-value of test                       :  1.1e-3


-----------------------------------------------
CPU time used                    :  00:02:18.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:45.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:00.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:54.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  8.3e-3

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:32.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 4.70e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.07e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:31.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:32.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.28
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:51.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.31
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:48.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.91
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.43
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:51.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.58
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:43.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.30
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.03
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.19
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.89
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17639.62
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.26
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.00
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.35
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.16
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.62
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.51
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.79
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.22
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.07
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.11
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.79
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.58
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.35
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.26
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.85
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.18
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.96
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.65
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.43
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  102.08
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.57
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.26
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4895.89
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.22
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.74
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.36
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.34
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4991.74
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.75
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.96
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.94
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:25.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.55
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:27.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.34e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 8.20e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.02e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 8.91e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.40
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.05
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.86
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:07.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.45
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:08.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9883.88
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10140.09
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:47.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4957.96
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:49.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4802.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:50.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.64
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4034.09
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11888.11
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:29.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11698.94
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:30.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.65
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999981953

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.44
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000027901

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:34.85

 All tests were passed




Server wird beendet - Lösche Semaphor 172785670.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:51.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5489
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:49.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4236
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:39.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:37.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:55.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:57.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:03.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:05.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:58.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:02.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     962
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    3.48
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:15.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:44.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.62
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.69
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.09
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.81
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:09.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   30.38
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.38
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.62
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.14
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.13
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:49.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1567.70
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:02:00.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7070.01
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:49.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:12.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.08
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:09.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.62
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.64
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5088.51
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:03.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45605
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869605
  j =  1                              :        399908794
  j =  2                              :            45597
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45347
p-value of test                       :    0.9936


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869347
  j =  1                              :        399909310
  j =  2                              :            45339
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:31.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:17.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:46.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:02.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:54.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:35.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.55e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 4.65e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      : 5.09e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:22.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:38.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:40.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.74
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.19
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.66
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.66
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.41
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.23
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.46
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:45.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9940

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.60
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:40.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17559.87
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.30
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.79
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.38
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.58
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.14
p-value of test                       :    0.9922


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.96
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.11
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.15
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.72
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.13
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.48
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.46
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.60
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.04
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.88
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.95
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.33
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.43
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.03
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.69
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.32
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.20
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5064.90
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.43
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.19
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.45
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.85
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4877.16
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.73
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.34
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.31
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :    2.66
p-value of test                       :  3.9e-3



-----------------------------------------------
CPU time used                    :  00:02:27.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.77
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:25.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 4.24e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.64e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 9.25e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.83
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.45
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.38
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:08.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.87
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:08.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9982.38
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10084.35
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.011
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:10.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:04:25.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4782.87
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:52.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4851.79
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:55.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4150.80
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.45
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11731.77
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:32.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11920.04
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:31.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.42
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000228565

Normal statistic for number of bits   :    1.81
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.05
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000011470

Normal statistic for number of bits   :   0.091
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:05.14

 All tests were passed




Server wird beendet - Lösche Semaphor 173670406.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5535
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:51.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:38.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7084
p-value of test                       :    0.9970


-----------------------------------------------
CPU time used                    :  00:02:39.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:57.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:04.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:05.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:55.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:01.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.70
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    2.10
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:49.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    4.29
p-value of test                       :  6.3e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     352
p-value of test                       :  1.8e-3

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:13.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.80
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:43.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.15
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.00
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.97
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.49
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.39
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.69
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.33
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.36
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.30
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:44.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1373.45
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:55.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6869.78
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.76
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.85
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:02.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.80
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.83
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:33.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4936.50
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:17.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46033
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870033
  j =  1                              :        399907939
  j =  2                              :            46023
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45833
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869833
  j =  1                              :        399908339
  j =  2                              :            45823
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:28.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:18.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:45.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:59.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:55.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:34.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.06e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.61
p-value of test                       :    0.9955

-----------------------------------------------
CPU time used                    :  00:00:22.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:37.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.011
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:38.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.06
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:48.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.16
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.73
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.40
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.69
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.81
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:28.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.39
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.70
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17505.17
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.68
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.33
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.18
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.62
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.24
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.55
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.12
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.40
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.67
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.08
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.42
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.56
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.83
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.91
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.59
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.52
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.38
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.76
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.65
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.10
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.21
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.51
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4836.04
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.06
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.97
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:36.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.69
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.68
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4992.15
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.73
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.90
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.30
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:26.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.89
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:24.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 6.00e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 5.77e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.00
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.43
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.10
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:06.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.69
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:07.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10056.06
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9999.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:50.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4836.79
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:53.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4970.01
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:53.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.24
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4238.17
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11603.04
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:31.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11666.71
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:31.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.42
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000081247

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.34
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999891485

Normal statistic for number of bits   :   -0.86
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    2.48
p-value of test                       :  7.9e-3

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.88

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    2.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:13.14

 All tests were passed




Server wird beendet - Lösche Semaphor 174784518.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5376
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:50.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4443
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:38.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:56.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:03.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:04.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:55.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:01.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     860
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:49.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.98
p-value of test                       :  9.1e-3

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:15.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.11
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    2.15
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    2.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:41.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.65
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.21
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.50
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.04
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.14
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.97
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.97
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.86
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1416.48
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:59.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7039.02
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:39.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.61
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   49.44
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.94
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:02.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.09
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:33.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5108.30
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:59.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45945
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869945
  j =  1                              :        399908111
  j =  2                              :            45943
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45769
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869769
  j =  1                              :        399908466
  j =  2                              :            45761
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:29.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:19.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:45.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:59.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:55.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:15.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:33.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 5.21e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.46e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:32.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:33.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.01
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:48.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.91
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.84
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.81
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.96
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.01
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:40.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.79
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:28.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:17.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.24
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17273.72
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.67
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.93
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.00
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.83
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.94
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   57.84
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.85
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.88
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.19
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.05
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.63
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.95
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  445.88
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.93
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.31
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.66
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.59
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.11
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.61
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.68
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  472.63
p-value of test                       :  1.3e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5115.94
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.13
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.58
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.57
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.44
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4883.93
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.87
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.75
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.16
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :  -0.086
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:26.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.98
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:26.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9915

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.90e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 3.40e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.15e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 7.77e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.07
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.77
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.64
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:06.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:06.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10040.12
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9893.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:48.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.42
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:48.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4849.18
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:49.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4256.99
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11899.40
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11789.40
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:30.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.97
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999867824

Normal statistic for number of bits   :   -1.04
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.48
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000097579

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.82e-3
p-value of test                       :    0.9905

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.36
p-value of test                       :  9.2e-3

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.8e-3

Kolmogorov-Smirnov- statistic = D-    : 2.73e-3
p-value of test                       :    0.9972

Anderson-Darling statistic = A2       :    4.19
p-value of test                       :  7.4e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.97
p-value of test                       :    0.9985

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:52.11

 All tests were passed




Server wird beendet - Lösche Semaphor 175767558.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1467
p-value of test                       :  3.1e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334587
  j =  1                              :        599997066
  j =  2                              :             1467
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5317
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:53.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:41.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:40.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4437
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:58.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:59.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:08.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:08.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:05.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:07.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.14
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    2.05
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:14.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:43.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.44
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.17
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.44
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:11.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:11.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.21
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.35
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.16
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.05
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:55.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.22
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:02.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7097.23
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:55.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.58
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:17.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.59
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  149.74
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:40.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5260.06
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:56.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46059
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870059
  j =  1                              :        399907890
  j =  2                              :            46043
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45526
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869526
  j =  1                              :        399908952
  j =  2                              :            45518
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:32.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:21.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:52.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:08.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 6.41e-3
p-value of test                       :    0.9928

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:38.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.85e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:24.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:24.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:44.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:45.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.34
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.98
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.69
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.12
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.70
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.91
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:50.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.80
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.23
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.42
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.03
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:29.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.01
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17275.88
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.95
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.99
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.49
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.98
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.83
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.94
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.28
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.69
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.05
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.26
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.05
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.00
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.97
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.80
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.42
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.60
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.52
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.20
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.57
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.23
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.24
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5132.83
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.21
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.18
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.07
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.63
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5179.44
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.24
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.28
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.21
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :    0.99
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:25.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.34
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :    0.19
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:26.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 5.78e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.41
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.70
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.84
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:09.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.64e-3
p-value of test                       :    0.9962

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.51
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  259.10
p-value of test                       :  3.1e-3

-----------------------------------------------
CPU time used                    :  00:02:10.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10075.73
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10149.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.034
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.54
p-value of test                       :  5.6e-3

-----------------------------------------------
CPU time used                    :  00:04:32.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5005.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:55.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.75
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:59.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4137.48
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4275.42
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11927.77
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:35.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11748.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:37.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.82
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999980600

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.63
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000044233

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.45
p-value of test                       :    0.93

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:17.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    1.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:00.68

 All tests were passed




Server wird beendet - Lösche Semaphor 176685062.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1255
p-value of test                       :    0.9986

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334375
  j =  1                              :        599997490
  j =  2                              :             1255
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5382
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:50.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:39.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7466
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:39.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:56.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:57.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:03.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7515
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:04.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7198
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:53.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:59.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    2.51
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:46.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.98
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:12.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.82
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:42.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.97
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.13
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.92
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.72
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.36
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.39
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.14
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:44.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1366.02
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7143.20
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:45.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.89
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:11.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.74
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:02.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.58
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.15
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:35.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4845.52
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:56.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46134
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870134
  j =  1                              :        399907739
  j =  2                              :            46120
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45640
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869640
  j =  1                              :        399908721
  j =  2                              :            45638
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:28.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:18.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:01.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:55.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:34.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 7.95e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.024
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:33.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.016
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:34.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.51
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.75
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.74
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.37
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.81
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.69
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:43.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.94
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.98
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.01
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.99
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:28.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.18
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.90
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17460.11
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.96
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.51
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.39
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.73
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.32
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.42
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.84
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.85
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.94
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.79
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.39
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.62
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.83
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.67
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.36
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.92
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  192.16
p-value of test                       :  6.2e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.85
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.99
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.99
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.95
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  319.78
p-value of test                       :    0.9926


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.53
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.11
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.88
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.93
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  461.40
p-value of test                       :  4.0e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.07
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.35
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.56
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.97
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :   0.070
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:24.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.18
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :    1.82
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:26.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.46e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 8.72e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 7.83e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.40
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.84
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.80
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:09.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.51
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:08.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10136.76
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10065.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:57.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4764.06
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:49.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4952.90
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:50.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4241.20
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.45
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11932.62
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:28.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11976.18
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:31.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.70
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999937283

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.61
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999917663

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    2.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         : -6.56e-3
p-value of test                       :    0.50

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:12.65

 All tests were passed




Server wird beendet - Lösche Semaphor 178061318.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1272
p-value of test                       :    0.9939

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334392
  j =  1                              :        599997456
  j =  2                              :             1272
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1251
p-value of test                       :    0.9990    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334371
  j =  1                              :        599997498
  j =  2                              :             1251
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5428
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:52.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:40.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:40.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:57.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:04.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:05.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:55.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:01.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.15
p-value of test                       :    0.9988

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     862
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:43.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.79
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:10.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    3.39
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:08.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.54
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    2.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:36.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.50
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.34
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.58
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.40
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.33
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.23
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  482.97
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1403.41
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:58.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6948.78
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.93e-3
p-value of test                       :    0.9926

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.60
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:14.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.76
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   88.70
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:34.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4982.23
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:57.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45870
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869870
  j =  1                              :        399908263
  j =  2                              :            45864
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45614
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869614
  j =  1                              :        399908778
  j =  2                              :            45602
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 8.30e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:28.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:17.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:44.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:58.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:34.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 2.99e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 7.48e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:26.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:34.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:35.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.01
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.42
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.41
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:48.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.40
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.77
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.87
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:43.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.30
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.89
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.78
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17531.50
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.78
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.41
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.21
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.36
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.73
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.74
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.40
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.10
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.07
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.45
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.56
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  190.73
p-value of test                       :  7.6e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  416.85
p-value of test                       :    0.9972


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.39
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.54
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.73
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.24
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.12
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.86
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.55
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.73
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.51
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4930.14
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.82
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.00
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.55
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  317.50
p-value of test                       :    0.9943


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5048.35
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.12
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.53
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.18
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :    0.69
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:26.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.01
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:27.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.85e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 6.78e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.94
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.76
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:08.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.69
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:08.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10030.19
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10077.16
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.017
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:44.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4962.17
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:49.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4771.70
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:51.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4202.40
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.49
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11945.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11631.39
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:30.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.54
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999881087

Normal statistic for number of bits   :   -0.94
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.92
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999975401

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.43
p-value of test                       :    0.08

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:36.40
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           0.9990 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 179077126.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:40.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5371
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:52.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:40.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:39.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:56.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:04.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:04.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:54.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:00.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9919


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:14.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     125
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:43.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.43
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.21
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.36
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.56
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.80
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.19
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.68
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.45
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  195.97
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.16
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:43.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1399.85
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:00.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7044.84
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:43.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.28
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.76
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:02.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.72
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.49
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:35.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4928.96
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:00.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45858
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869858
  j =  1                              :        399908288
  j =  2                              :            45850
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45961
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869961
  j =  1                              :        399908081
  j =  2                              :            45955
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:28.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:18.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:45.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:59.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.023
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.069
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:34.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:35.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.48
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:49.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.19
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.56
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:48.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.70
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.07
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.24
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.31
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.44
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.79
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17518.78
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.86
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.34
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.73
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.96
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.48
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.15
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.18
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.84
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.40
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.23
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.41
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  441.96
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.76
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.17
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.17
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.08
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.93
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.51
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  104.77
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.24
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.31
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5007.02
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.75
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.53
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.63
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.83
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.95
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.92
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.53
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.43
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :   -0.79
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:25.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.51
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :    1.46
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:25.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.26e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.49e-3
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.15
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.52
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.05
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:07.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.60
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:09.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9953.80
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10240.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:47.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4911.95
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:49.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4976.49
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:50.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4037.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3991.20
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11981.51
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:29.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11801.58
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:30.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.17
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999946502

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   87.10
p-value of test                       :  2.9e-3


-----------------------------------------------
Total number of bits:  8000122047

Normal statistic for number of bits   :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.04
p-value of test                       :    0.02

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:46.37

 All tests were passed




Server wird beendet - Lösche Semaphor 180027398.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:51.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5481
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:52.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:40.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:39.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:55.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:56.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:04.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:03.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:54.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7467
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:59.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.13
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    3.87
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:15.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.90
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:45.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.17
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:54.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.23
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.18
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   36.72
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.81
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.98
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.01
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.58
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  286.36
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  396.36
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:44.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1446.42
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:01.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6907.98
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:45.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.12
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.06
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:03.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.37
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.66
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:35.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4999.54
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:56.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45833
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869833
  j =  1                              :        399908335
  j =  2                              :            45831
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45763
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869763
  j =  1                              :        399908478
  j =  2                              :            45755
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9939

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:28.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:18.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:45.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:59.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.58e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:35.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:36.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.79
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:49.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.41
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.66
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.08
p-value of test                       :    0.9962

-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.83
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.92
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.01
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:45.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.14
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.21
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.33
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17498.14
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.08
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.46
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.67
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.97
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.89
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:38.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.39
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.16
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.80
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.96
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.96
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.82
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.41
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.13
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.13
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  102.68
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.35
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.68
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.56
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.45
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.31
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.35
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.14
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.03
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.25
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.67
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.71
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.07
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5029.14
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.72
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.73
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.28
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:22.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.46
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:23.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   0.011
p-value of test                       :    0.50

Sample variance                       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   0.033
p-value of test                       :    0.49

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.04e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 4.64e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 5.76e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.57
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.85
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.98
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:08.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:08.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10207.68
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9897.73
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:04:05.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.53
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:49.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    4.36
p-value of test                       :  6.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5113.95
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:50.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4275.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4020.22
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12056.89
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11998.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:31.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.28
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000091951

Normal statistic for number of bits   :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.40
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999932237

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         : -9.74e-3
p-value of test                       :    0.50

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:23.63

 All tests were passed




Server wird beendet - Lösche Semaphor 181075974.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5328
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:53.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:40.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:39.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4436
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:56.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:04.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:05.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:56.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7480
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:00.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:14.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.09
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:42.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.71
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.79
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.95
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   30.93
p-value of test                       :    0.9951

-----------------------------------------------
CPU time used                    :  00:01:10.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.90
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   96.66
p-value of test                       :  3.2e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.55
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.27
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  473.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:44.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1434.97
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6940.92
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.78
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.72
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:03.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.64
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   78.55
p-value of test                       :    0.9984


-----------------------------------------------
CPU time used                    :  00:01:34.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5012.92
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  1.3e-3


-----------------------------------------------
CPU time used                    :  00:02:56.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45743
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869743
  j =  1                              :        399908516
  j =  2                              :            45739
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46051
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870051
  j =  1                              :        399907902
  j =  2                              :            46043
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:28.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:17.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:00.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:54.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:33.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.24e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:33.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:33.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.23
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.39
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.69
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.52
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:49.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.64
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.54
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:41.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.18
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.96
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:29.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.27
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:30.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.77
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17335.36
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.59
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.97
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.89
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.47
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.48
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.98
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.53
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.63
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.70
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.13
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.06
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.38
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.72
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.95
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.13
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.92
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.24
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.76
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.14
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.96
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.23
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.46
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.61
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.37
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.06
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.97
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.62
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4893.38
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.80
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.24
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.31
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :   0.088
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:28.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.20
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :    1.01
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:25.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.76e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.80e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.10
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.59
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.54
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:05.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.71
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:06.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9886.56
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.7e-3

Anderson-Darling statistic = A2       :    3.56
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10288.74
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:45.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4778.87
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:48.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5062.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.06
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.21
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11728.91
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11727.48
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:30.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.00
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999991934

Normal statistic for number of bits   :  -0.064
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.23
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999954461

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.55
p-value of test                       :    0.06

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:41.38
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 32  CouponCollector, r = 20         3.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 182059014.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:49.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5470
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:56.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:40.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:58.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:06.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:05.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7153
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:59.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:04:03.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:15.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     122
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:44.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.00
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.62
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.26
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.82
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.44
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  382.92
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:48.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1590.34
p-value of test                       :  2.7e-3

-----------------------------------------------
CPU time used                    :  00:02:05.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6885.41
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:50.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.85
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.30
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:09.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.56
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:37.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5029.96
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:00.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46055
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870055
  j =  1                              :        399907895
  j =  2                              :            46045
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45720
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869720
  j =  1                              :        399908567
  j =  2                              :            45706
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:30.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:19.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:47.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9953


-----------------------------------------------
CPU time used                    :  00:02:04.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:36.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 8.11e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 4.53e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:39.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.57
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.73
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.54
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.05
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.83
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:46.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.33
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.79
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:28.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.04
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17617.63
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.76
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.36
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.56
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.04
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.24
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:38.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.34
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.09
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.33
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.96
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.74
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.22
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.15
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  183.71
p-value of test                       :  4.0e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.33
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.75
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.50
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.14
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.06
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.48
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.25
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5191.07
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.01
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.83
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:36.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.26
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.92
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5115.93
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.07
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.98
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.63
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :    1.22
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:25.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.28
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :  -0.064
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:23.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 9.25e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.65e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 8.91e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.97
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.46
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:06.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.23
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:07.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9985.08
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10161.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.047
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:04:23.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4842.25
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:53.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.40
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:54.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.75
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11887.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:31.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11882.89
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:32.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.05
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000020587

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.02
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999875093

Normal statistic for number of bits   :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.91
p-value of test                       :    0.03

Sample variance                       :    1.10
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:06.44

 All tests were passed




Server wird beendet - Lösche Semaphor 182976518.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997299
  j =  2                              :             1349
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5501
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:57.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:43.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:46.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:04.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:05.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:18.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:19.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:23.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:04:26.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    3.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:49.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9935

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     329
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:14.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.34
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.79
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     174
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:43.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.95
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.69
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.32
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.40
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.68
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :  102.63
p-value of test                       :  7.4e-5    *****

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.50
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.84
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  268.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.74
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:07.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1364.63
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:04.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6893.32
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:03.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.66
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.99
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:16.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.28
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:48.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:40.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5030.83
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:59.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46291
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870291
  j =  1                              :        399907422
  j =  2                              :            46283
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45813
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869813
  j =  1                              :        399908376
  j =  2                              :            45809
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:31.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.66e-3
p-value of test                       :    0.9983

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:26.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:54.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:18.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    3.57
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:38.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.62e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:24.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:28.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:27.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:44.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.62
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:51.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   40.60
p-value of test                       :    0.9956

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.25
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.97
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:51.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.90
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.27
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.54
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:54.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.52
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.09
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.87
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17467.41
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.34
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.92
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.14
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.11
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.79
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.44
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.57
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.58
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.74
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.84
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.13
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.46
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  445.92
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.45
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.93
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.88
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.32
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.29
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   92.80
p-value of test                       :    0.9983


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.14
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.13
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.04
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.45
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.53
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.27
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.72
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.22
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4860.40
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.13
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.70
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.88
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :   -2.32
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:02:23.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.08
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:24.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.57
p-value of test                       :    0.94

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.46e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 8.76e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 5.29e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.56
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:37.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.91
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:36.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.93
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:19.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.67
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:19.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9835.45
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10143.15
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:04:09.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5018.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:55.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4968.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:58.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4258.20
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11812.39
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:33.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12178.61
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:35.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.28
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000131839

Normal statistic for number of bits   :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.45
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999964547

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:35.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:38.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.095
p-value of test                       :    0.54

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:12:57.96
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 31  CouponCollector, r = 10         7.4e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 184221702.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:50.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5387
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:56.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4485
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:42.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4159
p-value of test                       :    0.9966


-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:58.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:06.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:06.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:56.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:04.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     837
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.89
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     639
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.20
p-value of test                       :  7.3e-3

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:16.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    2.03
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     173
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:44.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.04
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.60
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.97
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.46
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.65
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.89
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.10
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.71
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:43.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.48
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:00.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7058.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:40.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.20
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.73
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:02.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.25
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.15
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:36.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4997.07
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:18.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46237
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870237
  j =  1                              :        399907530
  j =  2                              :            46229
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45969
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869969
  j =  1                              :        399908065
  j =  2                              :            45963
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:19.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.71
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:28.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:19.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:45.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:59.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:55.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:36.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.53e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 2.49e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:43.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:41.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.26
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.48
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.53
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.57
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.97
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.50
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:42.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.87
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.09
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.97
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.26
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  160.04
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17342.77
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.65
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.98
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.48
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.99
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.89
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.07
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.62
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.67
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.07
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.28
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.41
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.20
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.41
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.24
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.36
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.91
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.19
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  443.57
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.79
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.38
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.52
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.43
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5079.13
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.89
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.84
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.30
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.44
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4988.33
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.28
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.37
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.83
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :    1.61
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:25.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.12
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:24.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 6.29e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.07e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.25
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.55
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:04.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.90
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:06.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10058.60
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10007.10
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:38.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-3
p-value of test                       :    0.9980

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.77
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5178.70
p-value of test                       :  2.0e-3

-----------------------------------------------
CPU time used                    :  00:01:47.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:50.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4090.10
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3966.80
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11734.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11722.24
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.76
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999994961

Normal statistic for number of bits   :  -0.040
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.57
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  7999944252

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.68
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.61
p-value of test                       :    0.9955

Sample variance                       :    1.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   0.042
p-value of test                       :    0.48

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:34.02

 All tests were passed




Server wird beendet - Lösche Semaphor 185565190.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5445
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:56.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:41.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:56.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4209
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:57.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:06.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:06.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:57.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:03.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:50.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     263
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:17.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:43.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.56
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.88
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.80
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.71
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.99
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.85
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.13
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.58
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:43.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1446.79
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:00.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7221.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:41.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.42
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.14
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:02.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.77
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.42
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:34.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4870.01
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:02.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46149
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870149
  j =  1                              :        399907705
  j =  2                              :            46143
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45901
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869901
  j =  1                              :        399908200
  j =  2                              :            45897
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:29.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:18.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:45.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:59.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 7.83e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:34.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:35.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:49.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.13
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.60
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.16
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:48.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.39
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.99
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:44.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.89
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.55
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:28.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  157.07
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9910

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17406.39
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.96
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.43
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.23
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.31
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.08
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.37
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.51
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.98
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.18
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.06
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.72
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.14
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.46
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.96
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.00
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.09
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.25
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.96
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.01
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.99
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.24
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.07
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5104.96
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.11
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.28
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.75
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.53
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.20
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.16
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.42
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.99
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:23.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.94
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:24.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 9.03e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.12
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.80
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.64
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:06.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.07
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:05.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10002.68
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10128.03
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:41.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4684.41
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4845.12
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:50.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.25
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4037.21
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11728.09
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11557.09
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:28.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.30
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999726368

Normal statistic for number of bits   :   -2.16
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.71
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999933125

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   0.066
p-value of test                       :    0.47

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:23.18

 All tests were passed




Server wird beendet - Lösche Semaphor 186613766.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1460
p-value of test                       :  5.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334580
  j =  1                              :        599997080
  j =  2                              :             1460
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5454
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:55.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:40.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:57.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:58.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:07.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:07.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:59.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:05.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.20
p-value of test                       :  7.1e-3

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:48.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.18
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.31
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.19
p-value of test                       :    0.9917

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:15.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:44.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.27
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.45
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.78
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:11.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.24
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.78
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.04
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:44.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1395.71
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:02.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7021.93
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:46.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.63
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.49
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:03.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.54
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.86
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5035.13
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:07.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45994
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869994
  j =  1                              :        399908012
  j =  2                              :            45994
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45802
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869802
  j =  1                              :        399908397
  j =  2                              :            45800
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:30.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:20.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:46.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 4.46e-3
p-value of test                       :    0.9952

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:36.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 4.10e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:22.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:42.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.77
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.81
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.76
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.44
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.81
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:55.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:45.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.43
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.46
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.77
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:29.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.70
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.87
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  151.11
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17629.37
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.88
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.66
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.68
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.02
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.13
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.95
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.46
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.20
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.51
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.84
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.18
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.66
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.47
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.09
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.87
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.36
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.35
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  167.55
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.70
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.38
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.72
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4844.72
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  428.26
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.14
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.06
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.19
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.66
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.04
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.60
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.24
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :    0.14
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:22.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.17
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :   -1.54
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:24.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   0.082
p-value of test                       :    0.47

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 7.54e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.01e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.00
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.78
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:06.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:05.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10076.96
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 9.07e-3
p-value of test                       :    0.9902

Anderson-Darling statistic = A2       :    3.43
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9639.77
p-value of test                       :    0.9950

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:44.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.59
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:47.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4677.80
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:50.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.97
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4227.01
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11891.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11954.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:29.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.67
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999966035

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.00
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000047068

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:30.62

 All tests were passed




Server wird beendet - Lösche Semaphor 187629574.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5417
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:55.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4448
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:40.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:57.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:06.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7444
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:06.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:56.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:01.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.60
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    2.36
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    2.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:48.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:15.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:47.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.34
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.60
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.93
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.75
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.20
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.00
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  389.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:43.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.07
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6976.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.36
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.50
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:03.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.12
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:46.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5225.97
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:06.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45790
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869790
  j =  1                              :        399908424
  j =  2                              :            45782
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45674
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869674
  j =  1                              :        399908657
  j =  2                              :            45664
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:29.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:18.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:44.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    3.36
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:00.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:33.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.43e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 2.37e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:38.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.020
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:37.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.63
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:48.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.32
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.67
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:48.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.47
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.68
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:36.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.83e-3
p-value of test                       :    0.9950

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.36
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   68.77
p-value of test                       :  3.1e-3

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.86
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.82
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.61
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.46
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17314.42
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.21
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.12
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.40
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.16
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.79
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.08
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.08
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.86
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.10
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.11
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:34.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.31
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.21
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.68
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.93
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.40
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:40.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.49
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.95
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.35
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.27
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.10
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.21
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.02
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4828.82
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.93
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.48
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:32.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.02
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.15
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.80
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.14
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.40
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.54
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   -1.34
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:12.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.40
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :    1.81
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:12.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.65e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.90e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:40.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.42
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.42
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:54.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:54.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10330.88
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.58
p-value of test                       :  4.8e-4    *****

Anderson-Darling statistic = A2       :    4.19
p-value of test                       :  7.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10277.44
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:50.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:51.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.057
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:22.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.23
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:39.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4816.82
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:29.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4057.57
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:12.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.62
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11670.36
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:10.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11739.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.61
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999959654

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.43
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  7999902546

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.28

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   02:58:35.98

 All tests were passed




Server wird beendet - Lösche Semaphor 188678150.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:50.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5403
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:43.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:37.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7147
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:36.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:55.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:02.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:03.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:54.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:00.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:52.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:11.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.63
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:33.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.80
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.89
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.47
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.16
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.00
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.03
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  277.72
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.71
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1527.58
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:01.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6908.08
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:47.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.82
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.89
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:02.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.87
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.19
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:36.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5216.55
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:15.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:13.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45883
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869883
  j =  1                              :        399908238
  j =  2                              :            45875
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45677
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869677
  j =  1                              :        399908651
  j =  2                              :            45667
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:28.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  1.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    4.22
p-value of test                       :  7.0e-3


-----------------------------------------------
CPU time used                    :  00:02:17.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:44.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:00.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:52.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:33.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:22.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 4.46e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:22.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:36.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:38.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.61
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:47.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.64
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:55.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.78
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.40
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.21
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.15
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:44.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.17
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.67
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.20
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:32.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.79
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:31.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.44
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17600.62
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:55.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.59
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.61
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.64
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.03
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.97
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:39.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.89
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.79
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.56
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.92
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.61
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.99
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.25
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.88
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.95
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.61
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.78
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.27
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.22
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.69
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.57
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:48.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.03
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.27
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.49
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.32
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.22
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.26
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.89
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5103.36
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.10
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.61
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:37.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.23
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :    1.16
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:18.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.53
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :    1.80
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:12.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:11.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.55
p-value of test                       :    0.06

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:14.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.06e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.94
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:29.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.45
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:11.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.04
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:11.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9958.53
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9987.25
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:56.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:49.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5011.80
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:50.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.17
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4272.01
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11703.26
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11992.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:30.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.26
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999989771

Normal statistic for number of bits   :  -0.081
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.56
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000143863

Normal statistic for number of bits   :    1.14
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :  -0.020
p-value of test                       :    0.51

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:17:01.86

 All tests were passed




Server wird beendet - Lösche Semaphor 168722457.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5446
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:44.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:37.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:36.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:02.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:02.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:54.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:00.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    2.28
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     563
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.08
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:12.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.32
p-value of test                       :  6.7e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:36.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.10
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.40
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.78
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.63
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.96
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.34
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.82
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.30
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:45.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1310.43
p-value of test                       :    0.9923

-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7067.05
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:45.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.86
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:12.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.20
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.94
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:35.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5009.00
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:16.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46009
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870009
  j =  1                              :        399907986
  j =  2                              :            46001
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45669
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869669
  j =  1                              :        399908665
  j =  2                              :            45663
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:32.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  7.8e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:18.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:45.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:00.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:53.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:33.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.71e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 1.95e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.18
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:35.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:35.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:48.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.51
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.35
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.10
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:39.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.62
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.46
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.83
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.40
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:37.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17127.68
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:55.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   17.88
p-value of test                       :    0.9950


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.94
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.93
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.27
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:39.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.89
p-value of test                       :    0.9916


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.06
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.52
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.32
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.77
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:40.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.34
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.14
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.82
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.52
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.64
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:48.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.89
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.50
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.03
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.80
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.93
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:47.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.42
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  456.90
p-value of test                       :  6.1e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4922.51
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  440.41
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.76
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.15
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.52
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.21
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.91
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.36
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.50
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:24.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.63
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:18.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:11.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 3.46e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :  9.3e-3

Kolmogorov-Smirnov- statistic = D-    : 6.38e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.66
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:30.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.02
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.52
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:07.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.46
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:10.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9961.79
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10039.15
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:04:01.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4954.30
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4913.96
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4020.12
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4069.91
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11823.67
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11619.97
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:29.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.92
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  8000011272

Normal statistic for number of bits   :   0.089
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.06
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999909719

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   0.039
p-value of test                       :    0.48

Sample variance                       :    2.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   0.047
p-value of test                       :    0.48

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:30.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:11:24.92

 All tests were passed




Server wird beendet - Lösche Semaphor 169279513.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5406
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:45.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:37.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7490
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:36.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:54.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:55.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:02.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:03.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:55.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:00.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.85
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:49.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.19
p-value of test                       :    0.9923

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:13.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:43.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.64
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.33
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.01
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.83
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.32
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:44.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1455.26
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:59.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6798.68
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:43.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.50
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.70
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:01.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.42
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.67
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:34.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5027.66
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:16.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45715
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869715
  j =  1                              :        399908573
  j =  2                              :            45709
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45885
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869885
  j =  1                              :        399908231
  j =  2                              :            45883
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:32.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:19.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:45.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:00.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:54.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:32.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.73e-4
p-value of test                       :  3.9e-3

Kolmogorov-Smirnov- statistic = D-    : 2.60e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.37e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:22.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:34.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.17
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:47.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.49
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.28
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:47.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.10
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.21
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.27
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:44.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.91
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.50
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.80
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.15
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17435.66
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.21
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.80
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.66
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.59
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.37
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.94
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.04
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.92
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.37
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.21
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:39.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.86
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.64
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.78
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.18
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.06
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.33
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.80
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.95
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.20
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.85
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.06
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.45
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4856.83
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.65
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.79
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.28
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.36
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5101.29
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  439.33
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.02
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.59
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:23.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.50
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:21.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.80e-3
p-value of test                       :    0.9905

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :  -0.011
p-value of test                       :    0.50

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.36e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 9.97e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.55e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.60
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:29.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.57
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.04
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:06.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.34
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:10.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10158.91
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9830.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:57.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.80
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:50.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4936.62
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:50.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3972.56
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.05
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11835.86
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11957.02
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.04
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999972596

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.85
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999885947

Normal statistic for number of bits   :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.52
p-value of test                       :    0.94

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         : 8.04e-3
p-value of test                       :    0.50

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.38

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:41.64

 All tests were passed




Server wird beendet - Lösche Semaphor 170262553.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5371
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:45.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:37.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:34.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:53.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:02.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:02.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:56.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:58.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.44
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     331
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:12.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.46
p-value of test                       :  5.8e-3

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:40.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.14
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.44
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.17
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.96
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.54
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.31
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.38
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:05.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6954.65
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:49.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.92
p-value of test                       :  1.0e-2

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   34.95
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:03:10.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.24
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.91
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:36.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5120.91
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:13.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:03.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46017
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870017
  j =  1                              :        399907970
  j =  2                              :            46009
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45871
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869871
  j =  1                              :        399908266
  j =  2                              :            45855
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:34.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:22.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:51.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:06.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9975

-----------------------------------------------
CPU time used                    :  00:01:55.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:36.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.55e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.77e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 7.13e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:39.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:39.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.19
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.02
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.21
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.93
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.03
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.24
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:46.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.96
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.58
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.32
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.52
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:39.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17620.20
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.00
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.16
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.24
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.68
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.44
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.18
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.59
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.10
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.58
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.57
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.15
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.33
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.36
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.31
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.89
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.37
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.47
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.13
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.83
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  100.21
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.67
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.67
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5019.13
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.38
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.90
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.07
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.22
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4872.29
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  438.02
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  155.02
p-value of test                       :    0.9920


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.74
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:27.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.09
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:26.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.63e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 6.42e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.90e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 5.87e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.36
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.21
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:06.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 7.44e-3
p-value of test                       :    0.9920

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:08.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9989.04
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9901.97
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.02
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:04:26.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4821.30
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:54.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4975.21
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4230.81
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.47
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11672.79
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:32.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11767.47
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:31.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.39
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999976385

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.89
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999995810

Normal statistic for number of bits   :  -0.033
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.43

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:33.45

 All tests were passed




Server wird beendet - Lösche Semaphor 171245593.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9993    *****


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5504
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:47.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:37.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:36.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7148
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:05.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:06.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7457
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:00.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:05.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    2.95
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:14.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:41.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.45
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.99
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.90
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.63
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.04
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.42
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.50
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.36
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.56
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.18
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1574.79
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:02:06.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7021.58
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:55.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.44
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.58
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:16.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.32
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.89
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:39.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5173.63
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  9.4e-3


-----------------------------------------------
CPU time used                    :  00:03:03.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46149
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870149
  j =  1                              :        399907708
  j =  2                              :            46137
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45829
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869829
  j =  1                              :        399908344
  j =  2                              :            45825
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:33.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:22.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-3
p-value of test                       :    0.9985

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  5.0e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:52.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:07.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:56.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:38.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.58e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.81e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 8.83e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9978

-----------------------------------------------
CPU time used                    :  00:00:23.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:24.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:43.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.50
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.13
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.52
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   51.55
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:01:50.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.67
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.32e-3
p-value of test                       :    0.9966

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   62.47
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.27
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.82
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.66
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17369.31
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.56
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.76
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.15
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.78
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.88
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.03
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.40
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.87
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.22
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.63
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.02
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.72
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.21
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  102.31
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.18
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.29
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.44
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.43
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.81
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.81
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.34
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.23
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.18
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.10
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.16
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.74
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4960.51
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  434.67
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.06
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.46
p-value of test                       :    0.9913


-----------------------------------------------
Normal statistic for number of jumps  :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:25.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.01
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:27.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 8.44e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.55e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 8.36e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.31
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.82
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.13
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:08.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.26
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:09.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9991.34
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9856.70
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:10.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:04:34.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 2.73e-3
p-value of test                       :    0.9972

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4695.57
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:55.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4836.04
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:58.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4045.93
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4247.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11697.70
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:35.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11931.58
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:36.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.73
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999858857

Normal statistic for number of bits   :   -1.12
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.70
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000057532

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.20e-3
p-value of test                       :    0.9946

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.68
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.66
p-value of test                       :  3.9e-3

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:11:46.69
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  1  SerialOver, r = 0               0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 172359705.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5470
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:49.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:38.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:38.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:55.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:03.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:04.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:54.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:04:01.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.57
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     640
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:13.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:41.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.38
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.91
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.62
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.83
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.92
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.82
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.43
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.24
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:42.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.31
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:59.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7067.32
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:41.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.58
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.85
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.64
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:03.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.22
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.08
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:35.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4993.16
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:07.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45740
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869740
  j =  1                              :        399908523
  j =  2                              :            45734
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45685
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869685
  j =  1                              :        399908636
  j =  2                              :            45673
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.95e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  9.7e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 8.84e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:29.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:17.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:44.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:59.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:54.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:33.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.10e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 6.13e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:34.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:34.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:48.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.38
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.57
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.05
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.02
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.00
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:38.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.13
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.7e-3

Anderson-Darling statistic = A2       :    3.94
p-value of test                       :  9.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   62.61
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.29
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.78
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17583.12
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.95
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.67
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.09
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.30
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.83
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.75
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.91
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.86
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.37
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.00
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.54
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.00
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.23
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.23
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.74
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.56
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.59
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.81
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.44
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.95
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.65
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.70
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4940.33
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.35
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.37
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.70
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.19
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5116.41
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  438.55
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.31
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:36.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.86
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:27.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.48
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:27.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.49
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.73
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.53
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:08.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:08.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.37
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.36
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9674.79
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:53.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4948.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.91
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4228.62
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3979.14
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11888.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11771.01
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.56
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999924122

Normal statistic for number of bits   :   -0.60
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.79
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000096787

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.77
p-value of test                       :    0.04

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   0.063
p-value of test                       :    0.47

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:11.75

 All tests were passed




Server wird beendet - Lösche Semaphor 173768729.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:40.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:51.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:38.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:56.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:04.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7122
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:04.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:55.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7457
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:00.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:49.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.53
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.88
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:15.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    2.55
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    2.19
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:45.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.33
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.09
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.11
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.64
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.17
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.04
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.99
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.73
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.63
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:42.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1500.46
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:57.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6738.74
p-value of test                       :    0.9956

-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.20
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:12.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.63
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:01.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.68
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.51
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:34.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5194.33
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:01.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45807
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869807
  j =  1                              :        399908387
  j =  2                              :            45805
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46050
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870050
  j =  1                              :        399907902
  j =  2                              :            46046
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 6.99e-3
p-value of test                       :    0.9908

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:29.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  7.5e-3

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:18.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:44.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:58.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:55.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:32.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 4.39e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:39.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:42.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.00
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.49
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.00
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.65
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.69
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.86
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.21
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.89
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.81
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.38
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17339.84
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.91
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.64
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.88
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.20
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.11
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.14
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.75
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.71
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.89
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.15
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.23
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.94
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.49
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.24
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.57
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.25
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.25
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.82
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.68
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.29
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.64
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.80
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4987.00
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.80
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.05
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.79
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.41
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4930.36
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.41
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.80
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.24
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -2.25
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:02:24.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.08
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:26.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.38e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:46.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.72e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 7.76e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.87
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.65
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:09.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.65
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:07.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.93
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9988.37
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:49.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:50.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.07
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:50.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4239.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11848.47
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:29.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11986.91
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:30.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.54
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000013207

Normal statistic for number of bits   :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.36
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999994340

Normal statistic for number of bits   :  -0.045
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:53.63

 All tests were passed




Server wird beendet - Lösche Semaphor 174686233.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:50.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1237
p-value of test                       :    0.9998    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334357
  j =  1                              :        599997526
  j =  2                              :             1237
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5520
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:53.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:41.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:58.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:00.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:11.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:10.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:04:08.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7453
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:13.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:50.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    2.93
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     552
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:15.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    2.62
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:42.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.09
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.11
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.55
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.16
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.00
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.36
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.63
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.40
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:50.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1394.28
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:02.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7081.17
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:54.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.86
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.81
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:09.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.50
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.24
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:40.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5118.44
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:31.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:05.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46196
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870196
  j =  1                              :        399907615
  j =  2                              :            46182
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45750
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869750
  j =  1                              :        399908504
  j =  2                              :            45742
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-3
p-value of test                       :    0.9984

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:30.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:24.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:53.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:09.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:39.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.74e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.55e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.72e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.66
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.035
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:51.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.027
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:50.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.87
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.58
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.14
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.50
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.48
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.73
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.40
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:54.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.87
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.14
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:29.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.74
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17093.64
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.14
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.04
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.63
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.96
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.28
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.45
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.91
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.58
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.86
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.77
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.30
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.23
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.92
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.97
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.00
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.99
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.28
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.25
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.03
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.87
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.29
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5135.39
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.79
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.56
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.90
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.79
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4954.21
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.31
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.52
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.58
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:25.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.18
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :   -1.15
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:26.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.39e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.72e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.69
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.77
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:41.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.60
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:27.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.52
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.19
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:26.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.7e-3

Anderson-Darling statistic = A2       :    5.08
p-value of test                       :  2.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10423.97
p-value of test                       :  1.5e-3

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9853.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:04:38.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5030.66
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:52.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4745.62
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:58.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4172.75
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4224.63
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12000.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:32.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11884.80
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:34.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.68
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000069034

Normal statistic for number of bits   :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.08
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999862664

Normal statistic for number of bits   :   -1.09
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -2.04
p-value of test                       :    0.98

Sample variance                       :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:12:27.80
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  4  CollisionOver, t = 2            0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 175669273.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:51.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:54.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:39.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:39.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:57.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:05.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:06.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:56.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7192
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:04:01.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.74
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.13
p-value of test                       :    0.9995    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:17.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:45.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.49
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.25
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.47
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.69
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.89
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.82
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.62
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:43.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1453.70
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:59.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7233.13
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:44.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.11
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:03.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.18
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.54
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:34.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5079.66
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:57.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46295
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870295
  j =  1                              :        399907413
  j =  2                              :            46289
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45699
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869699
  j =  1                              :        399908603
  j =  2                              :            45697
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:27.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:17.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:58.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:55.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:35.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.75e-6
p-value of test                       :    0.9999    *****

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.63e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 2.49e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:35.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:37.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.22
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.93
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.35
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.04
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:50.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.64
p-value of test                       :    0.9914

-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.30
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:44.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.55
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.42
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.12
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:28.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.22
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.69
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17546.29
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.69
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.02
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.80
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.79
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.28
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.29
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.68
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.43
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.45
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.03
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.02
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.80
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.40
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.18
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.97
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.97
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.59
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  544.22
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.82
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.82
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.17
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.50
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5132.87
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.23
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.57
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.99
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.17
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4822.30
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.43
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  247.97
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.37
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :   -0.48
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:26.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.20
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :   -1.06
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:26.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.14e-4
p-value of test                       :    0.9926

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :  4.8e-3

Anderson-Darling statistic = A2       :    3.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 8.59e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.41
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.53
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.50
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:07.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:07.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10062.12
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10059.83
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:49.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.64
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:49.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4924.28
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:50.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4210.29
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4181.68
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12308.70
p-value of test                       :  9.4e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11958.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.39
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999942074

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   86.54
p-value of test                       :  3.3e-3


-----------------------------------------------
Total number of bits:  7999988598

Normal statistic for number of bits   :  -0.090
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.95
p-value of test                       :    0.97

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.19
p-value of test                       :    0.12

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:52.97
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs mNP1, t = 5          0.9995 
 99  HammingIndep, L=1200, r=0       9.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 177176601.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5375
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:53.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:40.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:41.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:57.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:59.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:08.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:09.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:04:00.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:04:09.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.72
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:49.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    2.42
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.10
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:15.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:45.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.03
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.20
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.32
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.25
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.36
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.43
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.81
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.83
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.71
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.63
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:53.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1397.93
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:00.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7008.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:49.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.86
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.96
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:08.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.60
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.28
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:37.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5066.51
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:59.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46112
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870112
  j =  1                              :        399907778
  j =  2                              :            46108
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46071
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870071
  j =  1                              :        399907865
  j =  2                              :            46057
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:29.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:17.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  6.3e-3

Anderson-Darling statistic = A2       :    3.36
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:47.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:03.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.20
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:35.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.84e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 9.50e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.49e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 7.06e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.95
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:42.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.65
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.96
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.26
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.66
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:49.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.69
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.68
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.93
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:46.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.62
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.08
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.64
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:29.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.86
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:30.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.01
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17454.32
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:55.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.18
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.83
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.53
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.05
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.82
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.30
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.58
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.54
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.83
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.13
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.62
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.89
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.94
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.94
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.13
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.13
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  105.97
p-value of test                       :    0.9948


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.76
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.80
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.39
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.13
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.70
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.65
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.42
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.18
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.59
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.01
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5117.79
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.00
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.66
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.35
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:26.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.11
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    0.11
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:27.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.65
p-value of test                       :    0.95

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.48e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 7.15e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.01
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.13
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.40
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:07.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.81
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:07.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9812.49
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10243.36
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:04:20.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5051.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:54.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5095.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:54.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.16
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4253.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11949.03
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:29.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11897.20
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.73
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000004207

Normal statistic for number of bits   :   0.033
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.75
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000011089

Normal statistic for number of bits   :   0.088
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:00.78

 All tests were passed




Server wird beendet - Lösche Semaphor 178192409.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:41.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5523
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:53.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:40.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:41.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:58.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7560
p-value of test                       :  2.5e-3


-----------------------------------------------
CPU time used                    :  00:03:06.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:07.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:58.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7525
p-value of test                       :  8.2e-3


-----------------------------------------------
CPU time used                    :  00:04:02.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    2.51
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     650
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.84
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:16.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:39.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.49
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.54
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.35
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.19
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   83.01
p-value of test                       :  6.8e-3

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  317.70
p-value of test                       :  1.6e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  488.28
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:44.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1483.79
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:57.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7031.63
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.30
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:02.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.26
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  145.80
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:33.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4931.78
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:59.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45813
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869813
  j =  1                              :        399908379
  j =  2                              :            45803
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45754
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869754
  j =  1                              :        399908496
  j =  2                              :            45746
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:27.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:18.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:44.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:59.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:15.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:34.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.88e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 7.00e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:21.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:35.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:36.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.00
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.49
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.43
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.99
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.17
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.88
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:43.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.27
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.38
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.67
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:29.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.00
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17715.62
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.64
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.71
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.13
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.96
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   33.81
p-value of test                       :  8.9e-3


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.58
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.36
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.29
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.70
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.78
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.65
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  103.59
p-value of test                       :    0.9969


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.90
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.53
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.99
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.81
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :   99.65
p-value of test                       :    0.9988


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  442.12
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.06
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.79
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.40
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.87
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5116.42
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.80
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.38
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.90
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.22
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5050.17
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.58
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.48
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   28.74
p-value of test                       :  4.3e-3


-----------------------------------------------
Normal statistic for number of jumps  :    1.68
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:24.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.39
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:24.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 5.18e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:46.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 2.68e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.18
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.15
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.50
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:07.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:07.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9929.06
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10053.67
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.052
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:49.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.41
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:48.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4966.29
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:49.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4148.77
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.01
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11747.32
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11925.09
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.33
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999922625

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.08
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999839132

Normal statistic for number of bits   :   -1.27
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:01.60
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 34  Gap, r = 0                      1.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 179306521.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5435
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:52.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:39.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4187
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:57.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:06.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7089
p-value of test                       :    0.9964


-----------------------------------------------
CPU time used                    :  00:03:05.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:56.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:04:01.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.61
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    2.26
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:46.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.74
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:15.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:43.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.58
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.95
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.61
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.82
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.82
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.36
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:44.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.13
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:00.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7042.33
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:43.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.81
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.32
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:02.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.12
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.39
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:33.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5213.14
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:01.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45830
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869830
  j =  1                              :        399908342
  j =  2                              :            45826
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45860
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869860
  j =  1                              :        399908280
  j =  2                              :            45860
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:27.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:18.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:58.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:34.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 5.36e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:22.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:34.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -8.08e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:36.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.72
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.80
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.87
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.20
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.94
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.78
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.14
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:29.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.33
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17396.94
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.92
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.25
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.29
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.28
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.07
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.39
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.34
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.31
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.45
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.38
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.24
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.77
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.07
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.85
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.73
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.83
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.51
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.75
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.11
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.68
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.13
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.63
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5050.30
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.57
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.86
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:36.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.66
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.45
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4925.82
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.42
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.20
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   27.26
p-value of test                       :  7.1e-3


-----------------------------------------------
Normal statistic for number of jumps  :   -3.18
p-value of test                       :    0.9993    *****



-----------------------------------------------
CPU time used                    :  00:02:24.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.92
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :   -1.72
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:25.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.90
p-value of test                       :    0.97

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.28e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 4.70e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.54
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.89
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.81
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:06.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.83
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:07.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10167.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9990.04
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:48.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4795.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5056.19
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:50.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3975.78
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4013.42
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11532.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11649.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.54
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000060151

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.21
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999874154

Normal statistic for number of bits   :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.34
p-value of test                       :  9.6e-3

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:42.46
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0               0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 180355097.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:51.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5363
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:52.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:40.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:55.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:57.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7485
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:05.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:05.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:56.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:00.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:46.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:13.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.84
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:40.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.16
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.09
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.89
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.41
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.88
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:32.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.48
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:32.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.49
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:32.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.60
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.04
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:44.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1392.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:00.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7236.10
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 3.47e-3
p-value of test                       :    0.9965

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.76
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.81
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:03.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.47
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.30
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:34.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4908.72
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:57.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45836
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869836
  j =  1                              :        399908329
  j =  2                              :            45834
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45939
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869939
  j =  1                              :        399908126
  j =  2                              :            45931
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:27.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:17.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:44.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:00.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:34.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 7.94e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:24.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:22.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:36.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:38.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.22
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.16
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.57
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.42
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.33
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.67
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.85
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:44.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.50
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.53
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   12.53
p-value of test                       :  5.8e-3

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.62
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17440.89
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.68
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.40
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.70
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.73
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.95
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.08
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.71
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.43
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.20
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.48
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.67
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.99
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.48
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.26
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.08
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.01
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.37
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.12
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.06
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.35
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.73
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.56
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.84
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.86
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.78
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.39
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4839.21
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.54
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.98
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:36.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.54
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:24.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.14
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:25.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.31
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    1.98
p-value of test                       :    0.02

Sample variance                       :    1.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 7.20e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.41e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 8.95e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.22
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.25
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:24.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.32
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:24.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9842.78
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9870.84
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.078
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.35
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:54.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.88
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:49.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.87
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:49.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4205.87
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4031.29
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11647.02
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11726.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.52
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999981476

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.50
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999989198

Normal statistic for number of bits   :  -0.085
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:25.89

 All tests were passed




Server wird beendet - Lösche Semaphor 181403673.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1234
p-value of test                       :    0.9998    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334354
  j =  1                              :        599997532
  j =  2                              :             1234
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5439
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:53.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7111
p-value of test                       :    0.9924


-----------------------------------------------
CPU time used                    :  00:02:42.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:58.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:59.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:11.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7444
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:11.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:09.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:11.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.40
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    2.34
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.15
p-value of test                       :    0.9987

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:13.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    4.00
p-value of test                       :  8.7e-3

Stat. AD after spacings (mNP2-S)      :    3.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:44.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.76
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.64
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.47
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:11.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.75
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.70
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.00
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.35
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.26
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:53.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.38
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7112.93
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:54.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.29
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.94
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:15.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.28
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.16
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:38.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4962.25
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:57.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46134
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870134
  j =  1                              :        399907734
  j =  2                              :            46130
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45999
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869999
  j =  1                              :        399908005
  j =  2                              :            45993
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:31.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:20.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:50.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:05.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.52e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:43.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:46.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.07
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.48
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.10
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.97
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.45
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.94
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.72
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:49.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.21
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.25
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.19
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:28.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.41
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17237.33
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:54.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.86
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.06
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.39
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.01
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.20
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.16
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.27
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.03
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.40
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.55
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.02
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.77
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.88
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.37
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.50
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.73
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.96
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  443.54
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.83
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.89
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.35
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.06
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4754.96
p-value of test                       :    0.9935


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.33
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.96
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.98
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.94
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5168.79
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.51
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.76
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.19
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :    1.22
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:24.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.38
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :    0.51
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:24.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 3.86e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.50e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 7.93e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.10
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.82
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:07.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.95
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:06.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9984.06
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10062.70
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:04:25.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.98
p-value of test                       :  9.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4631.24
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:01:55.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.72
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:57.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4013.58
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4179.41
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11896.75
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:31.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11799.37
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:33.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.40
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000003673

Normal statistic for number of bits   :   0.029
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.83
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999900059

Normal statistic for number of bits   :   -0.79
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.18
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.57

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:18.51
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14           0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 182386713.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5365
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:55.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:41.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7478
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:41.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:58.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:06.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:07.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:57.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:01.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    2.38
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     843
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:48.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.76
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:14.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     172
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:40.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.37
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.76
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.69
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.12
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.60
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.50
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.39
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:44.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1408.01
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:01.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6891.00
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:42.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.75
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.61e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.93
p-value of test                       :  9.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   92.76
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:03:03.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.38
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.98
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:33.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4994.03
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:01.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46089
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870089
  j =  1                              :        399907824
  j =  2                              :            46085
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46260
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870260
  j =  1                              :        399907483
  j =  2                              :            46254
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:27.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:18.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:45.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:59.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:56.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:34.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.42e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.88e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 1.48e-5
p-value of test                       :    0.9912

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:22.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.070
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:43.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.13
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.16
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.93
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.87
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.40
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.92
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.40
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:45.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.42
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:29.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.70
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9964

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.30
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17293.81
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.39
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.13
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.98
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.67
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.73
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.10
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.84
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.16
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.27
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.19
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.41
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.03
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.97
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.46
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.92
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.02
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.22
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.12
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.55
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.94
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.74
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.54
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4988.72
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.46
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.87
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.51
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.52
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.60
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.14
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.64
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.02
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:24.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.35
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:24.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.99e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 9.47e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.68
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.95
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.22
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:05.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.78
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:06.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9950.95
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9945.88
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:48.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.01
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4985.34
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:49.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4068.12
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4182.63
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11804.16
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11653.46
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:28.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.84
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999773189

Normal statistic for number of bits   :   -1.79
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.57
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000057640

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :  -0.091
p-value of test                       :    0.54

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:11.21

 All tests were passed




Server wird beendet - Lösche Semaphor 183435289.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:39.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5406
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:54.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:41.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:42.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:58.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:59.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:09.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:10.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:03.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:04:06.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.95
p-value of test                       :  9.4e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.96
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:49.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    4.12
p-value of test                       :  7.6e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     560
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:14.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    4.00
p-value of test                       :  8.7e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     184
p-value of test                       :  4.0e-3

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    2.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:38.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.26
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.18
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.27
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.72
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.62
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.69
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.14
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  275.64
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  466.42
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:51.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1379.66
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:02.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7072.68
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.21
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.23
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:09.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.98
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.19
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:36.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5020.80
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:13.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45976
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869976
  j =  1                              :        399908050
  j =  2                              :            45972
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46294
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870294
  j =  1                              :        399907413
  j =  2                              :            46292
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:30.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :  1.4e-3

Anderson-Darling statistic = A2       :    5.14
p-value of test                       :  2.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  3.1e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:19.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:07.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:36.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.19e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.55e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.51e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.92e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:24.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : -1.72e-4
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:43.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.80
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.42
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.51
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.64
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.59
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.05
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:46.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.08
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.84
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.03
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.18
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:40.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17371.43
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.73
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.91
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.53
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.88
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.07
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.77
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.75
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.08
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.80
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.39
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.08
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.53
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.67
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.58
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.20
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.76
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.12
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.60
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.75
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.32
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.77
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.98
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.63
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.18
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.66
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.38
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4930.65
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.59
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.96
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.94
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:24.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.03
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :   -2.16
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:24.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 8.35e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 6.52e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.37
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.34
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.24
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:06.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:08.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10118.09
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10140.24
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:04:12.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.97
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:52.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.10
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:53.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.59
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.78
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:30.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12240.98
p-value of test                       :  3.7e-3

-----------------------------------------------
CPU time used                    :  00:01:31.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.31
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  7999931745

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.30
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999968024

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :  -0.047
p-value of test                       :    0.52

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    1.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:44.77

 All tests were passed




Server wird beendet - Lösche Semaphor 184483865.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5560
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:56.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:42.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7143
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:05.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:05.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7099
p-value of test                       :    0.9949


-----------------------------------------------
CPU time used                    :  00:03:55.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:01.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.07
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    2.28
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:49.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:16.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:46.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.61
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.73
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.02
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.13
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.36
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.12
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.94
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:43.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1434.64
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:01.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6998.93
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.25
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.16
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:03.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.27
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.81
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:34.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5190.88
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:59.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45897
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869897
  j =  1                              :        399908208
  j =  2                              :            45893
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45424
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869424
  j =  1                              :        399909155
  j =  2                              :            45418
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:29.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:18.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:45.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:36.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.13e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.88
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.61
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.40
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.94
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.25
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.86
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:41.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.50
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.74
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.56
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.0e-3

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  165.08
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17298.43
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.06
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.54
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.54
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.09
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.76
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.29
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.60
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   55.89
p-value of test                       :  3.8e-4    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.17
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.44
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.14
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.12
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.69
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.81
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.40
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.64
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.16
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.81
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.73
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.86
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.32
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.89
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4892.97
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.74
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.85
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.45
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.05
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5228.32
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.02
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.26
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.76
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:23.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.87
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :   -1.18
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:25.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.28
p-value of test                       :    0.01

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 4.89e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.90e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.60
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.85
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.80
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:07.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.98
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:07.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10124.50
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9981.49
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.028
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:40.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4837.01
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4955.57
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:50.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4022.25
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:20.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4197.04
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11841.43
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11793.97
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.11
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999993800

Normal statistic for number of bits   :  -0.049
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.58
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999949265

Normal statistic for number of bits   :   -0.40
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9938

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:30.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 75  RandomWalk1 J (L=50, r=25)      3.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 185466905.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5435
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:55.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:42.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4182
p-value of test                       :    0.9907


-----------------------------------------------
CPU time used                    :  00:01:58.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:58.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:05.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7167
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:05.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:56.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:01.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.99
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:48.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.56
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.66
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:14.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    2.35
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:43.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.39
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.05
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.09
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.73
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.13
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.04
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.48
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.40
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:43.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.08
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:00.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7290.39
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:42.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.46
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.07
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:03.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.83
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.13
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:35.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5158.27
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:59.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45801
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869801
  j =  1                              :        399908399
  j =  2                              :            45799
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45544
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869544
  j =  1                              :        399908915
  j =  2                              :            45538
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:29.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 3.59e-3
p-value of test                       :    0.9960

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:18.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:46.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:00.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:56.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 8.41e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.46e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 3.88e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:34.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.25
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:49.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.42
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.53
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.74
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.02
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.50
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.21
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:39.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.60
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.99
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.50
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.84
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17581.91
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.52
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.43
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.69
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.00
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.17
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.37
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.58
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.16
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.03
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.28
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.78
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.71
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.27
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.99
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.48
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.44
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.94
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.79
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.47
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.70
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.61
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4858.78
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.44
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.59
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.22
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.28
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4905.62
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.97
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.45
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.58
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:24.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.68
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :   -1.39
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:26.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 5.82e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.31
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.31
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.95
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:06.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.62
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:04.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10136.09
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9883.38
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.55
p-value of test                       :  5.3e-3

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:43.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.37
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:48.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4786.71
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:50.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.38
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4030.07
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12065.98
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11613.03
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:28.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.47
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000023398

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.78
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000096352

Normal statistic for number of bits   :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.83
p-value of test                       :    0.03

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:19.26

 All tests were passed




Server wird beendet - Lösche Semaphor 186515481.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5364
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:57.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:42.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:57.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:59.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:05.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:05.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:56.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7199
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:01.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9930

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:14.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:47.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.58
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.58
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.97
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.48
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:11.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.56
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.61
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.49
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.10
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:18.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.32
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:43.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1400.79
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:00.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6960.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.18e-3
p-value of test                       :    0.9958

Kolmogorov-Smirnov- statistic = D-    :    0.61
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   51.84
p-value of test                       :  7.9e-3

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.58
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:04.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.45
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.63
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5115.55
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:59.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45755
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869755
  j =  1                              :        399908493
  j =  2                              :            45749
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46018
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870018
  j =  1                              :        399907966
  j =  2                              :            46014
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:29.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:18.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:00.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:35.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.80e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 7.51e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 9.66e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:22.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:34.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:35.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.84
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.46
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.90
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.97
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.98
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.56
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.03
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.13
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.60
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.57
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    4.79
p-value of test                       :  3.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16945.22
p-value of test                       :    0.9956



-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.68
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.41
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.06
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.91
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.10
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.74
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.04
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.01
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.21
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.01
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.12
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.51
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.87
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.72
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.72
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.12
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.89
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  546.44
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.18
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.38
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.20
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.96
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.21
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  427.20
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.51
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.40
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.87
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4986.91
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  476.45
p-value of test                       :  4.3e-4    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.58
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.75
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :   -1.27
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:24.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.75
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:25.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.96e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 5.05e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.07
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.51
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.41
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:05.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10125.74
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10039.88
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    3.66
p-value of test                       :  1.3e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:48.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9950

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:48.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4988.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.64
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.56
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11594.70
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11725.97
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.47
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000038290

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.08
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999985580

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.26e-4
p-value of test                       :    0.9996    *****

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.66
p-value of test                       :  3.9e-3

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.56
p-value of test                       :    0.06

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:35.22
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 R (L=10000, r=15)   4.3e-4
 93  HammingCorr, L = 300            1.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 187498521.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1471
p-value of test                       :  2.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334591
  j =  1                              :        599997058
  j =  2                              :             1471
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5409
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:58.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:42.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:56.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:05.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:04.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:55.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7496
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:04:00.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    5.70
p-value of test                       :  1.4e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.24
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.51
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    2.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:15.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:43.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.61
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.10
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.64
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.07
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:11.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.56
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.89
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.29
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  183.16
p-value of test                       :    0.9922

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  381.01
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:44.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1481.56
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:01.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7155.77
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:43.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.51
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.81
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:04.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.70
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.90
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:35.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4952.73
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:59.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45605
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869605
  j =  1                              :        399908795
  j =  2                              :            45595
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45492
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869492
  j =  1                              :        399909020
  j =  2                              :            45484
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:28.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:18.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:45.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:01.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:56.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:34.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 2.44e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.93e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 5.74e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:22.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.25
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:34.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:34.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  102.89
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.72
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.90
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.91
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.58
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17697.68
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.74
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.59
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.98
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.32
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.24
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.12
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.27
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.20
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.63
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.71
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.29
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.87
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.64
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.13
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   47.17
p-value of test                       :    0.9936


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.75
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.10
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.10
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.59
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.05
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.72
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.48
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5158.78
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.22
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.40
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.99
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.68
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5098.36
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.52
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.58
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.98
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:19.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.65
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:20.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 9.83e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.70
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.39
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.71
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10207.13
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9947.52
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.02
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:23.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.73
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.08
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:32.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4247.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4070.30
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11557.04
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11639.59
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.16
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999966251

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.22
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999917309

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   02:59:50.37

 All tests were passed




Server wird beendet - Lösche Semaphor 188514329.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5452
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:43.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:36.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:35.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:54.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:55.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7452
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:02.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:03.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:54.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:00.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     940
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    2.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:52.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.31
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:11.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.51
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:34.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.40
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.13
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.17
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.77
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.88
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.32
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.93
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.90
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  199.49
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.39
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:45.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.06
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:00.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6899.68
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:42.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.83
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:02.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.13
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.26
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:36.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5070.16
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:08.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45990
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869990
  j =  1                              :        399908024
  j =  2                              :            45982
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46167
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870167
  j =  1                              :        399907670
  j =  2                              :            46159
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:29.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:18.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:45.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:00.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:52.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.97e-3
p-value of test                       :    0.9921

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :  1.8e-3

Anderson-Darling statistic = A2       :    5.07
p-value of test                       :  2.7e-3

-----------------------------------------------
CPU time used                    :  00:01:15.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:33.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.47e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 3.77e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.57
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:00:22.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:35.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:37.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.48
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:47.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.16
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.20
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:48.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.52
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.05
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:40.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.49
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.43
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:33.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:32.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.45
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17530.49
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   59.04
p-value of test                       :  9.1e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.87
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.31
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.38
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.56
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.20
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.23
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.58
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.88
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.00
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.09
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.97
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.37
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.45
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.95
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:47.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.98
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  106.86
p-value of test                       :    0.9937


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  550.88
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.01
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.80
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:47.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.21
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.47
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4964.39
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.49
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.88
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.08
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.73
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4855.89
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.26
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.95
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.61
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :    0.24
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:26.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   35.70
p-value of test                       :  3.6e-4    *****


-----------------------------------------------
Normal statistic for number of jumps  :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:13.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.35
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.16
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.33
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:09.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:12.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10141.47
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9942.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.96
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:04:02.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.80
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:49.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.55
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:49.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4215.00
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4116.84
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12018.23
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11921.74
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:29.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.68
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000167446

Normal statistic for number of bits   :    1.32
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.03
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999866429

Normal statistic for number of bits   :   -1.06
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 2.17e-5
p-value of test                       : 1 -  2.2e-5    *****

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -2.25
p-value of test                       :    0.99

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:16:15.67
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 81  LinearComp, r = 0               3.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 168755226.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:50.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5511
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:44.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:37.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7173
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:36.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4432
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:54.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4438
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:04.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:04.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:58.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:02.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:47.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.93
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.96
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.86
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:12.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.43
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:42.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.71
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.04
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.94
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.96
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:11.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.34
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.44
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.13
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  278.86
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.01
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:52.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1551.75
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:06.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7226.58
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.51
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   14.72
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.59
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:16.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.97
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:47.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.89
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:40.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5129.51
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:21.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45905
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869905
  j =  1                              :        399908193
  j =  2                              :            45899
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46026
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870026
  j =  1                              :        399907950
  j =  2                              :            46022
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:31.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:18.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9975


-----------------------------------------------
CPU time used                    :  00:02:03.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:54.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 8.02e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.67e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:39.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:40.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.92
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.84
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.44
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:51.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.87
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.25
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   13.70
p-value of test                       :    0.9928

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.17
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.75
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.14
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:31.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.16
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.43
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17725.08
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.70
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.74
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.90
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.55
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.92
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.37
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.28
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.59
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.75
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.90
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.01
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.16
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.74
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.96
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.68
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.46
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.79
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.54
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.24
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.32
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.15
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.55
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4820.23
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.60
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.96
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:37.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.08
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  439.31
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5173.23
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.30
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.56
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:36.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.07
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:25.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.73
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:26.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.81e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 8.52e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:47.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.03e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 8.26e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:46.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.79
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.84
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.75
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:08.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.26
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:10.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9858.73
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10169.96
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:11.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.54
p-value of test                       :    0.9945

-----------------------------------------------
CPU time used                    :  00:04:28.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.61
p-value of test                       :  2.4e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    6.88
p-value of test                       :  4.1e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4567.75
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:01:54.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.78
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:58.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.15
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3975.13
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11782.91
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:34.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11693.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:36.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.93
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000076999

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.01
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000148846

Normal statistic for number of bits   :    1.18
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.90

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:14:26.19
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 95  HammingIndep, L=30, r=0         0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 169050138.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5352
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:49.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:39.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:38.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4473
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:55.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:03.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:04.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7147
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:53.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:00.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.25
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:17.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:48.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.44
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.27
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.99
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.05
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.88
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.74
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.44
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:42.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.29
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:56.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6945.81
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:42.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.52
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:10.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.32
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:02.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.34
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.92
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:37.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4962.81
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:08.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46014
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870014
  j =  1                              :        399907976
  j =  2                              :            46006
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45529
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869529
  j =  1                              :        399908944
  j =  2                              :            45525
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:28.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:17.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:44.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:55.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:32.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 3.42e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.82e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 6.12e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:35.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:36.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.83
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:47.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.96
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.03
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.27
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.42
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.24
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.19
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.39
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:01:29.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:10.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.79
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17566.92
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.78
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.67
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.60
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.55
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.51
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.33
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.72
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.25
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.65
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.90
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.89
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.47
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.79
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  179.37
p-value of test                       :  7.5e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.51
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.31
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.17
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.54
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.69
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.29
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.50
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.44
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.78
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.48
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.03
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.82
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.93
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.19
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  452.99
p-value of test                       :  4.8e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.88
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.58
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:27.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.20
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:27.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   0.082
p-value of test                       :    0.47

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.18
p-value of test                       :    0.01

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 2.71e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.47e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 9.21e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.76
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.06
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.58
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:09.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:09.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9825.43
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9936.08
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:47.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.13
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:48.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5044.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:50.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.19
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.97
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11633.56
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:28.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11877.56
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.60
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  7999987521

Normal statistic for number of bits   :  -0.099
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.13
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000168745

Normal statistic for number of bits   :    1.33
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.95
p-value of test                       :    0.97

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:51.93

 All tests were passed




Server wird beendet - Lösche Semaphor 170885146.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5407
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:49.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:38.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:37.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:55.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7488
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:03.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:03.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:54.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:01.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.09
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.39
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.96
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:16.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:47.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.61
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.03
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.06
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.81
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.40
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.10
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.23
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:46.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.07
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:00.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7196.31
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:41.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.33
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:03.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.98
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.02
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:35.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5035.01
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:58.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46071
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870071
  j =  1                              :        399907860
  j =  2                              :            46067
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45738
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869738
  j =  1                              :        399908525
  j =  2                              :            45736
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:29.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:18.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:45.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:00.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:54.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:32.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.05e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 4.19e-4
p-value of test                       :  8.9e-4    *****

Anderson-Darling statistic = A2       :    4.20
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 8.20e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:33.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:33.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.61
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:47.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.48
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.28
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.59
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.02
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.80
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:39.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.87
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.97
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.62
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17482.95
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.36
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.91
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.22
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.18
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.11
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.55
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.11
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.34
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.43
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.46
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.21
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.96
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.15
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.95
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.64
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.55
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.32
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.93
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  167.00
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   39.26
p-value of test                       :    0.9997    *****


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.13
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.27
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4864.23
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.20
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.82
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.73
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.87
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5156.36
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  437.41
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.51
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.64
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:26.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.51
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :   -2.80
p-value of test                       :    0.9974



-----------------------------------------------
CPU time used                    :  00:02:26.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.26e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 6.88e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.07
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.88
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.89
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:08.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.13
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:07.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10078.09
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10148.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:45.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4998.86
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:49.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4948.90
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:50.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.16
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4040.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11689.98
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11890.24
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:29.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.61
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000027802

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.99
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000003418

Normal statistic for number of bits   :   0.027
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9922

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.91
p-value of test                       :    0.03

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:09.07
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 77  RandomWalk1 C (L=1000, r=20)    0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 171638810.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5372
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:46.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4235
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:37.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:36.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:55.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7126
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:03.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:03.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:53.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:01.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.67
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:45.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.64
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.99
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:13.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.15
p-value of test                       :    0.9985

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:46.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.76
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.66
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.52
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.29
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.41
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.20
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.39
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  170.92
p-value of test                       :    0.9990    *****

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.02
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1503.92
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:02.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7148.61
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:45.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.19
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.84
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:02.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.56
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.43
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:34.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4977.38
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:00.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45539
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869539
  j =  1                              :        399908926
  j =  2                              :            45531
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45809
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869809
  j =  1                              :        399908388
  j =  2                              :            45797
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 4.70e-4
p-value of test                       :    0.9995    *****

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:30.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:18.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:44.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:58.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:33.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 3.15e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:35.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:35.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.48
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:47.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.09
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.69
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.63
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.02
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:39.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.00
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.38
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.56
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.44
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17478.57
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.67
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.51
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.40
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.07
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.82
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   15.70
p-value of test                       :    0.9987


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.98
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.77
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.95
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.36
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.32
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.27
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.90
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.55
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.80
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.46
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.69
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.40
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.37
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.71
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.55
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.70
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4886.74
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.74
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.17
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.75
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.64
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.18
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.41
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.65
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.35
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:23.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.85
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:26.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 8.74e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.50e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 8.38e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.88
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.19
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.99
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:07.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.97
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:07.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10078.06
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9895.41
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:59.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5078.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:48.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4843.99
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:51.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.95
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.33
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12031.81
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11819.60
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:30.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   84.88
p-value of test                       :  4.6e-3


-----------------------------------------------
Total number of bits:  7999948419

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.59
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000042496

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   0.036
p-value of test                       :    0.49

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :  -0.037
p-value of test                       :    0.51

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:51.15
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 34  Gap, r = 0                      0.9990 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 172425242.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:38.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:49.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5475
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:51.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:38.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:37.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4437
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:54.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:03.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:03.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:55.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:01.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.50
p-value of test                       :  5.1e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.17
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.71
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     566
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.98
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:15.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:44.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.94
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.33
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.06
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.81
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.17
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.70
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.64
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.46
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.28
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:49.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.49
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:03.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7196.00
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:49.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.91
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:09.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.84
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.94
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:36.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5111.41
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:14.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46134
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870134
  j =  1                              :        399907736
  j =  2                              :            46126
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45668
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869668
  j =  1                              :        399908666
  j =  2                              :            45664
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:30.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:20.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:05.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:35.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 3.93e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 4.75e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.11
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:41.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.63
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.83
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.38
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.26
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.26
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.99
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.96
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.26
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.51
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.53
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.20
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   20.32
p-value of test                       :  3.9e-5    *****

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.72
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:42.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17311.04
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:54.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.60
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.12
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.55
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.32
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.88
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.33
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.07
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.65
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.76
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.89
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.73
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.45
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.40
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.13
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.67
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.48
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.03
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.31
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.43
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.09
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:43.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.30
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.51
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.16
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.76
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  245.70
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.24
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  445.03
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.66
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.29
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.91
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.86
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:23.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.20
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  : -1.49e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:26.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.30e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 6.13e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.85
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.69
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.52
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:06.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.56
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:08.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10018.78
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10142.71
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:04:27.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4837.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5051.17
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4270.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4116.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11802.33
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:32.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11825.97
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:33.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.41
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999948998

Normal statistic for number of bits   :   -0.40
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.57
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999961604

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.5e-3

Anderson-Darling statistic = A2       :    3.81
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.64
p-value of test                       :  4.1e-3

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:13.13
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 70  MatrixRank, L=5000              3.9e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 173408282.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5561
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:52.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:39.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:38.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:55.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:03.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:04.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7485
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:54.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:59.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.02
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:14.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    3.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:43.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.13
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.80
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.47
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.03
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.20
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:10.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.37
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.29
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.00
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:42.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1469.31
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:54.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7013.95
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:44.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.42
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:00.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.31
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.57
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:34.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5156.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:13.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45803
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869803
  j =  1                              :        399908401
  j =  2                              :            45789
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45781
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869781
  j =  1                              :        399908444
  j =  2                              :            45769
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:28.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:17.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:44.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :  4.8e-4    *****

Anderson-Darling statistic = A2       :    5.13
p-value of test                       :  2.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  1.2e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:59.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:35.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.63e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:35.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.068
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:36.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  111.70
p-value of test                       :  5.0e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.65
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.93
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:48.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.96
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.86
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.47
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.77
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.32
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.32
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.39
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.82
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17433.13
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.22
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.16
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.47
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.81
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.01
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.32
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.40
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.79
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.54
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.77
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.48
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.90
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.36
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.22
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.02
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.21
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.43
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.76
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.58
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.70
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.47
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.93
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4919.60
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.78
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  155.95
p-value of test                       :    0.9907


-----------------------------------------------
CPU time used                    :  00:00:36.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.47
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.96
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.26
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.56
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.09
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.29
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :   -1.31
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:26.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.34
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :   -1.77
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:25.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 4.87e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 8.07e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.31
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.29
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.17
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:05.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 6.15e-3
p-value of test                       :    0.9935

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.84
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:08.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9881.94
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.32
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.41
p-value of test                       :    0.9920

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:49.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4823.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:50.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.09
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:52.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4234.00
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.05
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11831.03
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:29.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11801.93
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:30.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.26
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  7999902732

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.55
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000007570

Normal statistic for number of bits   :   0.060
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.87

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.12

Sample variance                       :    2.73
p-value of test                       :  3.5e-3

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:35.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 59  WeightDistrib, r = 0            5.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 174620698.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:39.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5360
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:51.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4241
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:38.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:38.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4235
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:03.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:03.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:54.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:00.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    2.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:12.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.16
p-value of test                       :    0.9977

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:42.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.23
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.73
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.71
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   84.37
p-value of test                       :  5.1e-3

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.12
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.37
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:43.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1360.39
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:00.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7046.48
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:41.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.52
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.90
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:03.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.39
p-value of test                       :    0.9957


-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.99
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:33.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5056.80
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45837
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869837
  j =  1                              :        399908328
  j =  2                              :            45833
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45557
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869557
  j =  1                              :        399908892
  j =  2                              :            45545
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9915


-----------------------------------------------
CPU time used                    :  00:02:28.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:17.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:43.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:58.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:56.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:34.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 7.93e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:34.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:33.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:48.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.64
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.87
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.36
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:48.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.57
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:37.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.43
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.29
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.76
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.33
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17816.19
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.04
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.50
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.83
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.10
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.86
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.25
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.51
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.70
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.16
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.13
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.11
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.69
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.17
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.64
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.33
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.78
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.11
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.73
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.95
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.85
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.98
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5089.66
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.58
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.83
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.79
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.54
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.61
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.67
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.87
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.72
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :   0.016
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:24.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.87
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :    1.07
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:23.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 4.81e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.89e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 8.96e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.50
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.05
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.70
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:07.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.84
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:07.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9957

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9991.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10178.06
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:44.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4823.83
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:49.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4945.05
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:52.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.70
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.76
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11786.71
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11990.60
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:30.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.65
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999804416

Normal statistic for number of bits   :   -1.55
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.92
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999901973

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:33.55

 All tests were passed




Server wird beendet - Lösche Semaphor 175636506.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1480
p-value of test                       :  1.0e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334600
  j =  1                              :        599997040
  j =  2                              :             1480
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5290
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:52.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:39.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:39.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4450
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:55.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7160
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:03.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:03.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:54.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:00.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:46.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    3.85
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.51
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    2.13
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    6.53
p-value of test                       :  5.7e-4    *****

-----------------------------------------------
CPU time used                    :  00:02:13.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:44.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.74
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.59
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.96
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.06
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   27.63
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.41
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.25
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.32
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:43.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1456.67
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:00.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7189.34
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:41.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.77
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:16.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.66
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:02.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.64
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.98
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:34.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5240.33
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:55.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45971
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869971
  j =  1                              :        399908059
  j =  2                              :            45969
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45867
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869867
  j =  1                              :        399908270
  j =  2                              :            45859
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:28.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:17.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:44.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:58.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:56.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.037
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.078
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:34.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.85
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:48.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.28
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.07
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.51
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.33
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.34
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:39.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.65
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.51
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.23
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.01
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.12
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.83e-3
p-value of test                       :    0.9927

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  172.48
p-value of test                       :  7.5e-3

-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17716.44
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.60
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.14
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.65
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.41
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.90
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.30
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.84
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.69
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.67
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.52
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.58
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.75
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  435.95
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.53
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.73
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.87
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.01
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.11
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.08
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.97
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.08
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.91
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4799.31
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.38
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.36
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.31
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.99
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4876.61
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.42
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.63
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.60
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :    1.14
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:24.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.98
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :    1.14
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:24.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.74
p-value of test                       :    0.04

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 7.40e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 8.75e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.75
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.52
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.87
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:07.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.85
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:07.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10016.97
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10065.85
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:45.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.95
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:49.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.70
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:51.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4311.33
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.14
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11541.70
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:28.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12052.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:29.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.06
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000059917

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.37
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999905591

Normal statistic for number of bits   :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:26.43
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP2S, t = 9         5.7e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 176521242.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1472
p-value of test                       :  2.0e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334592
  j =  1                              :        599997056
  j =  2                              :             1472
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5459
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:55.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:40.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4244
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:57.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:06.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:05.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:55.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:59.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     867
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    2.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.87
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:15.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:47.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.14
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.90
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.48
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.24
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.23
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.99
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  475.98
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:49.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1363.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:02.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6883.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:49.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.31
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:08.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.41
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.64
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:36.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5250.84
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:14.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46068
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870068
  j =  1                              :        399907869
  j =  2                              :            46058
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45621
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869621
  j =  1                              :        399908763
  j =  2                              :            45611
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:32.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:20.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:07.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  2.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.35
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:57.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.18e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.37e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.36
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:24.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:22.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.61
p-value of test                       :  4.5e-3

-----------------------------------------------
CPU time used                    :  00:01:44.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.41
p-value of test                       :    0.9918

-----------------------------------------------
CPU time used                    :  00:00:49.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.75
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.96
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.83
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.74
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:55.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.51
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:45.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.01
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.29
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.09
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.71
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  163.43
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:39.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17704.53
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.72
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.19
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.32
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.30
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.95
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.88
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.36
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.01
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.85
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.14
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.19
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.00
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.44
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.38
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.30
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.30
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.79
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  578.26
p-value of test                       :  8.7e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.63
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.99
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.13
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  455.44
p-value of test                       :  7.0e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.12
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.99
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.91
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.61
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.62
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.64
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.67
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.91
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:25.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.85
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :   -0.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:24.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.57e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 8.78e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 8.95e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.63
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.68
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.10
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:06.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.12
p-value of test                       :    0.9999    *****

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.99
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:10.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9866.17
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.68
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10350.17
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:01:01.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:04:23.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4821.92
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4955.11
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4207.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.04
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11905.58
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:31.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11833.68
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:31.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.72
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000022609

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.72
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999900512

Normal statistic for number of bits   :   -0.79
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :  -0.068
p-value of test                       :    0.53

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.55
p-value of test                       :    0.94

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:45.10

 All tests were passed




Server wird beendet - Lösche Semaphor 177569818.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:51.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5329
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:52.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4452
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:40.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:40.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:02.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:03.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:54.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:00.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    2.46
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:13.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     129
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    2.05
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:44.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.65
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.28
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.72
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.53
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.53
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.99
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.75
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.60
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.47
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.26
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:43.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1367.18
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:57.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6895.94
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.31
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.02
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:01.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.37
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.89
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:33.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5049.88
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:16.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45737
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869737
  j =  1                              :        399908531
  j =  2                              :            45727
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45903
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869903
  j =  1                              :        399908198
  j =  2                              :            45895
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:29.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:17.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:44.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    5.14
p-value of test                       :  2.5e-3


-----------------------------------------------
CPU time used                    :  00:01:58.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:34.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 9.65e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.51e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.031
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:21.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:33.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:33.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.62
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.13
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.25
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.73
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.95
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.12
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:38.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.33
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.72
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.12
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.15
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17451.14
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.43
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.80
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.57
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.11
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.15
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.33
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.27
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.08
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.54
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.04
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.22
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.93
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.31
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.02
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.19
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.37
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.80
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.03
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.68
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.60
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.19
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.16
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5064.34
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.83
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.36
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.57
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.53
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.93
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.57
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.82
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.24
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  :    1.56
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:22.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.50
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :   -1.08
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:24.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.25e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 5.05e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   20.59
p-value of test                       :  8.3e-3

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.39
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.13
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:08.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.69
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:07.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9894.50
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9779.93
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:49.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4780.85
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:50.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4762.93
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:50.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4352.10
p-value of test                       :  5.4e-3

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3972.85
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11931.57
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11810.30
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:30.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.11
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999980459

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.06
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999832403

Normal statistic for number of bits   :   -1.32
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9934

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    2.88
p-value of test                       :  2.1e-3

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:33.79

 All tests were passed




Server wird beendet - Lösche Semaphor 178585626.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1500
p-value of test                       :  1.5e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334620
  j =  1                              :        599997000
  j =  2                              :             1500
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5273
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:53.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4245
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:39.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4467
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:56.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:02.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:03.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:53.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7125
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:59.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.64
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    2.02
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:12.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:40.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.34
p-value of test                       :    0.9998    *****

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.14
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.01
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.50
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.17
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.35
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.80
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.71
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.29
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:43.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.34
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:00.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7141.78
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:40.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.44
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.30
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:02.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.37
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.28
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:33.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4885.91
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:08.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45957
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869957
  j =  1                              :        399908087
  j =  2                              :            45955
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45641
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869641
  j =  1                              :        399908721
  j =  2                              :            45635
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:28.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:17.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:44.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:58.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:35.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.73e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.67e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:34.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:35.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.16
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.76
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.13
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.67
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:48.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.40
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.79
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:37.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.29
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.48
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.96
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.28
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17357.60
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.38
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.63
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.09
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.80
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.64
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.59
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.12
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.48
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.23
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.21
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.94
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.01
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.54
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.45
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.03
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.64
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.53
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.16
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.95
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.87
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.31
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.69
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5075.28
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.20
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.09
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.26
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.25
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4878.28
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.96
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.12
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:36.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.25
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:24.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.03
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :  -0.015
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:25.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.99e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:46.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.65e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 7.45e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   27.26
p-value of test                       :  6.4e-4    *****

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.58
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.86
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:05.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.15
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:06.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9798.75
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9973.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.19
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:03:48.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4796.00
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:49.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4791.69
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:51.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4024.14
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4161.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12046.58
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11671.61
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.20
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000082255

Normal statistic for number of bits   :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.03
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999990377

Normal statistic for number of bits   :  -0.076
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :  -0.076
p-value of test                       :    0.53

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    2.52
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:45.81
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  4  CollisionOver, t = 2            1.5e-4
 26  SimpPoker, r = 0                0.9998 
 86  LongestHeadRun, r = 0           6.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 179666970.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:50.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1475
p-value of test                       :  1.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334595
  j =  1                              :        599997050
  j =  2                              :             1475
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5488
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:55.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4447
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:40.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4434
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:57.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:03.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:04.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:55.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:59.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     640
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:13.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.09
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.82
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.91
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:36.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.22
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.39
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.92
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.88
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.72
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.73
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.49
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.22
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  453.44
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1581.94
p-value of test                       :  4.3e-3

-----------------------------------------------
CPU time used                    :  00:02:00.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6847.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:41.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.14
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.23
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:03.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.12
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:46.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.82
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:33.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5101.80
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:07.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46133
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870133
  j =  1                              :        399907738
  j =  2                              :            46125
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46360
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870360
  j =  1                              :        399907283
  j =  2                              :            46354
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:28.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:17.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:44.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:58.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:34.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.43e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 4.83e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:36.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:36.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.47
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.75
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.32
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.65
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.08
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.88
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:38.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.79
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.49
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:39.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17333.14
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.87
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.15
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.75
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.10
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.12
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.39
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.48
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.43
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.48
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.80
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.62
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.31
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.98
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.69
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.34
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.07
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.63
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.18
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.13
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.81
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.64
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.63
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5102.05
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.25
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.49
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.25
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  304.25
p-value of test                       :    0.9990


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4987.18
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.99
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.14
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.19
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:24.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.29
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:24.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.83
p-value of test                       :    0.03

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.80e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 5.58e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.42
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.10
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.44
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:06.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.51
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:07.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9890.92
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9701.38
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.068
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:44.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4907.72
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:51.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4314.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4003.50
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12065.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12011.15
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:29.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.05
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000111100

Normal statistic for number of bits   :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.59
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000007630

Normal statistic for number of bits   :   0.060
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:49.47

 All tests were passed




Server wird beendet - Lösche Semaphor 180650010.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:50.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5338
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:56.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7140
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:41.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7459
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:04.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:04.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:54.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:59.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.75
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:47.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    2.02
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    2.12
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.48
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:13.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:41.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.64
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.80
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.85
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.86
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.74
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.88
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.93
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.78
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.20
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.42
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:43.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1390.28
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:01.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7094.45
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:42.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.32
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.70
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:04.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.45
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.38
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:33.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4892.24
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:08.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45459
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869459
  j =  1                              :        399909083
  j =  2                              :            45457
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45891
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869891
  j =  1                              :        399908220
  j =  2                              :            45887
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:29.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:18.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:44.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:59.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:56.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 8.27e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:38.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:37.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.50
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:48.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.78
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.87
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:47.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.03
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.04
p-value of test                       :    0.9936

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.10
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:40.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.68
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.42
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.90
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:39.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17582.54
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.62
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.58
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.04
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.56
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.82
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.94
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.74
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.01
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.46
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.71
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.60
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.26
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.93
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.42
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.18
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.87
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.55
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  559.85
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.40
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   49.11
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.59
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.21
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4933.25
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  327.75
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.50
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.98
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.46
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.64
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.65
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.75
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.92
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :   -1.15
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:22.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.22
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :  -0.100
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:22.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 2.83e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.51e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 8.24e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.50
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.48
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.84
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:07.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.54
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:09.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10140.10
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10034.36
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    3.20
p-value of test                       :  6.8e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.09
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:48.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.30
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:48.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4802.62
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:51.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.19
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11515.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12062.51
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:30.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   81.01
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000029320

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.10
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000116482

Normal statistic for number of bits   :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.60
p-value of test                       :    0.06

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.28

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.84
p-value of test                       :    0.03

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.48
p-value of test                       :    0.07

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:52.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 93  HammingCorr, L = 300            6.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 181698586.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5462
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:59.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:43.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:45.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:00.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4151
p-value of test                       :    0.9977


-----------------------------------------------
CPU time used                    :  00:02:00.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:12.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:09.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:13.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:46.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:13.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.44
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.77
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.55
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.76
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.17
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   84.97
p-value of test                       :  4.5e-3

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.35
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.91
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.43
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:57.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1395.25
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:06.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7060.28
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:58.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.18
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:14.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.70
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:46.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   91.08
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5070.36
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:28.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:02.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46224
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870224
  j =  1                              :        399907555
  j =  2                              :            46218
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45794
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869794
  j =  1                              :        399908416
  j =  2                              :            45786
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:30.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:24.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:52.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:08.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9908

-----------------------------------------------
CPU time used                    :  00:01:38.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.70e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:24.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:24.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:52.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:54.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.93
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.07
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.35
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.34
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.62
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.06
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.36
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:51.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.65
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.47
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.026
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.58
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17484.76
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.49
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.79
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.46
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.44
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.11
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.23
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.22
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.75
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.92
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.19
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.23
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.71
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  440.35
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.23
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.82
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.36
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.52
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.98
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.13
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.22
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.65
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.42
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5202.97
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.23
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.73
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.55
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.89
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5120.87
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.42
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.67
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.28
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :   -2.50
p-value of test                       :    0.9937



-----------------------------------------------
CPU time used                    :  00:02:25.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.46
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:25.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.51
p-value of test                       :    0.07

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.21e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.00e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 9.16e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.44
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.08
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.42
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:08.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.32
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:23.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9987.58
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9843.94
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:10.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:04:36.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.26
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:51.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.52
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:54.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4264.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3928.90
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11833.89
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:32.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11787.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:35.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.86
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000086428

Normal statistic for number of bits   :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.30
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000090520

Normal statistic for number of bits   :    0.72
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:11:21.27

 All tests were passed




Server wird beendet - Lösche Semaphor 182747162.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1248
p-value of test                       :    0.9993    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334368
  j =  1                              :        599997504
  j =  2                              :             1248
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5410
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:51.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:40.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:58.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:05.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:06.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:55.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:01.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.15
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    6.62
p-value of test                       :  5.3e-4    *****


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:14.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:38.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.71
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.45
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.68
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.75
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.84
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.67
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.67
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.90
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:44.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1422.83
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:01.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7199.35
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.08
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:02.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.78
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   92.55
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:33.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5015.25
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:00.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46277
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870277
  j =  1                              :        399907448
  j =  2                              :            46273
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45863
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869863
  j =  1                              :        399908281
  j =  2                              :            45849
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:28.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:18.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:45.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:59.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:55.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:35.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:22.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:35.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:35.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.68
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.38
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.08
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.41
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.53
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.60
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:38.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.44
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.81
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.82
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:28.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.51
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.47
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   92.87
p-value of test                       :    0.9942

-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17385.80
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.99
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.77
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.47
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.51
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.58
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.00
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.59
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.03
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.51
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.49
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.54
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.72
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.79
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.35
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.90
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.48
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.47
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.30
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.35
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.76
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.17
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.77
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4938.01
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.70
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.81
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.61
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.43
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5026.37
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.46
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.39
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.92
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :    1.47
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:24.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.46
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :   -1.21
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:22.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 1.95e-3
p-value of test                       :    0.9980

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.27
p-value of test                       :    0.99

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 7.12e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 6.33e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.03
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.72
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.31
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:06.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.45
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:07.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10161.36
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9943.41
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:48.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4977.91
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:48.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.44
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:50.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4147.63
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.60
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11818.01
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12036.25
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:30.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.97
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000084802

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.51
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999989093

Normal statistic for number of bits   :  -0.086
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:53.28
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  7  CollisionOver, t = 7            0.9993 
 23  ClosePairs NP, t = 5            5.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 184123418.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5390
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:57.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:41.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:56.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:57.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:05.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:05.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:55.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:01.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     861
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.56
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:14.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:42.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.05
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.42
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.37
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.39
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.62
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.55
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.68
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.05
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:44.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.34
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:01.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7033.45
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:41.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.49
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.14
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:02.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.81
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.10
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:35.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5231.80
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:00.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46047
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870047
  j =  1                              :        399907912
  j =  2                              :            46035
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45997
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869997
  j =  1                              :        399908011
  j =  2                              :            45987
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:28.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:18.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:45.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:00.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:55.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.00e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.08e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:21.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:36.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:35.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.66
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.06
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.53
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.39
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.43
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.89
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:41.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.37
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.93
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.90
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.15
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.63
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17364.96
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.01
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.31
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.86
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.44
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.46
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.79
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.98
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.29
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.06
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.68
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:38.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.06
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.29
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.19
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.78
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.51
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.60
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.98
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  445.49
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.97
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.58
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.07
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.00
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.27
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.16
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  152.24
p-value of test                       :    0.9950


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.14
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.36
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5172.19
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.20
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.54
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.72
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:24.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.94
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:24.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.20

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.79
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.39
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:07.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:08.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10000.46
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9791.61
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:42.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.48e-3
p-value of test                       :    0.9985

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4671.81
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4811.20
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:50.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4280.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.63
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11812.16
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11880.62
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:29.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.06
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000086497

Normal statistic for number of bits   :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.76
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000072442

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:33.62

 All tests were passed




Server wird beendet - Lösche Semaphor 185139226.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5314
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:57.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:41.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:57.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:58.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:06.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:05.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:55.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:04:01.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    2.72
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    2.37
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.57
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:15.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:42.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.81
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.24
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.23
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.94
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:10.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.69
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:20.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.51
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.70
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.57
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:44.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1340.22
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:01.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7037.28
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.03
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.43
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:02.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.92
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.90
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:34.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4829.17
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:01.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45776
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869776
  j =  1                              :        399908451
  j =  2                              :            45770
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45975
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869975
  j =  1                              :        399908053
  j =  2                              :            45969
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 6.72e-3
p-value of test                       :    0.9913

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:27.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:18.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:45.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:01.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:54.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:35.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 9.85e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:37.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:36.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.65
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:48.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.11
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.81
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.27
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.83
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.50
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.71
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:41.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.77
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.78
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.68
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17322.29
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.74
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.54
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.80
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.07
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.99
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.39
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.09
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.64
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.46
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.81
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.63
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.14
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.31
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.11
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.85
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.44
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.39
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.62
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.93
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.97
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.68
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.85
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4903.49
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.94
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.85
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.48
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.91
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4876.43
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.86
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.57
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.63
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:23.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.58
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:23.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    2.74
p-value of test                       :  3.4e-3

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 3.84e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.24
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.44
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.75
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:05.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.24
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:07.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9698.10
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9773.73
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      : -3.31e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:41.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4766.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:48.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4834.84
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:49.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.52
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4035.98
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11427.62
p-value of test                       :    0.9955

-----------------------------------------------
CPU time used                    :  00:01:28.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11921.78
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:29.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.43
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999975434

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.22
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999954377

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 5.70e-3
p-value of test                       :    0.9940

Anderson-Darling statistic = A2       :    3.37
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.56
p-value of test                       :    0.9947

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    2.52
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:23.61

 All tests were passed




Server wird beendet - Lösche Semaphor 186187802.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5361
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:56.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:41.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:58.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:06.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:05.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7199
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:55.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7526
p-value of test                       :  7.9e-3


-----------------------------------------------
CPU time used                    :  00:04:01.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.65
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    3.09
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     835
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:49.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.88
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:14.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.32
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:45.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.36
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.69
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.59
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.94
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.10
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.90
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.11
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  388.71
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:44.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1491.32
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:02.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7043.31
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:41.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.55
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:02.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.35
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.10
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:33.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5131.80
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:58.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45811
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869811
  j =  1                              :        399908381
  j =  2                              :            45805
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46061
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870061
  j =  1                              :        399907880
  j =  2                              :            46057
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:28.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:18.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:46.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:01.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:55.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:33.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 6.74e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.53e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:21.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.066
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:21.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:37.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:37.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.26
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:48.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.00
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.01
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.00
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.71
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:44.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.26
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.18
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.86
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.50
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.98
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17277.06
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.18
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.60
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.39
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.37
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.06
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.81
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.61
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.04
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.34
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.94
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.91
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.34
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.13
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.67
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.57
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.43
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.54
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.88
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.21
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.57
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.90
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.44
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4856.23
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.40
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.91
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.10
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.97
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.12
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.63
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.11
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.20
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :    1.12
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:24.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.91
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :   -0.14
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:23.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 4.35e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.70e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 8.57e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.53
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.27
p-value of test                       :    0.9959

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:06.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.24
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:05.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9946.08
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10060.20
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:55.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:40.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4928.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:48.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.68
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:50.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.89
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.44
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11758.37
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11943.47
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.05
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999923186

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.04
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999760625

Normal statistic for number of bits   :   -1.89
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.20

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    2.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:36.68

 All tests were passed




Server wird beendet - Lösche Semaphor 187203610.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5370
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:55.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:41.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:56.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:58.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:06.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:06.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:56.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:00.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:47.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:15.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     129
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    2.05
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:44.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.61
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.51
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.36
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.49
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.77
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.92
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.57
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.68
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.70
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.36
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:46.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1462.46
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:02.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6989.59
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.24
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:03.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.04
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.66
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5229.22
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:00.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45922
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869922
  j =  1                              :        399908162
  j =  2                              :            45910
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45946
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869946
  j =  1                              :        399908111
  j =  2                              :            45940
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:28.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 3.64e-3
p-value of test                       :    0.9960

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:19.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:45.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:00.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:54.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:35.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.31e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:34.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.88
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.28
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.74
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.50
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:48.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.99
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   15.75
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.79
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:44.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.15
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:29.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:29.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:17.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.07
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:39.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17369.56
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.12
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.57
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.15
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.48
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.31
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:37.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.41
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.20
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.22
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.36
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.03
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.76
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.54
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.84
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.42
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.58
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.11
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.57
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.10
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.57
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.43
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.10
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.86
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.56
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.55
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.45
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.74
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.34
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5091.84
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.73
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.11
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.47
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :   -1.87
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:24.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.00
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:25.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   0.082
p-value of test                       :    0.47

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 5.31e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 9.82e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.07
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.64
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.09
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:04.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:04.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9969.97
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 8.66e-4
p-value of test                       :    0.9991    *****

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9714.37
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:39.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.77
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:48.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:50.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4216.95
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4045.89
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12099.04
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11787.16
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.83
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999966140

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.93
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000046114

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:54.14
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 64  WeightDistrib, r = 26           0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 188186650.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5471
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:43.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:37.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:35.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4452
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7492
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:01.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:01.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:53.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:58.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:53.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     338
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:09.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:35.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.68
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.60
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.76
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.85
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.27
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.76
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.91
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:42.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1434.64
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:59.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6934.23
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.60
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.78
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:04.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   88.77
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:38.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5050.62
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:15.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45809
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869809
  j =  1                              :        399908387
  j =  2                              :            45799
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46208
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870208
  j =  1                              :        399907584
  j =  2                              :            46208
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:13.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:28.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:18.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:45.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:00.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:52.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9928

-----------------------------------------------
CPU time used                    :  00:01:32.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 8.17e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.76e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 2.28e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:40.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:39.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.21
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:47.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.95
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.11
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.17
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:47.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.50
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.63
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   14.22
p-value of test                       :    0.9902

-----------------------------------------------
CPU time used                    :  00:01:38.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.16
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.13
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:32.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:30.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.63
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17613.26
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.55
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.46
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.90
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.55
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.57
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.03
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.83
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.22
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.52
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.61
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.02
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  108.38
p-value of test                       :    0.9915


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.05
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.07
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.18
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.64
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.33
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.76
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.81
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.31
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.90
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.43
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5062.08
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.29
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.36
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.44
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.49
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.50
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.88
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.77
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:34.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.21
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:14.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.07
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:13.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.80e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 4.78e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.68
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.97
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.95
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:12.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.78
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:10.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10127.53
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9890.94
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:04:11.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4716.63
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:49.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4800.56
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:50.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.19
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4160.20
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11862.03
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:28.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11878.27
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:31.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.15
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000070531

Normal statistic for number of bits   :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.27
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000049519

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:10.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:28.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:16:46.95

 All tests were passed




Server wird beendet - Lösche Semaphor 168787995.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:55.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5338
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:44.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:37.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:36.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:54.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:03.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:03.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:57.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:00.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.90
p-value of test                       :  9.9e-3

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:47.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.79
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.61
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.36
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     329
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    4.33
p-value of test                       :  6.0e-3

Stat. AD after spacings (mNP2-S)      :    3.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:11.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:42.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.61
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.76
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.95
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.98
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   30.89
p-value of test                       :    0.9952

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.86
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.56
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1373.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:07.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6916.28
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:49.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.62
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.32
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:09.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.83
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.96
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:39.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5146.18
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:23.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:16.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45989
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869989
  j =  1                              :        399908023
  j =  2                              :            45987
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45862
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869862
  j =  1                              :        399908279
  j =  2                              :            45856
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:30.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:17.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:44.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:00.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:54.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:35.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.33e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.03e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.47e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.35
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:40.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:39.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.19
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:50.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.13
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.85
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.78
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.52
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.59
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.52
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:46.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.39
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.95
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.87
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:33.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.56
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.88
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17520.53
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.86
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.50
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.59
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.25
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.77
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:37.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.89
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.82
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.13
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.30
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.64
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.31
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.12
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.61
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.15
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   48.51
p-value of test                       :    0.9905


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.31
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.08
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.40
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.09
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.14
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.83
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.39
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.43
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  332.25
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.76
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.89
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.66
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.62
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.38
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.34
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:36.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.88
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:30.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.25
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :  -0.028
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:27.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   0.092
p-value of test                       :    0.46

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.58e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 6.07e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.34e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 9.78e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.55
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:30.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.89
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.79
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:09.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.82
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:09.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9985.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9951.45
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.22
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:04:21.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4949.51
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:52.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.08
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:53.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.37
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4212.68
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11796.72
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:34.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11681.86
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:32.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.22
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999870707

Normal statistic for number of bits   :   -1.02
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.13
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000055888

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:13.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:11.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:15.26

 All tests were passed




Server wird beendet - Lösche Semaphor 169607195.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:56.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1465
p-value of test                       :  3.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334585
  j =  1                              :        599997070
  j =  2                              :             1465
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5439
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:50.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:38.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:37.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4209
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:54.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:03.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:04.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:56.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:02.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    2.10
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    3.98
p-value of test                       :  8.9e-3

-----------------------------------------------
CPU time used                    :  00:01:49.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:19.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     126
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:52.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.89
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:55.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.36
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.30
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.63
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.33
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.80
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.87
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.99
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.65
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  489.48
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:44.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1516.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:59.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6916.84
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:45.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.17
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:07.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.22
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.72
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:39.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5259.84
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:11.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45840
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869840
  j =  1                              :        399908323
  j =  2                              :            45834
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46045
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870045
  j =  1                              :        399907917
  j =  2                              :            46031
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:28.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:18.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 7.54e-3
p-value of test                       :    0.9913

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:59.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:55.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:34.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.41e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 9.24e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:40.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:40.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.86
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.73
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:55.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   59.90
p-value of test                       :  1.0e-2

-----------------------------------------------
CPU time used                    :  00:00:49.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.74
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:55.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:45.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.54
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:29.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.97
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:30.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.12
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.19
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17199.04
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.54
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.84
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.64
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.02
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.84
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.23
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.15
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.91
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.08
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.68
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.87
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.85
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.88
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.68
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.69
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.74
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  192.36
p-value of test                       :  6.1e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.43
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.09
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.09
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.22
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.83
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4959.70
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.40
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.13
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.07
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.32
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4856.70
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.87
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.78
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.70
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:27.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.77
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :    1.11
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:25.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.61
p-value of test                       :    0.95

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.13e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.44e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 7.15e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.47
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.16
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.09
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:07.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.34
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:09.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10162.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10145.16
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:04:16.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.06
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:51.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4996.98
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:53.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.15
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4025.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12039.80
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:30.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11925.78
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:31.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.31
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999819242

Normal statistic for number of bits   :   -1.43
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.98
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999987677

Normal statistic for number of bits   :  -0.097
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    2.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:51.96

 All tests were passed




Server wird beendet - Lösche Semaphor 170786843.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1482
p-value of test                       :  8.6e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334602
  j =  1                              :        599997036
  j =  2                              :             1482
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5390
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:48.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:38.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:38.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:55.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4433
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:03.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:03.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:54.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7181
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:02.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.23
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:15.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:44.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.68
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.30
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.06
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.43
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.90
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.97
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.03
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:46.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1412.23
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:02.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7168.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:40.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.55
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.82
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.66
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:04.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   18.58
p-value of test                       :  2.3e-3


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.94
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5073.12
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:14.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45837
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869837
  j =  1                              :        399908328
  j =  2                              :            45833
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46094
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870094
  j =  1                              :        399907816
  j =  2                              :            46086
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

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CPU time used                    :  00:05:01.17

Generator state:




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HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


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CPU time used                    :  00:02:28.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-3
p-value of test                       :    0.9982

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


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CPU time used                    :  00:02:17.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  8.0e-3

Kolmogorov-Smirnov- statistic = D-    : 3.41e-3
p-value of test                       :    0.9964

Anderson-Darling statistic = A2       :    3.80
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9959


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


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CPU time used                    :  00:01:45.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04


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CPU time used                    :  00:02:01.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

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CPU time used                    :  00:01:54.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

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CPU time used                    :  00:01:15.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

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CPU time used                    :  00:01:32.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

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CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

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CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


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Normal statistic                      :   -0.84
p-value of test                       :    0.80

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CPU time used                    :  00:00:22.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

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CPU time used                    :  00:00:22.35

Generator state:




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HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

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CPU time used                    :  00:01:33.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

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CPU time used                    :  00:01:34.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


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Number of degrees of freedom          :   67
Chi-square statistic                  :   59.06
p-value of test                       :    0.74

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CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


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Number of degrees of freedom          :   67
Chi-square statistic                  :   58.31
p-value of test                       :    0.77

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CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


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Number of degrees of freedom          :   67
Chi-square statistic                  :   43.15
p-value of test                       :    0.99

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CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.60
p-value of test                       :    0.53

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CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


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Number of degrees of freedom          :   37
Chi-square statistic                  :   16.17
p-value of test                       :    0.9988

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CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


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Number of degrees of freedom          :   37
Chi-square statistic                  :   47.12
p-value of test                       :    0.12

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CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
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   N =  1,  n = 500000000,  r =  0,   g = 10


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Number of degrees of freedom          :   29
Chi-square statistic                  :   25.87
p-value of test                       :    0.63

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CPU time used                    :  00:01:39.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.98
p-value of test                       :    0.56

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CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.75
p-value of test                       :    0.32

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CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.66
p-value of test                       :    0.45

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CPU time used                    :  00:01:29.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.01
p-value of test                       :    0.39

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CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


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Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

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CPU time used                    :  00:01:18.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


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Number of degrees of freedom          :    2
Chi-square statistic                  :    5.82
p-value of test                       :    0.05

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CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.66
p-value of test                       :    0.54

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CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17552.52
p-value of test                       :    0.26



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CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.86
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.78
p-value of test                       :    0.96


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Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.71
p-value of test                       :    0.54


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Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.06
p-value of test                       :    0.52


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Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.63
p-value of test                       :    0.13


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CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.81
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.92
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.98
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.79
p-value of test                       :    0.53


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Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.68
p-value of test                       :    0.69


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CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.43
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.27
p-value of test                       :    0.50


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Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.70
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.02
p-value of test                       :    0.18


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Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.66
p-value of test                       :    0.39


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CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.55
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.51
p-value of test                       :    0.91


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Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.71
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.23
p-value of test                       :    0.62


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Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.68
p-value of test                       :    0.04


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CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.13
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.91
p-value of test                       :    0.62


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Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5093.24
p-value of test                       :    0.18


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Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.01
p-value of test                       :    0.75


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Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.21
p-value of test                       :    0.97


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CPU time used                    :  00:00:36.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.51
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.72
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.01
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.35
p-value of test                       :    0.70


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Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.67
p-value of test                       :    0.97


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CPU time used                    :  00:00:36.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.75
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :   -1.22
p-value of test                       :    0.89



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CPU time used                    :  00:02:24.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.58
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :    1.59
p-value of test                       :    0.06



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CPU time used                    :  00:02:23.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.36e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 8.04e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.35
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.25
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.79
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:08.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.27
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:08.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9850.42
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9725.22
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:43.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5044.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4977.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4286.46
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4065.27
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11791.15
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11681.19
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:30.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.11
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000094663

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.90
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999898553

Normal statistic for number of bits   :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-3
p-value of test                       :    0.9990

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.33
p-value of test                       :    0.01

Sample variance                       :    2.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:30.50
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  7  CollisionOver, t = 7            8.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 171704347.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:52.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5332
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:47.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:38.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:37.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:55.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:03.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:03.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:54.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:00.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.91
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.47
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.60
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.53
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:12.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:41.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.18
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.21
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.71
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.40
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.69
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.04
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.30
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.74
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:42.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1385.07
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:03.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7197.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:40.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.70
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.91
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:02.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.00
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.11
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4983.28
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:19.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45810
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869810
  j =  1                              :        399908385
  j =  2                              :            45800
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45704
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869704
  j =  1                              :        399908595
  j =  2                              :            45698
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:28.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:18.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:44.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:59.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:55.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.81e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:26.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.05
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:37.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:37.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:48.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.28
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   32.55
p-value of test                       :    0.9999    *****

-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.15
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.92
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.56
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.67
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:39.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.44
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.40
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.28
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:29.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.57
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17309.55
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   57.40
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.29
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.61
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.15
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.95
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.85
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.91
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.44
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.83
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.76
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.30
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.25
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.89
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.23
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.90
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.36
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.86
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.05
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.13
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.59
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.73
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.03
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.50
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.16
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.71
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.95
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.31
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.27
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.79
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.54
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.95
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :  -0.019
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:25.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.61
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:25.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 3.87e-3
p-value of test                       :    0.9960

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.74
p-value of test                       :    0.96

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    2.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 3.09e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   20.09
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.36
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.45
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:07.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.13
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:09.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9759.89
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10035.19
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:47.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5057.93
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:50.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4940.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:51.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4231.09
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3984.13
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11898.93
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11871.66
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:30.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.18
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999943973

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.55
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000019882

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:35.31
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 61  WeightDistrib, r = 28           0.9999 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 172556291.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  4.0e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5330
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:50.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:38.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:38.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4230
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:03.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:03.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:54.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:00.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.13
p-value of test                       :  7.6e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.63
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     961
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.70
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:13.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:42.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.63
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.57
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.96
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.73
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.55
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.79
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.50
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:42.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1334.10
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7142.15
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:41.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.59
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.29
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:02.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   17.48
p-value of test                       :  3.7e-3


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.59
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5123.91
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:11.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45838
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869838
  j =  1                              :        399908326
  j =  2                              :            45834
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45631
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869631
  j =  1                              :        399908740
  j =  2                              :            45627
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:28.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:18.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:44.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:59.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:34.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 4.07e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.43e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.67e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:21.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:34.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:35.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.13
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:47.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.74
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.31
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.82
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:48.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.23
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.95
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:38.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.48
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.37
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.08
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:29.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  3.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  100.15
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:39.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17487.96
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.60
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.90
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.78
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.08
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.89
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.50
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   16.80
p-value of test                       :    0.9960


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.49
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.60
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.62
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.42
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.54
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.99
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.71
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.31
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.37
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.34
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.98
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.20
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.12
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.09
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5152.53
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.48
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.15
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.88
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.37
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4868.09
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.34
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.81
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.10
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:25.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.75
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :   -1.29
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:24.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:12.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :  3.0e-3

Kolmogorov-Smirnov- statistic = D-    : 5.76e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    3.70
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.00e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 5.63e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.66
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.39
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.75
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:08.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.25
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:07.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10135.32
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9881.66
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:50.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4967.96
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4844.40
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:51.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4038.23
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.89
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11809.53
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:28.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11891.02
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:29.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.72
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000080812

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.88
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999989189

Normal statistic for number of bits   :  -0.085
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.53e-3
p-value of test                       :    0.9919

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.67
p-value of test                       :    0.05

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:29.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:29.06
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  2  SerialOver, r = 22              4.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 173473795.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5487
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:56.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4231
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:39.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:55.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:02.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:02.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:54.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:59.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.03
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    2.58
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.58
p-value of test                       :  4.8e-3

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:13.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:44.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.35
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.68
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.43
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.03
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.28
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.36
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.16
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.33
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.73
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:42.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1472.09
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:59.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7083.45
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:44.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.57
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:01.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.25
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.02
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:34.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5072.88
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:02.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46105
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870105
  j =  1                              :        399907793
  j =  2                              :            46099
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46074
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870074
  j =  1                              :        399907854
  j =  2                              :            46070
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    3.46
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:29.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:19.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 2.04e-3
p-value of test                       :    0.9979

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:44.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9963

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:59.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:56.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-5
p-value of test                       :    0.9929

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.00e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 3.37e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:35.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:35.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.83
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:48.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.02
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.32
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.03
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.94
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:43.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.34
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.5e-3

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.93
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.97
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.08
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17437.35
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.91
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.16
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.08
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.56
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.77
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:38.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.92
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.37
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.54
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.00
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.47
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:38.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.66
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.13
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.27
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.69
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.66
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.55
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.50
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.97
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.52
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.14
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.42
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  447.93
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.13
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.55
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  239.75
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.07
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.39
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4981.62
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.29
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.54
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.00
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:24.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.57
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :    1.43
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:24.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.62
p-value of test                       :  4.6e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.90
p-value of test                       :    0.9981

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 4.47e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.83e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.34
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.01
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.07
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:06.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.43
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:08.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10055.53
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9968.25
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:04:00.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4962.57
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:50.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4833.62
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:50.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4188.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12084.75
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:29.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11755.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:30.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.45
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000165253

Normal statistic for number of bits   :    1.31
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.75
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999986504

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:30.77

 All tests were passed




Server wird beendet - Lösche Semaphor 174522371.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1261
p-value of test                       :    0.9975

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334381
  j =  1                              :        599997478
  j =  2                              :             1261
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5641
p-value of test                       :  1.5e-3


-----------------------------------------------
CPU time used                    :  00:03:56.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:40.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:39.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:55.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7469
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:04.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7456
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:03.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:57.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7138
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:59.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.84
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:13.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:46.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.64
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.71
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.67
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.88
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.66
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.26
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.35
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.10
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1407.75
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:02.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6908.74
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:49.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.70
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.92
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:08.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.34
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  159.21
p-value of test                       :  8.2e-3


-----------------------------------------------
CPU time used                    :  00:01:37.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4988.85
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:58.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45832
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869832
  j =  1                              :        399908338
  j =  2                              :            45828
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45877
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869877
  j =  1                              :        399908250
  j =  2                              :            45869
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:30.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:18.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:48.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 9.60e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:07.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.89e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 9.59e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:40.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.90
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.91
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.99
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.52
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:45.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.73
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.17
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.36
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.60
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17275.62
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.75
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.09
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.24
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.80
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.18
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.65
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   56.40
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.68
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.36
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.26
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.89
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.50
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.78
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.93
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.92
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.44
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.63
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.08
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.81
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.34
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.94
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.73
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.93
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.11
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.22
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.58
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5023.40
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.19
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.90
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.14
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :   -0.63
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.48
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:22.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.40e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.66e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 9.63e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.31
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.81
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.26
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:06.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.60
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:08.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10188.11
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9824.87
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.76
p-value of test                       :    0.9971

-----------------------------------------------
CPU time used                    :  00:04:24.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:54.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4756.73
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:57.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.88
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11738.13
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:32.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11877.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:31.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.35
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000019969

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.17
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000044419

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   0.072
p-value of test                       :    0.47

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.57
p-value of test                       :    0.06

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.09

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:13.34

 All tests were passed




Server wird beendet - Lösche Semaphor 175570947.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5452
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:53.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:39.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:55.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4452
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:04.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:03.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:54.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:04:00.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.08
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:46.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.81
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:12.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:38.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.79
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.00
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.57
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.90
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.83
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.83
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.67
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1407.93
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:00.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6964.46
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:39.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.86
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.58
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:02.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.09
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.84
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:33.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4975.44
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:11.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46141
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870141
  j =  1                              :        399907720
  j =  2                              :            46137
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46259
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870259
  j =  1                              :        399907485
  j =  2                              :            46253
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :  9.7e-8    *****

Anderson-Darling statistic = A2       :   10.27
p-value of test                       :  1.1e-5    *****

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  4.0e-5    *****


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:29.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:18.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:44.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:58.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:34.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:38.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:39.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.85
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:47.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.57
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.81
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.53
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.12
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.21
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:38.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.88
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.67
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.57
p-value of test                       :  7.6e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.66
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   94.89
p-value of test                       :    0.9911

-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17449.51
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.17
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.40
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.46
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.94
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.11
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.10
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.80
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.72
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.94
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.83
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.22
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.31
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.25
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.79
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.33
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.95
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.43
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.27
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.08
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.19
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.98
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.34
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.41
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.11
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.82
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.31
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.96
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.54
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.56
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.67
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.69
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :  -0.024
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:22.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.09
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :   0.057
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:24.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.63
p-value of test                       :    0.95

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.11e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.67e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.87
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.22
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.66
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:08.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.18
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:07.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9815.40
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10037.01
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:44.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.15
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:50.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.02
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:51.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4243.20
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4097.12
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11656.62
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:28.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11848.93
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:31.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.97
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000010591

Normal statistic for number of bits   :   0.084
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.71
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000036703

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:09.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 6.23e-3
p-value of test                       :    0.9934

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.28
p-value of test                       :    0.99

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:06.55
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 46  MaxOft, t = 8                   4.0e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 176586755.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  6.2e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5350
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:54.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:39.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:57.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:04.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:03.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:53.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:04:00.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:43.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:06.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.37
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:33.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:55.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.78
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.39
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.64
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.72
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.46
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.59
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.15
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  376.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:43.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1495.00
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:00.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7011.26
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.70
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:02.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.39
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.82
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:32.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5016.91
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:02.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45299
p-value of test                       :    0.9967


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869299
  j =  1                              :        399909407
  j =  2                              :            45289
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46089
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870089
  j =  1                              :        399907825
  j =  2                              :            46083
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:29.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:17.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:44.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:58.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:35.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 9.77e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.32e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 8.07e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:34.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.078
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.46
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:49.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.24
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.93
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.44
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:51.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.19
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:38.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.36
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.98
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17446.67
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.46
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.18
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.23
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.78
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.84
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.84
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.76
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.45
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.07
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.06
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:37.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.08
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.33
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.14
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.06
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.11
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.79
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.77
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.47
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.74
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.00
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.76
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.81
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4756.37
p-value of test                       :    0.9933


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.47
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.67
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.40
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.16
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5211.15
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.44
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.19
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.03
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:24.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.54
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:25.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.01e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:46.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 6.42e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.95
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.23
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.63
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:07.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.81
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:07.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9846.15
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9744.05
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.59
p-value of test                       :  4.7e-3

-----------------------------------------------
CPU time used                    :  00:03:43.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5007.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:48.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4978.12
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:52.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3989.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.02
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11984.09
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11900.58
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.88
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999994691

Normal statistic for number of bits   :  -0.042
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.40
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000037666

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   0.088
p-value of test                       :    0.46

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:30.38
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  2  SerialOver, r = 22              6.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 177635331.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:39.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5427
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:53.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:38.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4250
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:55.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:03.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:02.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7166
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:52.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:59.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.18
p-value of test                       :    0.9953

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9957

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:46.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:13.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.51
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:41.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   18.77
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.25
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.70
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.04
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.35
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.27
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.34
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.34
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.10
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.26
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:43.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1472.87
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:58.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7112.37
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:42.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.43
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.08
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:02.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.06
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.16
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:33.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5260.11
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:57.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46090
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870090
  j =  1                              :        399907823
  j =  2                              :            46084
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46081
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870081
  j =  1                              :        399907840
  j =  2                              :            46077
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:29.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:19.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:44.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:59.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:35.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 6.99e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:21.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.019
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:34.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:33.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.99
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.35
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.17
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:48.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.34
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.97
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.57
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:37.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.07
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.00
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.56
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.36
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.21
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:39.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17452.18
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.52
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.20
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.39
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.69
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.09
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.42
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.23
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.25
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.04
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.59
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.33
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.24
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.08
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.90
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.10
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.36
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.63
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.45
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.87
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.00
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.60
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.44
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5233.81
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.11
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.35
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.57
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.02
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.61
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.87
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.64
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.20
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:22.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.99
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :    2.35
p-value of test                       :  9.4e-3



-----------------------------------------------
CPU time used                    :  00:02:23.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.17e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.63
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.82
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.90
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.38
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:07.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10032.10
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10091.89
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.033
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:52.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.29
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4734.16
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:50.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.52
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4235.69
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11744.95
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:28.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11903.35
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:29.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.36
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000073723

Normal statistic for number of bits   :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.69
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000011650

Normal statistic for number of bits   :   0.092
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   0.028
p-value of test                       :    0.49

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    0.12
p-value of test                       :    0.9992    *****

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.59
p-value of test                       :    0.06

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:25.45

 All tests were passed




Server wird beendet - Lösche Semaphor 178552835.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:50.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5443
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:57.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:40.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:56.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:57.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:04.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:03.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:55.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:04:00.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.40
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:46.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    2.01
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     648
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    2.58
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:13.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:40.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.37
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.93
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.62
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.54
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.95
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.93
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.36
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:44.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1473.57
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:59.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7114.98
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.47
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:03.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.63
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.66
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5023.60
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:55.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46069
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870069
  j =  1                              :        399907869
  j =  2                              :            46055
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46016
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870016
  j =  1                              :        399907970
  j =  2                              :            46012
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:27.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:18.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:44.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 4.15e-3
p-value of test                       :    0.9955

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:58.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:56.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:36.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:34.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.15
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:49.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.05
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.14
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.30
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.89
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.77
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.14
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:55.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.99
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.84
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.38
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.13
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  156.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17374.59
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.49
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.94
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.99
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.92
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.94
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.20
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.68
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.72
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.90
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.87
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.72
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.97
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.61
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.97
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.02
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.18
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.15
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.03
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.46
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.46
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.69
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.64
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5054.91
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.68
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.32
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.71
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.63
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.10
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.69
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.91
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:34.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.48
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :    0.93
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:21.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.58
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :   -2.01
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:21.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.73e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:46.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.79e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.26
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.66
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:06.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.82
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:08.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9976.67
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10006.32
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.086
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:43.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.04
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.38
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:51.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4021.30
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.24
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11812.45
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:29.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11657.31
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:30.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.95
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000054463

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.61
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  7999973001

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    2.63
p-value of test                       :  4.8e-3

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:44.85

 All tests were passed




Server wird beendet - Lösche Semaphor 179601411.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1262
p-value of test                       :    0.9973

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334382
  j =  1                              :        599997476
  j =  2                              :             1262
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5361
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:57.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:42.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:41.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:57.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:04.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:03.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:54.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:59.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.9911

Test on the Nm values of W_{n,i}(mNP1):    6.36
p-value of test                       :  6.7e-4    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     819
p-value of test                       :    0.9967

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    3.09
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:11.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.30
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.45
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.19
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.64
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.92
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.73
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.72
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.14
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  482.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:44.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1502.99
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:00.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7100.65
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.70
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.65
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:04.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.82
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   93.96
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:33.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5044.53
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:54.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45787
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869787
  j =  1                              :        399908428
  j =  2                              :            45783
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46137
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870137
  j =  1                              :        399907732
  j =  2                              :            46125
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:28.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:18.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:44.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9991    *****


-----------------------------------------------
CPU time used                    :  00:01:58.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.16e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:36.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 2.63e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:34.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:34.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.00
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:48.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.99
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.59
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:48.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.36
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.13
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   14.41
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:36.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.05
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.64
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.75
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.25
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.93
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:39.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17500.15
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   60.78
p-value of test                       :  6.0e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.10
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.13
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.59
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.07
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.05
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   14.53
p-value of test                       :    0.9991    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.02
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.70
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.22
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.29
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.96
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.87
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.77
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.92
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.00
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.43
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.75
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.84
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.36
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.16
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.60
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4904.10
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.91
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.74
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.18
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.86
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.76
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.38
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.71
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.97
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :    1.07
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:21.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.64
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :   -1.00
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:20.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9983

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 4.06e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.59
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.02
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.21
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:06.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.23
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:07.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9781.08
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9918.05
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:49.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9920

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4895.91
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:47.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:50.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4159.97
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4116.95
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12074.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11777.28
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:30.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.21
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999950141

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.83
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999943106

Normal statistic for number of bits   :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:22.61
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP1, t = 3          6.7e-4
 49  MaxOft AD, t = 32               0.9991 
 75  RandomWalk1 M (L=50, r=25)      0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 180584451.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5456
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:00.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:41.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:56.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:57.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:04.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:04.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:54.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:59.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.15
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    2.75
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     836
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    3.69
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:46.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.07
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     328
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:11.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:42.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.45
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.89
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.64
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.18
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  202.52
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:44.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1484.19
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:00.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7031.76
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:41.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.49
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.9e-3

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   85.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:04.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.44
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.03
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:33.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4890.36
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:12.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:58.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45505
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869505
  j =  1                              :        399908995
  j =  2                              :            45495
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45873
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869873
  j =  1                              :        399908258
  j =  2                              :            45865
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:27.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:20.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:47.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:58.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:56.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:36.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 9.65e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.20e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:34.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:35.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.81
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.92
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:48.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.65
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.61
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.02
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.03
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.29
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:17.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.42
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17287.95
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.04
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.42
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.45
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.08
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.93
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.43
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.60
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.10
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.39
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.06
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.86
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.78
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.91
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.70
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.41
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.31
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.99
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.63
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.87
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.80
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.39
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.84
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4992.39
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.72
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.07
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.95
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.92
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5260.29
p-value of test                       :  5.1e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.77
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.17
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.24
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :    1.93
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:23.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.73
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:22.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.72e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.18e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.38
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.96
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.00
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:04.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.6e-3

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:07.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9988.81
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:49.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4993.92
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:55.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4897.07
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:52.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4203.65
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3951.01
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11729.71
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:30.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11615.71
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:31.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.76
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999982457

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.46
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000000592

Normal statistic for number of bits   : 4.68e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.09

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:34.13

 All tests were passed




Server wird beendet - Lösche Semaphor 181633027.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5561
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:00.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:42.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:45.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:59.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:58.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:06.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:04.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:54.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:04:01.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.09
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.79
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:14.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.98
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:44.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.13
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   36.58
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.04
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.84
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.66
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.85
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.70
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  399.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:45.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1504.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:00.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7042.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.96
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:15.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.64
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:03.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.99
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.27
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:33.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5149.07
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:58.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45995
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869995
  j =  1                              :        399908012
  j =  2                              :            45991
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45697
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869697
  j =  1                              :        399908609
  j =  2                              :            45691
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:27.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:18.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 8.99e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:59.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.29
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.37e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 4.24e-4
p-value of test                       :  7.6e-4    *****

Anderson-Darling statistic = A2       :    4.86
p-value of test                       :  3.4e-3

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.54e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:21.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:35.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:36.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.52
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.99
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.42
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.98
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.78
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.93
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:37.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.63
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.92
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.69
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17575.27
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.18
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   16.87
p-value of test                       :    0.9958


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.32
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.14
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.66
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.68
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.47
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.74
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.10
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.29
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.06
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.82
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.69
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.89
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.98
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  110.26
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.66
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.70
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.78
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.50
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.91
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.60
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4862.80
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  441.71
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.29
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.22
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5243.22
p-value of test                       :  8.2e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.85
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.58
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.19
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:21.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.93
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:22.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.69e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 5.94e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.53
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.79
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.34
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:05.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.00
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:06.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9903.57
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9920.35
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:55.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:43.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4931.23
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4975.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:49.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.83
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4207.10
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11789.18
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11761.45
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:30.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.98
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999997685

Normal statistic for number of bits   :  -0.018
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.17
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000055258

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.53
p-value of test                       :    0.06

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:07.04

 All tests were passed




Server wird beendet - Lösche Semaphor 182648835.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:49.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5602
p-value of test                       :  7.3e-3


-----------------------------------------------
CPU time used                    :  00:04:01.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:43.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7198
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:45.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4159
p-value of test                       :    0.9966


-----------------------------------------------
CPU time used                    :  00:01:58.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4205
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:00.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:07.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:05.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:56.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7531
p-value of test                       :  6.8e-3


-----------------------------------------------
CPU time used                    :  00:04:01.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.60
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    6.49
p-value of test                       :  5.9e-4    *****

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:50.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     565
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.66
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     330
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:10.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:40.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.39
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.20
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.49
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.28
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.94
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.65
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.68
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.74
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.40
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  486.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:44.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1444.55
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:01.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6987.85
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:42.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.82
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:03.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.43
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.71
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:44.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5013.61
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:31.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:23.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46120
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870120
  j =  1                              :        399907764
  j =  2                              :            46112
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45757
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869757
  j =  1                              :        399908489
  j =  2                              :            45751
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:27.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:18.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:46.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9996    *****


-----------------------------------------------
CPU time used                    :  00:01:59.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:56.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:35.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 8.32e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.082
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:37.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:35.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.61
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:48.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.02
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.04
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:38.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.67
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 9.24e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.23
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17457.23
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.90
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.55
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.63
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.35
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.30
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.55
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   56.34
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.49
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.41
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.25
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:37.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.44
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.45
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.26
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.52
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.70
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.33
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.90
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.00
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.23
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.74
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  329.12
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.22
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.60
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.44
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.17
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.67
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.02
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4840.68
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.19
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.43
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.49
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:22.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.32
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:24.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    2.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.76e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 8.98e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.74e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.22
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.12
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.63
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:06.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:06.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10033.17
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9947.72
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:55.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:41.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4943.24
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:49.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4839.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:50.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4011.74
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4283.65
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11835.98
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11377.77
p-value of test                       :    0.9984

-----------------------------------------------
CPU time used                    :  00:01:30.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.54
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000005407

Normal statistic for number of bits   :   0.043
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.73
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999919499

Normal statistic for number of bits   :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    2.48
p-value of test                       :  8.0e-3

-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:04.06
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP2, t = 3          5.9e-4
 49  MaxOft AD, t = 32               0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 183697411.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1247
p-value of test                       :    0.9993    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334367
  j =  1                              :        599997506
  j =  2                              :             1247
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5353
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:04:01.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:45.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:45.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:58.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:58.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:06.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:06.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:56.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:04:01.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    2.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:49.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:14.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:43.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.39
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.64
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.26
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.83
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:10.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.29
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.54
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.71
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.47
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.06
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:44.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1407.66
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:01.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7179.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:42.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.38
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.41
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:03.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.72
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.61
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:33.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4962.40
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:57.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45900
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869900
  j =  1                              :        399908204
  j =  2                              :            45892
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45908
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869908
  j =  1                              :        399908185
  j =  2                              :            45906
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:27.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:18.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:45.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:59.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:36.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.82e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.53e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.46e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:33.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:34.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.05
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.95
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.92
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.36
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:48.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.46
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.99
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.88
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:37.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.34
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.76
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.052
p-value of test                       :    0.9969

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.79
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.12
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17741.25
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.57
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.06
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.73
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.21
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.18
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.36
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.30
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.11
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.11
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.02
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.80
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.44
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.63
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.49
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.61
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.84
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.07
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.76
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.20
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.79
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.87
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.63
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.86
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.22
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.60
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.41
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.02
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5081.78
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.59
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.57
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.69
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.08
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:22.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   0.098
p-value of test                       :    0.46

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 8.89e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.93e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.17
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.30
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:05.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.93
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:07.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10124.36
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9883.58
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.13
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:41.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4830.55
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:48.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4841.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:50.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4204.31
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4043.64
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12128.83
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12062.03
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.11
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999987977

Normal statistic for number of bits   :  -0.095
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.88
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000072067

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.47
p-value of test                       :    0.07

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:10.17
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 184745987.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5476
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:01.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:44.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:47.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:59.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:01.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:07.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:07.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:59.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:02.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     950
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    3.05
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     546
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    2.10
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:13.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:44.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.01
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.80
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.71
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.20
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.18
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.21
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.08
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.11
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:44.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1393.28
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:01.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7163.51
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:43.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.27
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:04.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.14
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.51
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:33.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4919.85
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:11.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:56.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46240
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870240
  j =  1                              :        399907524
  j =  2                              :            46232
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45927
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869927
  j =  1                              :        399908150
  j =  2                              :            45919
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:27.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:19.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:46.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:59.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:56.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:36.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.39e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.41e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.96
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:35.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.33
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.24
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.35
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.63
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:48.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.94
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.55
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.58
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:38.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.96
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.39
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.12
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.50
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.30
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17263.19
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.45
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.23
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.02
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.94
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.35
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.35
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.22
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.69
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.83
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.60
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.39
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.09
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.59
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.61
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.25
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.72
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.47
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.45
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  100.58
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.48
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.44
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.77
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.48
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.89
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.92
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5248.84
p-value of test                       :  7.0e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.90
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.91
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.57
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :   -1.58
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:22.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.86
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:22.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.33e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 9.47e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.98
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.30
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.89
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:05.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.74
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:06.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9742.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10120.45
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:43.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.9998    *****

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4650.69
p-value of test                       :    0.9929

-----------------------------------------------
CPU time used                    :  00:01:48.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.42
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:51.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.28
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.87
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11849.94
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11803.65
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:30.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.78
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999962471

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.23
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999911543

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:37.65

 All tests were passed




Server wird beendet - Lösche Semaphor 185794563.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5510
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:04:04.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:45.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:44.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:00.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:03.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:14.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:10.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:04:04.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7100
p-value of test                       :    0.9947


-----------------------------------------------
CPU time used                    :  00:04:06.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    2.69
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:49.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.76
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.29
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    3.35
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     268
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:16.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.73
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:43.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.73
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.16
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.75
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.13
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.23
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.16
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.56
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:48.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.02
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:04.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7220.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:49.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.92
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.46
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:07.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.23
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.64
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:36.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4998.84
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:58.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46127
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870127
  j =  1                              :        399907750
  j =  2                              :            46119
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45974
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869974
  j =  1                              :        399908056
  j =  2                              :            45966
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:29.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:18.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  8.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:06.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:57.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:36.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.15e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 5.24e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 8.89e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:39.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.05
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.75
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.79
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.24
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.78
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.86
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.19
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:46.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   61.67
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.06
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  173.92
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:00:39.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17483.65
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.46
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.22
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.47
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.99
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.64
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.44
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.88
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.48
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.93
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.83
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.24
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.18
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.60
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.07
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.51
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.58
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.49
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.63
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.77
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.24
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.83
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.91
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5170.71
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.03
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.14
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.70
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.17
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.21
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.98
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.96
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.37
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:23.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.80
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :   -1.26
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.84
p-value of test                       :    0.97

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 8.11e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 4.27e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.60
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.04
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.34
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:08.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.10
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:07.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10113.55
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.0e-3

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9784.94
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.091
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:04:22.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.85
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:52.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:54.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4212.13
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11805.07
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:32.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11851.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:32.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.25
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999959603

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.03
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000051064

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.70
p-value of test                       :    0.04

Sample variance                       :    2.36
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:15.47

 All tests were passed




Server wird beendet - Lösche Semaphor 186810371.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:59.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:43.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:46.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4453
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:00.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:59.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:08.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:07.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:56.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:01.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:47.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    2.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:13.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:42.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.84
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.14
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.01
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.53
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.22
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.02
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.67
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  377.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:44.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1499.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:00.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6942.08
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:43.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.05
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.08
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:04.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.80
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.26
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:32.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4996.76
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:55.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46088
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870088
  j =  1                              :        399907826
  j =  2                              :            46084
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45697
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869697
  j =  1                              :        399908611
  j =  2                              :            45687
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:27.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:18.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:45.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:59.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:17.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:35.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 2.86e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 9.69e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:21.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:33.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:34.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.97
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:49.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.08
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.06
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.86
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.28
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.53
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:37.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.00
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.73
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17683.57
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.83
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.59
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.42
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.80
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.72
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.27
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.30
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.75
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.16
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.08
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.67
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.23
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.52
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.74
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.71
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.48
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.39
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.18
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.33
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.15
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.26
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.40
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.43
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  312.83
p-value of test                       :    0.9937


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.42
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.14
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.49
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.87
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.77
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.63
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.91
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:23.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.71
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:22.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.22e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 8.53e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.17e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.92
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.69
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.74
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:06.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.03
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:05.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10145.65
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9782.68
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.97
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:43.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4832.30
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:48.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4989.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4116.27
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.82
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11830.23
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:28.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11791.50
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:29.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.74
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999994817

Normal statistic for number of bits   :  -0.041
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.54
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999888062

Normal statistic for number of bits   :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.09

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:48.38

 All tests were passed




Server wird beendet - Lösche Semaphor 187891715.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5529
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:43.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4460
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:37.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:35.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:54.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:02.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:02.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:54.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:04:00.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.75
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     941
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:54.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     627
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    2.03
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     263
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:12.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:37.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.32
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.33
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.34
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.91
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.63
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.22
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  273.65
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.90
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:47.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.40
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:59.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7214.99
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.83
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.44
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:03.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.12
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.11
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:37.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5027.32
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:15.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:13.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45895
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869895
  j =  1                              :        399908212
  j =  2                              :            45891
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45272
p-value of test                       :    0.9977


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869272
  j =  1                              :        399909461
  j =  2                              :            45262
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:28.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:18.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:45.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.36e-3
p-value of test                       :    0.9915

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:00.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:52.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 5.69e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:37.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:38.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.35
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.14
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.80
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.67
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:50.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.37
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.52
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.71
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:43.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    4.59
p-value of test                       :  4.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   77.05
p-value of test                       :  3.9e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.05
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.01
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:31.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:28.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.85
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17213.03
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.53
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.87
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.02
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.31
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.60
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.66
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.98
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.85
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.57
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.90
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.69
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.62
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  449.91
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.46
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  103.95
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:46.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.40
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.86
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.74
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.34
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   44.61
p-value of test                       :    0.9973


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.34
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.03
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.84
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.54
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.95
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:34.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.77
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.24
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4941.61
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.18
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.96
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:33.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.10
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :   0.097
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:13.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.55
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:14.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.38

Sample variance                       :    1.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.00e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:47.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.26e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.96
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.10
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:13.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.82
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:09.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9835.21
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10149.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:04:05.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4813.65
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:48.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4973.04
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:49.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4043.71
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.97
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11630.14
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11808.58
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.20
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000070222

Normal statistic for number of bits   :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.40
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999913391

Normal statistic for number of bits   :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.47
p-value of test                       :    0.07

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:17:18.85
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 66  MatrixRank, L=30, r=0           3.9e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 168820764.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1481
p-value of test                       :  9.4e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334601
  j =  1                              :        599997038
  j =  2                              :             1481
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5403
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:45.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:37.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:36.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:54.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:02.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7515
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:02.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7457
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:54.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:00.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.83
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:47.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     554
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:12.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.99
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    2.18
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:45.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.58
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.21
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.53
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.01
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.40
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.09
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.79
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.70
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:49.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1383.22
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:00.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6971.01
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:45.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.72
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.58
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:02.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.96
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.41
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:36.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4926.26
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:04.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46093
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870093
  j =  1                              :        399907819
  j =  2                              :            46083
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45855
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869855
  j =  1                              :        399908293
  j =  2                              :            45849
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:30.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:17.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:45.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:00.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:54.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:32.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.16e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:21.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:34.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.95
p-value of test                       :    0.9984

-----------------------------------------------
CPU time used                    :  00:01:34.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.89
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.02
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.67
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.47
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.93
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.90
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.07
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:40.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.01
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.16
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.75
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.06
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:10.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.02
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:40.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17328.65
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.42
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.42
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.78
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.03
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.12
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.62
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.93
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.54
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.36
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.49
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.65
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.67
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  442.68
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.08
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.84
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.62
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.31
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  446.18
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.06
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.09
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:42.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.91
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.47
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4887.50
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.20
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.69
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:34.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.70
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  322.73
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5069.57
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.81
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.07
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.15
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:17.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.75
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:23.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.55
p-value of test                       :  1.0e-3

Anderson-Darling statistic = A2       :    5.20
p-value of test                       :  2.4e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.62
p-value of test                       :  4.3e-3

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.83e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:47.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 3.66e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.84
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.73
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   40.00
p-value of test                       :  4.5e-3



-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.26
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:09.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.37
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:11.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9947.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9744.62
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.057
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.078
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:04:02.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4972.14
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4990.07
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3984.14
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.67
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11906.83
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11628.75
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.98
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999980174

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.21
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000030211

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   0.072
p-value of test                       :    0.47

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:23.60
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           9.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 169672732.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:52.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5435
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:46.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:38.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:37.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:55.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:55.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:02.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:03.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:54.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7102
p-value of test                       :    0.9944


-----------------------------------------------
CPU time used                    :  00:04:00.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    6.21
p-value of test                       :  8.1e-4    *****


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    2.21
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:47.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    5.67
p-value of test                       :  1.4e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    2.62
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     269
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:17.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    2.48
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:50.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.31
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.23
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.45
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.00
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.86
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1458.52
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:00.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7096.16
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:41.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.23
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.98
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:00.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.41
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.06
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:34.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5004.08
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:07.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46103
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870103
  j =  1                              :        399907795
  j =  2                              :            46101
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45961
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869961
  j =  1                              :        399908086
  j =  2                              :            45945
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 7.70e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:32.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:19.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:44.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:00.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:54.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:32.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.09e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.96e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 8.97e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9964

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.31
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:22.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:34.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.99
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:48.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.98
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.41
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.07
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.81
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.87
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.31
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:43.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.66
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.51
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  161.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17494.93
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.58
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.52
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.60
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.42
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.41
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.01
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.69
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.35
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.57
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.09
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.01
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.36
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.91
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.07
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.10
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.23
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.69
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.37
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.18
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.32
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.49
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4864.07
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.58
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.16
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.54
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.25
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.46
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.21
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.51
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.92
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :  -0.064
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:21.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.15
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:27.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 8.49e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:46.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.05
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.99
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.80
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:09.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:08.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9887.92
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9925.48
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:58.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.08
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:49.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5000.09
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:50.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.46
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:20.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4187.65
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11741.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11889.65
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:30.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.31
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000149200

Normal statistic for number of bits   :    1.18
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.13
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000028579

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.78
p-value of test                       :    0.96

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.79
p-value of test                       :    0.96

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.7e-3

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.57
p-value of test                       :    0.94

Sample variance                       :    0.18
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:56.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs NP, t = 3            8.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 170524700.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5259
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:45.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:37.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:36.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:54.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:01.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:01.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:52.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:57.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:45.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.28
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.88
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:12.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:45.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.90
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.32
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.00
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.78
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:10.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.32
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.91
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.43
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.36
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.22
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:45.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1527.39
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:05.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7168.96
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.54
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.90
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:09.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.38
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.15
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:34.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5244.26
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:02.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45697
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869697
  j =  1                              :        399908606
  j =  2                              :            45697
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45569
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869569
  j =  1                              :        399908865
  j =  2                              :            45563
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:32.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:19.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:01.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:33.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.029
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:37.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:38.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.55
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:48.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.28
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.20
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.27
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:48.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.63
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:43.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.52
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.92
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.68
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17474.38
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.73
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.70
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.37
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.13
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.45
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:36.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.53
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.97
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.20
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.54
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.79
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.74
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.29
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.70
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.13
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.75
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.62
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.53
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.63
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.10
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.72
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.65
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.29
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.86
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.08
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.31
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.66
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.78
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4815.32
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  304.72
p-value of test                       :    0.9977


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.96
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.90
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :   -0.11
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:25.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.78
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :  -0.042
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:27.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 4.85e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 5.70e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.09
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.30
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.89
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:07.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.20
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:06.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9769.23
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10057.09
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.059
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:04:15.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.89
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:50.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.01
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:51.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4059.20
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4182.23
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11762.38
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:29.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11684.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:31.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.07
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999999752

Normal statistic for number of bits   : -1.96e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.78
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999857918

Normal statistic for number of bits   :   -1.12
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:04.25

 All tests were passed




Server wird beendet - Lösche Semaphor 171376668.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5497
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:48.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4195
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:37.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:35.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:54.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:53.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:01.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7184
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:02.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:54.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:58.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.60
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.99
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    2.62
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:44.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:13.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    3.33
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     126
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:47.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.28
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.93
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.31
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.96
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.36
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.78
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.32
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.88
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:42.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1392.53
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:59.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7094.00
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:40.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.12
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.75
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:02.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.84
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.50
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:33.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4929.82
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:56.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45753
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869753
  j =  1                              :        399908498
  j =  2                              :            45745
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45940
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869940
  j =  1                              :        399908124
  j =  2                              :            45932
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:30.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:20.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:45.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:59.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:33.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:33.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.66
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:48.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.98
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.73
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.86
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:48.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.92
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:37.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.29
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.32
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.29
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.66
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17213.13
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.11
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.58
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.37
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.84
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.69
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   16.79
p-value of test                       :    0.9974


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.85
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.45
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.64
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.48
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.37
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.11
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.39
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.08
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.14
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.83
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.71
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.99
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.84
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.17
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.49
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.82
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5115.19
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.74
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.64
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.06
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.47
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4831.10
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  316.76
p-value of test                       :    0.9903


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.38
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.30
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:23.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.18
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:25.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    2.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 6.18e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 8.88e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.09
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.51
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.02
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:07.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.01
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:07.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9938.09
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10239.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:56.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.75
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4671.87
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5004.08
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:52.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4325.80
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.18
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11855.17
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11726.09
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:30.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.70
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999818108

Normal statistic for number of bits   :   -1.44
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.07
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000052390

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         : -5.40e-4
p-value of test                       :    0.50

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    1.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:19.15

 All tests were passed




Server wird beendet - Lösche Semaphor 172261404.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1268
p-value of test                       :    0.9956

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334388
  j =  1                              :        599997464
  j =  2                              :             1268
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5417
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:54.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4229
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:40.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:55.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4229
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:55.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:02.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:02.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:53.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:58.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.88
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     929
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:45.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:11.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    2.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:41.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.58
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.08
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.53
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.05
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.42
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.32
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.46
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.95
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:45.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1414.14
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:59.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6931.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:40.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.08
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:03.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.31
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.45
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:35.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4725.75
p-value of test                       :    0.9993    *****


-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:56.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45939
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869939
  j =  1                              :        399908126
  j =  2                              :            45931
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45479
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869479
  j =  1                              :        399909045
  j =  2                              :            45473
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:28.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:20.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:45.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:59.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:35.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.81e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 6.30e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.18e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:21.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.041
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:34.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:35.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.19
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:47.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  108.54
p-value of test                       :  1.0e-3    *****

-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.14
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:51.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.05
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:47.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.26
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.44
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:37.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.66
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.79
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.84
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.36
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.98
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.76
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17062.33
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.10
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.98
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.68
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.21
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.94
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.79
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.94
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.80
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.95
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.13
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.88
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.99
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.63
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.56
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.38
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.09
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.69
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.58
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.13
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.42
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.09
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.40
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.38
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.93
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.78
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.74
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.30
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.16
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.63
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.73
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:34.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.86
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :   -0.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:22.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.43
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :    0.19
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:25.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.95e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:46.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.59e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 5.92e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9937

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.60
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.68
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.77
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:07.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.61
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:08.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9906.96
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10004.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:54.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.17
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4835.43
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:51.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.35
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4266.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11898.72
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:28.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11737.90
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:30.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.60
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999832070

Normal statistic for number of bits   :   -1.33
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.08
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000015217

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.60
p-value of test                       :    0.05

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:07.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 42  Permutation, t = 7              0.9993 
 60  WeightDistrib, r = 20           1.0e-3
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 173277212.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:50.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1502
p-value of test                       :  1.3e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334622
  j =  1                              :        599996996
  j =  2                              :             1502
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5473
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:59.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:41.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:57.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:57.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:04.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:03.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:51.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:57.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.70
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     645
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:12.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    2.76
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:45.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.63
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.17
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.11
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.44
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.65
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.80
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.25
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.95
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.83
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:43.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1461.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:00.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7029.33
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:43.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.58
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.53
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:25.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.42
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.44
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:34.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5120.18
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:59.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46109
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870109
  j =  1                              :        399907785
  j =  2                              :            46103
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46141
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870141
  j =  1                              :        399907725
  j =  2                              :            46127
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:29.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:18.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:44.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:58.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:54.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:34.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.93e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 6.37e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:00:24.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.43e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 6.67e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:21.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:34.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.96
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.21
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.81
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.88
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:39.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   71.35
p-value of test                       :  1.7e-3

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.70
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.66
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  159.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17168.92
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.78
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.02
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.72
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.62
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.24
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.47
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.60
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.91
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.59
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.91
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.15
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.04
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.72
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.14
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.48
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.50
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.85
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.27
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.46
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.45
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  452.58
p-value of test                       :  9.0e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.31
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.87
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.76
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.93
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.36
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.16
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5130.71
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.02
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.60
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.68
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :    0.94
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:24.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.91
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :    1.52
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:25.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.19
p-value of test                       :    0.99

Sample variance                       :    2.56
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 6.13e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.74e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 6.88e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.59
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.82
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:05.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.81
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:07.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9931.70
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9985.49
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:04:03.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.90
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4779.40
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:51.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4222.88
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.88
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11720.56
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11907.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:30.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.67
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999962756

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.59
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  7999966704

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:26.75
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 10  CollisionOver, t = 14           1.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 174293020.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5392
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:04:00.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7157
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:42.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4413
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:57.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7183
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:05.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:03.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:53.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:59.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:12.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.24
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.05
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    2.13
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     117
p-value of test                       :    0.9970

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:43.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.45
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.18
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.61
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.84
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.39
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.92
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  380.36
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:44.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1421.56
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:00.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7197.08
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.47
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.22
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:03.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.25
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.39
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5043.12
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:55.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46133
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870133
  j =  1                              :        399907736
  j =  2                              :            46129
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45597
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869597
  j =  1                              :        399908810
  j =  2                              :            45589
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:28.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:19.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:46.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:58.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:35.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 9.32e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.11
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:31.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   94.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.60
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.84
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:48.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.15
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.09
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:36.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.06
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.40
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.62
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17394.81
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.26
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.62
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.54
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.14
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.16
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.94
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.72
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.97
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.11
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.16
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.18
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.88
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.20
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.42
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.45
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.75
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.91
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.13
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.45
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.86
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.97
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5187.23
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.20
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.61
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.03
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.83
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4877.57
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.42
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.12
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:34.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.10
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :   -1.02
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:22.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.91
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:23.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.93e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 6.44e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.04e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.60
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.35
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.47
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:06.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.59
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:06.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10226.00
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9982.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:39.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5044.00
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:49.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.17
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:50.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4039.80
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.97
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11777.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11608.28
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.93
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999986081

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.56
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000138502

Normal statistic for number of bits   :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9923

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:41.19

 All tests were passed




Server wird beendet - Lösche Semaphor 175308828.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5561
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:01.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:44.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:46.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:01.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:01.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:10.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:06.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:57.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:59.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:49.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.68
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:13.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:37.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.01
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.34
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.37
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.65
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.84
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.85
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.16
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1390.97
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:04.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7230.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.39
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.46
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:09.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.90
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.59
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:36.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5161.82
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:55.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45965
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869965
  j =  1                              :        399908071
  j =  2                              :            45963
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45620
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869620
  j =  1                              :        399908762
  j =  2                              :            45616
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:30.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:18.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.63
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  5.7e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 6.17e-3
p-value of test                       :    0.9931

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:04.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:56.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:36.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 8.26e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.43e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 4.47e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:24.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.22
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.36
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.60
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.57
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.04
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.32
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.19
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:46.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9942

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.36
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.028
p-value of test                       :    0.9988

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.48
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17154.80
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.92
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.81
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.54
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.98
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.23
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.16
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.64
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.23
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.50
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.68
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.53
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.60
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.14
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.86
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.26
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.38
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.54
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.47
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.22
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.89
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.85
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4814.91
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.47
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.07
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:36.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.95
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.79
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4993.95
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.13
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.29
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.22
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :   0.034
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:22.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.71
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    2.39
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 2.24e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.22e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.51
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.33
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.95
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:04.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.04
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:06.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10071.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10169.69
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:04:24.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.51
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:53.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4785.24
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3914.81
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.37
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11779.18
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:32.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11643.06
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:31.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.57
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999815366

Normal statistic for number of bits   :   -1.46
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.67
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999901226

Normal statistic for number of bits   :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    2.07
p-value of test                       :    0.02

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:55.87

 All tests were passed




Server wird beendet - Lösche Semaphor 176324636.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  5.3e-4    *****


-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5579
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:04:00.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:43.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7475
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:43.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:57.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:57.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:04.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7169
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:05.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7142
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:54.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:59.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:12.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:39.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.97
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.27
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.14
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.86
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.59
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.89
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.32
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.04
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:45.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.89
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:59.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7185.28
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:42.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.31
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.64
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:02.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.07
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.97
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:32.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5035.88
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:59.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45998
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869998
  j =  1                              :        399908007
  j =  2                              :            45992
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45913
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869913
  j =  1                              :        399908177
  j =  2                              :            45907
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:28.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 4.58e-3
p-value of test                       :    0.9948

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:18.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:45.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:57.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 6.99e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:35.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:36.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.09
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.71
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:51.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.84
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.27
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.34
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.98
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:37.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.42
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  4.0e-3

Anderson-Darling statistic = A2       :    5.22
p-value of test                       :  2.4e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   69.29
p-value of test                       :  2.8e-3

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.98
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.82
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.74e-4
p-value of test                       :    0.9994    *****

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  171.44
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17486.99
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.79
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.61
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.94
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.62
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.56
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.31
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.69
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.30
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.99
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.93
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  189.10
p-value of test                       :  9.4e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.51
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.18
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.89
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.94
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.25
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.74
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.22
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.54
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  444.53
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.64
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.63
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  324.29
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.60
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.66
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.23
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5079.19
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.24
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.21
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.10
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :   -1.14
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:22.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.06
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:23.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 7.61e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.71e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 7.23e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.44
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.80
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.59
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:05.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.36
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:07.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9888.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10050.93
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:48.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.24
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.38
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:52.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3982.60
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3954.64
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11898.92
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11583.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:29.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.08
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999860681

Normal statistic for number of bits   :   -1.10
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.75
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000037954

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:28.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:06.35
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  2  SerialOver, r = 22              5.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 177405980.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9902


-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5441
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:04:01.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:44.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7188
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:46.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:58.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:59.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:04.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:01.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:51.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7479
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:58.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.30
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:49.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.99
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     529
p-value of test                       :    0.9983

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:12.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.30
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:41.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.97
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.83
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.92
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.71
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.71
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:09.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.58
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.95
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.38
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.08
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:44.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.14
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:59.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6974.91
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:42.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.83
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.02
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:02.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.52
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.85
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:34.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5123.70
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:00.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45931
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869931
  j =  1                              :        399908140
  j =  2                              :            45927
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45845
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869845
  j =  1                              :        399908312
  j =  2                              :            45841
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:28.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:16.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:45.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:58.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:55.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:35.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.72e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.54e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:21.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:34.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.59
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.00
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.35
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.63
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:47.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:51.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.93
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.84
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:38.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.28
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.97
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.35
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17843.68
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.30
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.35
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.32
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.53
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.39
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.80
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.09
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.64
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.94
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.69
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.34
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.92
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.08
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.46
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.47
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.44
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.45
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.87
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.77
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.48
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:43.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.31
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.26
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5019.41
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.48
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.49
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.79
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.34
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5115.41
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.48
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.56
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.33
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:21.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.12
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:23.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.48e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.84e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 6.28e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.66
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.55
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.48
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:05.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:06.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9969.11
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10025.85
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.081
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:41.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:48.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.89
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:51.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4006.40
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4038.40
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11820.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:28.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11579.76
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:31.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.24
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999978239

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.03
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000070174

Normal statistic for number of bits   :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.88
p-value of test                       :    0.03

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:28.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:45.64

 All tests were passed




Server wird beendet - Lösche Semaphor 178454556.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:40.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5345
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:01.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:44.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:47.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:02.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4244
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:04.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:13.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:11.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:05.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:04:06.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:48.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    2.05
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:12.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:41.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.63
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.30
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.33
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.06
p-value of test                       :    0.9959

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.16
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.21
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.46
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.79
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.14
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.50
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:52.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1572.31
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:02:06.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6993.21
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:56.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.20
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.78
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:17.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.53
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:46.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.11
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5153.04
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:54.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45594
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869594
  j =  1                              :        399908815
  j =  2                              :            45588
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46212
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870212
  j =  1                              :        399907579
  j =  2                              :            46206
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:32.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 7.68e-3
p-value of test                       :    0.9904

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:20.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:51.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:07.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:57.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:38.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:24.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:43.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.91
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.62
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.32
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.30
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.65
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.47
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:51.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.26
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.25
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.17
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.14
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17045.83
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.87
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.70
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.54
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.87
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.37
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.27
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.47
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.02
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.69
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.27
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.77
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.23
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.24
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.94
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.18
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.11
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.29
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.00
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.70
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.29
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.16
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.02
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4923.21
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.34
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.51
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.12
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.98
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5061.93
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.27
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.71
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.35
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:23.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.94
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:25.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.04
p-value of test                       :    0.98

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 8.55e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 4.74e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.65
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.43
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.47
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:07.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:06.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10185.70
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.05e-3
p-value of test                       :    0.9958

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10271.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:04:29.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.92
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:55.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4969.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:58.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4039.36
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4070.31
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11434.09
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:35.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11760.56
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:36.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   81.89
p-value of test                       :  8.5e-3


-----------------------------------------------
Total number of bits:  8000093625

Normal statistic for number of bits   :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.52
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000052354

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.63
p-value of test                       :    0.95

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.48
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.27
p-value of test                       :    0.01

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:26.89

 All tests were passed




Server wird beendet - Lösche Semaphor 179503132.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5394
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:00.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:43.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:43.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4210
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:00.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:01.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:11.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:08.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:03.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7494
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:04:05.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     863
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.82
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:47.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.64
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.70
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    2.08
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    3.86
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:12.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.19
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    2.42
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    2.99
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:40.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.79
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.24
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.54
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.20
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.23
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.57
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.51
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.36
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.31
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:55.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1453.22
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:05.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6963.21
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:56.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.79
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.51
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:17.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.45
p-value of test                       :    0.9940


-----------------------------------------------
CPU time used                    :  00:00:46.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.82
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:39.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4903.77
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:56.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45553
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869553
  j =  1                              :        399908898
  j =  2                              :            45545
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45894
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869894
  j =  1                              :        399908219
  j =  2                              :            45880
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:32.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:21.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:53.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:10.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:57.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:38.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.85e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.067
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:43.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:44.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.18
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.18
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   94.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.76
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.18
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.12
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.94
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:51.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.21
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.66
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.23
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.26
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17088.16
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.44
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.91
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.74
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.93
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.60
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.09
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.88
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.34
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.39
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.84
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.32
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.89
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.53
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.90
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.70
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.45
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.04
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.06
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.93
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.34
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  328.90
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4899.13
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.36
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.03
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  324.86
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.42
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.70
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.12
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.21
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.61
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:25.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.39
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :   -1.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:25.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 6.58e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 8.85e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.73
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.71
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:05.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  155.36
p-value of test                       :    0.9916

-----------------------------------------------
CPU time used                    :  00:02:09.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9983.80
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10037.26
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:10.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:04:33.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.27
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.96
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:59.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4191.58
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4188.71
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11999.23
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:35.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11998.29
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:36.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.43
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000033703

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.40
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999927413

Normal statistic for number of bits   :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.58
p-value of test                       :    0.94

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :  -0.051
p-value of test                       :    0.52

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    2.40
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:01.45

 All tests were passed




Server wird beendet - Lösche Semaphor 180617244.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1259
p-value of test                       :    0.9979

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334379
  j =  1                              :        599997482
  j =  2                              :             1259
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5602
p-value of test                       :  7.3e-3


-----------------------------------------------
CPU time used                    :  00:03:54.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:40.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:39.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4449
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:57.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:58.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:05.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:05.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7478
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:58.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:01.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     948
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    2.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:13.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:38.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.19
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.39
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.91
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.63
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.64
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.17
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.99
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.38
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.75
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:48.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.92
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:06.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7008.95
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:49.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.96
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.19
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:08.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.65
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.63
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:36.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5031.52
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:01.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45550
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869550
  j =  1                              :        399908903
  j =  2                              :            45544
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46103
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870103
  j =  1                              :        399907796
  j =  2                              :            46099
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:31.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:21.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:49.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:05.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:56.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.47e-4
p-value of test                       :  8.1e-3

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    3.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : -8.48e-4
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:39.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:40.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.65
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.21
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.90
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.83
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.67
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.30
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:45.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.66
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.96
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.36e-5
p-value of test                       : 1 -  4.4e-5    *****

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  182.78
p-value of test                       :  1.6e-3

-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17408.35
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.83
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.42
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.92
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.39
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.66
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.68
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.07
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.19
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.31
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.29
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.27
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.90
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  450.97
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.70
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.51
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.01
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.26
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.48
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.03
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.22
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.10
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.19
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.64
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.27
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.47
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.10
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.71
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5152.92
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.13
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.95
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.78
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :    1.52
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:24.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.78
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:25.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.40e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 9.11e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9904

-----------------------------------------------
CPU time used                    :  00:00:46.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.69e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.04
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.13
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.00
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:06.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.44
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:07.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9939.14
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9897.60
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:04:22.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5063.56
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:54.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4790.67
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:54.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4042.29
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.56
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:31.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11726.73
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:31.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.08
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999914885

Normal statistic for number of bits   :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.17
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999951041

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.2e-3

Anderson-Darling statistic = A2       :    5.33
p-value of test                       :  2.1e-3

Tests on the sum of all N observations
Standardized normal statistic         :    3.00
p-value of test                       :  1.4e-3

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    3.66
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    2.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:13.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    2.30
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:34.70

 All tests were passed




Server wird beendet - Lösche Semaphor 181764124.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:39.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:50.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5375
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:54.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4431
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:42.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:42.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:57.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4231
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:59.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:06.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:06.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:59.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:04:04.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:47.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:14.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.16
p-value of test                       :    0.9981

Test on the Nm values of W_{n,i}(mNP1):    2.01
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:43.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.06
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.86
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.85
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.54
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.85
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.13
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.53
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.05
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.88
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:49.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1459.84
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:04.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7016.02
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:53.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.25
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.75
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:11.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.03
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.25
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5078.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:09.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45972
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869972
  j =  1                              :        399908058
  j =  2                              :            45968
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46141
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870141
  j =  1                              :        399907724
  j =  2                              :            46129
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  8.3e-3

Anderson-Darling statistic = A2       :    3.30
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:31.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:19.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:49.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:05.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:56.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  4.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.59
p-value of test                       :  4.7e-3

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:36.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.39e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.46e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:24.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:44.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:46.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.17
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.51
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.72
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.68
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.49
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9967

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.57
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.92
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:29.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.00
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.31
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17599.58
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.98
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.13
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.93
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.95
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.78
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.24
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   63.99
p-value of test                       :  2.0e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.46
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.67
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.45
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.39
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.55
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.75
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.11
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  108.42
p-value of test                       :  5.6e-3


-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.03
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.45
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  452.69
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.09
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.66
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.61
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.63
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.43
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.56
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.30
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.88
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.02
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5068.77
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.51
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.21
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.15
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :   -1.49
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:25.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.30
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :  -0.064
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:24.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.02e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.60
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.55
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.32
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:08.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.59e-3
p-value of test                       :    0.9907

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  249.39
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:08.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9769.01
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10154.03
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:11.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:04:24.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4698.42
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:53.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5007.09
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4225.40
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.46
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11836.05
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:32.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11983.66
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:34.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.37
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000052015

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.36
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999979229

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:15.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:16.79

 All tests were passed




Server wird beendet - Lösche Semaphor 182943772.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5328
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:53.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:40.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4476
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:04.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:05.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:56.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:01.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:46.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:14.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:42.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.96
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.22
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.13
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.06
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.28
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.77
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.67
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.32
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.04
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.92
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:44.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1395.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:59.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6787.02
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:41.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.44
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.62
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:03.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.26
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.43
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:34.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5043.14
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:16.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45514
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869514
  j =  1                              :        399908976
  j =  2                              :            45506
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45508
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869508
  j =  1                              :        399908991
  j =  2                              :            45494
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:27.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:18.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 8.39e-5
p-value of test                       : 1 -  8.4e-5    *****

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9912

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:00.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:36.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.20e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:36.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.16
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.10
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   94.53
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.66
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.15
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.72
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.88
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:39.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.73
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.81
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17475.71
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.55
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.25
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.84
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.03
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   57.07
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.06
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.91
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.97
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.58
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.38
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.76
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.19
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.22
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.31
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.15
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.35
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.97
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.52
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.84
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.47
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.52
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4846.67
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.33
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.58
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.83
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.69
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5103.75
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  327.35
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.50
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:34.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.69
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :    1.50
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:20.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.40
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:22.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 1.74e-3
p-value of test                       :    0.9982

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -2.15
p-value of test                       :    0.98

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 4.09e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:46.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.56
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.48
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.34
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:07.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.67e-3
p-value of test                       :    0.9906

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.09
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:08.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10137.35
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9895.00
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:45.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4949.14
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:49.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4934.39
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:50.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4070.33
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4206.33
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12046.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:29.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11724.20
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.35
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000094804

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.69
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999998714

Normal statistic for number of bits   :  -0.010
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :  -0.069
p-value of test                       :    0.53

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    2.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    2.70
p-value of test                       :  3.8e-3

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:06.90

 All tests were passed




Server wird beendet - Lösche Semaphor 184188956.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5458
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:55.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:41.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:57.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:58.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:05.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:04.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:55.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7490
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:04:00.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.88
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.46
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.71
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:14.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.16
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:44.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.71
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.72
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.88
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.32
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.76
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.03
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.62
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.34
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:43.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1496.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:02.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7095.17
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:43.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.50
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.58
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:02.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.88
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.17
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:35.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4950.61
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:14.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46354
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870354
  j =  1                              :        399907294
  j =  2                              :            46350
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45559
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869559
  j =  1                              :        399908884
  j =  2                              :            45555
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:27.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:19.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:45.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:00.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :  4.3e-4    *****

Anderson-Darling statistic = A2       :    6.67
p-value of test                       :  4.9e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:35.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.96e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 7.34e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:38.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.35
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:49.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.94
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.46
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.99
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:49.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.48
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.79
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.63
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:43.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.86
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.18
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.88
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.63
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.02
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:37.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17285.21
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.09
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.10
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.03
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.88
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.33
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.85
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.66
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.50
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.85
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.87
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.56
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.02
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  413.63
p-value of test                       :    0.9980


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.27
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.87
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.27
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.92
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.14
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.96
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.07
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.67
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  319.80
p-value of test                       :    0.9926


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5105.79
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.19
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.54
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.92
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.97
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5319.06
p-value of test                       :  8.7e-4    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.25
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.05
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.91
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:23.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.22
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:25.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.016
p-value of test                       :    0.49

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.98e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.57e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 7.34e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.54
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.83
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.57
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:06.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.58
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:06.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9991.72
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9708.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.033
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:46.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5013.26
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:50.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.47
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:52.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4072.57
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4179.52
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11788.44
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:29.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11900.71
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:31.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.68
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000072592

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.07
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999992456

Normal statistic for number of bits   :  -0.060
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    3.15
p-value of test                       :  8.4e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:07.25
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 50  SampleProd, t = 8               4.9e-4
 79  RandomWalk1 J (L=10000, r=15)   8.7e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 185237532.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5403
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:55.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:42.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4489
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:58.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:58.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:06.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:05.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:59.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:04:02.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    2.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:49.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     561
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:14.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:46.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.90
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:55.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.37
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.98
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.66
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.23
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.98
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.06
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:20.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.66
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  262.76
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.99
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:45.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1380.70
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:03.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7190.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.87
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:05.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.73
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.59
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5014.14
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:16.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45873
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869873
  j =  1                              :        399908259
  j =  2                              :            45863
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45943
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869943
  j =  1                              :        399908118
  j =  2                              :            45935
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 8.24e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:32.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:27.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:56.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:09.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:36.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 2.46e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:42.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.67
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.86
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.16
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:49.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.95
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.01
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.60
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:44.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.25
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.02
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   13.44
p-value of test                       :  3.8e-3

-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.94
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17343.43
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.67
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.67
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.91
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.34
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.89
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.68
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.46
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.85
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.73
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.32
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.63
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.52
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.18
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.77
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.36
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.50
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  556.72
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.24
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.11
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.62
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.45
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.10
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.10
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.34
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.20
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.47
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.08
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.82
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.09
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :   -0.92
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:23.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.52
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.78
p-value of test                       :    0.96

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.59e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.31e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.71
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.29
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:06.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.75
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:07.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.58
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9626.95
p-value of test                       :    0.9962

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9978.66
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:04:13.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4852.35
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:51.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5072.24
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:52.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.01
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3990.81
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11899.29
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:30.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11907.03
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:30.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.31
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999894626

Normal statistic for number of bits   :   -0.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.29
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000122074

Normal statistic for number of bits   :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.58
p-value of test                       :    0.94

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:03.67

 All tests were passed




Server wird beendet - Lösche Semaphor 186253340.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:40.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:50.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:56.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:41.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4157
p-value of test                       :    0.9969


-----------------------------------------------
CPU time used                    :  00:01:58.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:04.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:05.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7504
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:56.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:01.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:49.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:15.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:42.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.15
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.27
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.54
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.51
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.06
p-value of test                       :    0.9924

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.28
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.38
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.83
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.91
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:44.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1483.85
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:00.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7058.56
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:44.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.45
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.01
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:09.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.26
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.30
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:34.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4989.35
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:12.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46156
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870156
  j =  1                              :        399907692
  j =  2                              :            46148
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45882
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869882
  j =  1                              :        399908241
  j =  2                              :            45872
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9952


-----------------------------------------------
CPU time used                    :  00:02:28.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:18.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:45.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:58.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:35.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.62e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.70e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.041
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.35
p-value of test                       :    0.9906

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:36.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:38.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.11
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.20
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.01
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.73
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.93
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.84
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:40.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.70
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.94
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.46
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.65
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.82
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.05
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17532.78
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.33
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.62
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.97
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.25
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.86
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.46
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.74
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.30
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.23
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.52
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.76
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.56
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.62
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.66
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.89
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.92
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.74
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.57
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.58
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.49
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.32
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.64
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4957.27
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.62
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.04
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.60
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.29
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4941.64
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.90
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.55
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.96
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:24.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.77
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :  -0.042
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:24.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :  -0.060
p-value of test                       :    0.52

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.26e-4
p-value of test                       :    0.9952

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 6.82e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.83
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.62
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 6.85e-3
p-value of test                       :    0.9927

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.96
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:05.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.41
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:06.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9882.23
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9795.02
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.040
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:53.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4887.61
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:49.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4998.63
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:50.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4174.67
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11841.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:29.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11820.82
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:30.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.68
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000076261

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.42
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000083212

Normal statistic for number of bits   :    0.66
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.55
p-value of test                       :    0.06

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:47.02

 All tests were passed




Server wird beendet - Lösche Semaphor 187269148.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5372
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:55.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:42.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4434
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:57.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:58.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:05.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:05.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:56.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:04:02.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:49.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.86
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:14.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.05
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:41.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.88
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.69
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.60
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:20.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.42
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.77
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.29
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.88
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:43.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1472.54
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:00.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7212.74
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.81
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:16.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.66
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:02.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.34
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.48
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:34.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4971.64
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:15.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45785
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869785
  j =  1                              :        399908431
  j =  2                              :            45783
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45700
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869700
  j =  1                              :        399908604
  j =  2                              :            45692
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:28.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:19.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:00.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:54.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:34.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:38.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:36.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   39.19
p-value of test                       :    0.9974

-----------------------------------------------
CPU time used                    :  00:00:48.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.66
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.02
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.45
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.67
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.48
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:38.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.79
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.33
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17398.24
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.18
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.11
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.00
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.06
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.46
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.56
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.51
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.48
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.13
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.83
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.76
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.25
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.89
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.02
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.81
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.06
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.06
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.28
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.71
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.84
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.24
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.50
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.96
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  325.81
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.97
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.95
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.54
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.54
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.40
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.06
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.76
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:22.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.96
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :   -2.29
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:02:22.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:10.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.01e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.32e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.20
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.44
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.32
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:05.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.76
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:04.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.60
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10191.29
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:36.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4843.83
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:47.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4702.07
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:50.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4043.41
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4183.03
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11975.02
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11988.23
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.47
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000049972

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.57
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000055753

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   0.036
p-value of test                       :    0.49

Sample variance                       :    1.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:01:59.60

 All tests were passed




Server wird beendet - Lösche Semaphor 188284956.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:50.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5435
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:43.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:36.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7501
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:35.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:54.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4200
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:02.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:02.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:54.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:00.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.9911

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:53.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    2.15
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:11.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:37.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.16
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.58
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.12
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.77
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.53
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.00
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.38
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  471.39
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1493.29
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:00.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7206.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.11
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.55
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:02.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.99
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.08
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:37.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4914.43
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:14.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45824
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869824
  j =  1                              :        399908355
  j =  2                              :            45818
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46063
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870063
  j =  1                              :        399907882
  j =  2                              :            46047
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:13.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:28.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:17.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:44.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:00.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:52.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:32.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.93e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 3.68e-4
p-value of test                       :  4.4e-3

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 6.34e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.057
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:39.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:39.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.73
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:48.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.97
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.16
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.37
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:50.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.26
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.52
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:43.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.07
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.71
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:31.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.97
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.24
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.46
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17439.35
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.58
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.88
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.77
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.35
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.18
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.01
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.23
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.20
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.02
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.38
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:40.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.56
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.40
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.65
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.14
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  107.98
p-value of test                       :  6.1e-3


-----------------------------------------------
CPU time used                    :  00:00:46.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.14
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.29
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.81
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.23
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.71
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.19
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.83
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5023.87
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.12
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.09
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:34.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.99
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.40
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5151.68
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  460.83
p-value of test                       :  2.3e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.05
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.83
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :    1.17
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:12.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.18
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:13.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:11.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    1.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.97e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:46.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 2.01e-3
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.76
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.75
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.53
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:13.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:09.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.89
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10016.10
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:04:03.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4838.10
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:48.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.86
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.51
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.74
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11759.90
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11826.70
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:30.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.27
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999946820

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.10
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999902372

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    2.79
p-value of test                       :  2.9e-3

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.88

Sample variance                       :    1.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:17:23.89

 All tests were passed




Server wird beendet - Lösche Semaphor 168853533.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5428
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:47.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:38.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:37.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4442
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:55.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:02.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:03.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:53.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:59.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.32
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:45.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:16.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.63
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:44.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.46
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.36
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.54
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.06
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.43
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  372.18
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:45.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1386.13
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:02.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7005.98
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:44.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.89
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.82
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:02.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.22
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.73
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:37.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5125.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:20.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46283
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870283
  j =  1                              :        399907442
  j =  2                              :            46267
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45572
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869572
  j =  1                              :        399908860
  j =  2                              :            45564
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:28.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:17.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:45.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:00.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.52e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:52.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:33.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.08e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 2.45e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 3.94e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.051
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:34.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.041
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:34.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.47
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:48.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.50
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.09
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.09
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.29
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.47
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:43.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.81
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.47
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.25
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:30.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.08
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:33.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:11.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.56
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17629.83
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.82
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.20
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.87
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.61
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.94
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.06
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.40
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.42
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.04
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.94
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.38
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.42
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  438.15
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.70
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.00
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.68
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.39
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.41
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.50
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.82
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.87
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.57
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5046.43
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.46
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.61
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.14
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.20
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.70
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  329.82
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.56
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.14
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :    1.78
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:29.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.27
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:30.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.78
p-value of test                       :    0.04

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.34e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.25
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.60
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.78
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:10.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.47
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:09.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10028.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9750.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:04:02.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.93
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:48.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.80
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:49.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4034.56
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4040.33
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11576.82
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11889.27
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:31.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.44
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000062125

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.03
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999918818

Normal statistic for number of bits   :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:10.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.19

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:14:32.60

 All tests were passed




Server wird beendet - Lösche Semaphor 169639965.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5602
p-value of test                       :  7.3e-3


-----------------------------------------------
CPU time used                    :  00:03:47.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:38.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:37.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:55.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4444
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:55.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:02.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:04.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:53.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:59.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:49.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.48
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    2.06
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    3.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:16.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.61
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:49.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.35
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:54.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.25
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.55
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.40
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.07
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.16
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:42.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1375.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:59.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7093.55
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:40.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.72
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.52
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:01.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.16
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.19
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:35.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5119.19
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:15.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:22.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45883
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869883
  j =  1                              :        399908237
  j =  2                              :            45877
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46045
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870045
  j =  1                              :        399907913
  j =  2                              :            46039
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:31.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:18.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:00.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:53.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:32.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.65e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.13
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:34.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:34.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.45
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:47.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.48
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.35
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.37
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:49.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.87
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.38
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:55.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.88
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:43.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.61
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.63
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:29.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.29
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:29.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.65
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:38.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17462.22
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.76
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.90
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.99
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.85
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.50
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.83
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.15
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.21
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.95
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.40
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.75
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.02
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.91
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.75
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.36
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.15
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.06
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  590.26
p-value of test                       :  3.3e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.63
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.35
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.32
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.06
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4932.21
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.07
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.90
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.71
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.12
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.98
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.11
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.73
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.33
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    0.93
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:30.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.61
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:27.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.74
p-value of test                       :    0.96

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    2.02
p-value of test                       :    0.02

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 5.10e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.91e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 7.71e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.83
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.38
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.27
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:06.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.68e-3
p-value of test                       :    0.9962

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.08
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:08.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10291.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10048.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.079
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:04:00.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5091.55
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:49.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4778.21
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:50.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.83
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.72
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11805.29
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:29.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11869.48
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:31.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.90
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000047932

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.90
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999863741

Normal statistic for number of bits   :   -1.08
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    2.40
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:45.21

 All tests were passed




Server wird beendet - Lösche Semaphor 170557469.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1503
p-value of test                       :  1.1e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334623
  j =  1                              :        599996994
  j =  2                              :             1503
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5440
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:48.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:38.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7476
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:37.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:55.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:55.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:02.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:03.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:54.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:59.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:13.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:42.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.24
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.29
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.42
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.06
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:10.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.73
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.24
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   85.53
p-value of test                       :  4.0e-3

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  205.22
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:43.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1489.90
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:00.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7189.78
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.71e-3
p-value of test                       :    0.9929

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   84.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:03.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.58
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.66
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:35.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4963.55
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:19.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45993
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869993
  j =  1                              :        399908015
  j =  2                              :            45991
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45543
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869543
  j =  1                              :        399908915
  j =  2                              :            45541
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:31.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:19.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:59.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:55.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:32.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.36e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.73
p-value of test                       :    0.9968

-----------------------------------------------
CPU time used                    :  00:01:35.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:36.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.07
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:47.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.92
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:47.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.15
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.11
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.38
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:38.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.06
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.57
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.32
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.70
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17316.33
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.37
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.49
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.26
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.77
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.96
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.31
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.93
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.62
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.29
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.28
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.80
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.92
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.27
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.91
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.96
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.45
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.79
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.01
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.31
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.07
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.28
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.02
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.36
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.27
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.81
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.02
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.49
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4786.73
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.27
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.55
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.62
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :    1.74
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:27.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.51
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :   -1.48
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:25.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 7.11e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:46.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.39e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 8.89e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.33
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.27
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.41
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:05.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.91
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:07.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9848.36
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10024.47
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:59.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.21
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4737.74
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:50.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4234.21
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4188.93
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11733.77
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:29.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11666.95
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.53
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999893738

Normal statistic for number of bits   :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.00
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000059989

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:55.27
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14           1.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 171409437.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:39.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:51.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5392
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:46.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:37.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7175
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:36.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:54.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:02.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7462
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:03.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:53.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:04:00.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:47.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.90
p-value of test                       :  1.2e-3

Test on the Nm values of W_{n,i}(mNP1):    5.03
p-value of test                       :  2.8e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     330
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:12.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.86
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:42.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.48
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.85
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.96
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.65
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.45
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.25
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.18
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.13
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.16
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:42.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:01.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6988.12
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:41.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.71
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:01.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.03
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.55
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:34.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5038.74
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:17.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45977
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869977
  j =  1                              :        399908050
  j =  2                              :            45969
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46034
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870034
  j =  1                              :        399907934
  j =  2                              :            46030
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:30.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:18.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:44.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:58.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:56.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:34.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.40e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:34.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:33.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:47.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.13
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.92
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:47.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.56
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.22
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.04
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:38.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.07
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.95
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.38
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17257.82
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.23
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.95
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.11
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.17
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.79
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.94
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.08
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.25
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.58
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.19
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.70
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.65
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.19
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.49
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  107.47
p-value of test                       :    0.9929


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.18
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.98
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.82
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.86
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.26
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.13
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.13
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.69
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  262.42
p-value of test                       :  2.0e-3


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.18
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.86
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.48
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.01
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.39
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.89
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:26.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.49
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :    1.39
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:24.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.89
p-value of test                       :    0.03

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 6.87e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.28
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.62
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.89
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:06.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.67
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:09.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10055.86
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9777.03
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.080
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:54.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4984.03
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.70
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:50.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4043.22
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4137.10
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11920.55
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:28.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11951.91
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.40
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999989171

Normal statistic for number of bits   :  -0.086
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.29
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999989939

Normal statistic for number of bits   :  -0.080
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.66
p-value of test                       :    0.95

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:34.04

 All tests were passed




Server wird beendet - Lösche Semaphor 172294173.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:49.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5422
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:51.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:39.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7199
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:37.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:55.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:55.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:01.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:02.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:53.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7484
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:59.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     627
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:11.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    4.65
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:02:39.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.37
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.22
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.26
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.48
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.24
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.59
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.99
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.72
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.52
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.52
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:43.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1455.52
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:00.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7087.85
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.95
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.81
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:03.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   13.69
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   85.37
p-value of test                       :    0.9914


-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5004.51
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:16.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45765
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869765
  j =  1                              :        399908472
  j =  2                              :            45761
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45784
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869784
  j =  1                              :        399908433
  j =  2                              :            45782
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 8.55e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:29.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:17.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:45.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:59.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:56.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:35.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.09e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.30e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:21.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:34.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:34.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.01
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:48.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.55
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.10
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:51.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.82
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:48.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.39
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.94
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.45
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:40.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.15
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.09
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.66
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.23
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9997    *****

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17442.58
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.90
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.97
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.31
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.70
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.63
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.20
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.23
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.95
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.13
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.02
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.73
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.65
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.44
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.52
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  105.79
p-value of test                       :  9.0e-3


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.98
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.55
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  590.71
p-value of test                       :  3.1e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.03
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.89
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.77
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.17
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.72
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.59
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.55
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.32
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.26
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4986.82
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.39
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.79
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.35
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.55
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :   -0.11
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:23.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 2.76e-4
p-value of test                       :    0.9997    *****

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.66
p-value of test                       :    0.9961

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 5.72e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.34e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.91
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.67
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.81
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:05.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.78
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:08.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9981.99
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9900.58
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:57.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4790.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:51.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.54
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.67
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11637.56
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:29.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12100.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.62
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000133030

Normal statistic for number of bits   :    1.05
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.96
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999941483

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.73

Sample variance                       :    2.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.2e-3

Anderson-Darling statistic = A2       :    3.44
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.26
p-value of test                       :    0.01

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:27.38

 All tests were passed




Server wird beendet - Lösche Semaphor 173375517.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5356
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:57.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:40.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:02.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:03.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:53.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:59.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:13.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:40.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.26
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.31
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:31.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.08
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:31.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.32
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:31.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  187.12
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.73
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:43.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1512.74
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:00.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7011.06
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:44.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.18
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.81e-3
p-value of test                       :    0.9950

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.49
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:01.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.36
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.67
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:34.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5181.93
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:14.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45747
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869747
  j =  1                              :        399908511
  j =  2                              :            45737
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46001
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870001
  j =  1                              :        399908001
  j =  2                              :            45995
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:28.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:17.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:44.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:59.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:35.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.15e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.71e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.45e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:38.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:37.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.21
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.39
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.42
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.46
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.61
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.44
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:41.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.56
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.30
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.05
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.95
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:37.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17736.77
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.47
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.78
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.54
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.10
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.09
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.42
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.92
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.66
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.10
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.17
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.71
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.73
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.39
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.79
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.45
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.52
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  589.19
p-value of test                       :  3.6e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.55
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.30
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.82
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.25
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5078.95
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.46
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.73
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.70
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.72
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.24
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.64
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.45
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.85
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :    1.25
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:22.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.99
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :   0.052
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:23.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 4.05e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 4.85e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.28
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.65
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.66
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:07.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.26
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:07.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10059.71
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10071.65
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:04:01.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4769.46
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:51.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4895.71
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:51.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3923.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4218.07
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12069.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:29.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11937.12
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:31.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.63
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000020623

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.93
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999944546

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    2.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:33.19

 All tests were passed




Server wird beendet - Lösche Semaphor 174391325.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5407
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:57.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:40.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:41.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:02.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:03.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:53.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:58.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:45.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:11.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.55
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.71
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    3.01
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:38.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   20.04
p-value of test                       :  5.5e-3

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.15
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.45
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.55
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.18
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.16
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.79
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.81
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.50
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:45.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1560.09
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:59.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6917.46
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:41.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.64
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.56
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:03.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.36
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.12
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:33.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4959.16
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:10.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45622
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869622
  j =  1                              :        399908759
  j =  2                              :            45616
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46094
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870094
  j =  1                              :        399907816
  j =  2                              :            46086
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:28.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:17.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:44.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:58.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :  4.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.94
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:01:55.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.0e-3

Anderson-Darling statistic = A2       :    3.71
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:22.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:21.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:35.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:35.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.56
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.21
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.49
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.22
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.95
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.31
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:37.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.58
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.68
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17544.10
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.21
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.83
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.89
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.57
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   38.89
p-value of test                       :  1.9e-3


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.93
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.40
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.61
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.01
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.12
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:37.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.17
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.60
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.15
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.45
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.11
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.81
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.16
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  422.33
p-value of test                       :    0.9950


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.02
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.64
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.17
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.97
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.69
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.69
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.26
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.64
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.44
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.53
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.44
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.96
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.57
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:22.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.10
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :   -1.92
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.17e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 6.96e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.36e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 8.42e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.32
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.64
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:06.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.18
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:06.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9842.26
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10248.86
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:45.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4999.16
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:50.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4969.85
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:50.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.42
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4184.89
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11476.08
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11890.21
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:30.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.07
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999951137

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.34
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999870674

Normal statistic for number of bits   :   -1.02
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:07.89

 All tests were passed




Server wird beendet - Lösche Semaphor 175439901.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:51.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5432
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:04:01.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:43.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:44.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:58.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:58.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:05.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7165
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:06.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:56.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:00.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.05
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9929

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:11.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.65
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:42.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.56
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.36
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.81
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.76
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.77
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.22
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.29
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.89
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  273.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.36
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1552.60
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:05.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6792.00
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:50.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.86
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.60
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:09.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.77
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.48
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:36.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5023.09
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:09.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45973
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869973
  j =  1                              :        399908060
  j =  2                              :            45961
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45744
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869744
  j =  1                              :        399908516
  j =  2                              :            45736
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:30.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  7.2e-3

Anderson-Darling statistic = A2       :    4.26
p-value of test                       :  6.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  4.5e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:18.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.27e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:06.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:56.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:37.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.66e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.96e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:44.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   94.25
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.38
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.51
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.54
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.95
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.47
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.09
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17237.74
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.17
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.66
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.13
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.22
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.19
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.25
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.29
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.40
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.75
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.67
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.31
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.81
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.19
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.25
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.07
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.90
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.02
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.58
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.04
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.72
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.04
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.19
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4764.57
p-value of test                       :    0.9915


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.46
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.50
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.37
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.13
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5194.29
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.90
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.77
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.90
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :   -1.33
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:21.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.58
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:23.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.81
p-value of test                       :    0.03

Sample variance                       :    2.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.08e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 6.76e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 7.13e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.33
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.07
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.82
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:06.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.56
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:07.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10123.10
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9970.96
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:04:24.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4908.38
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:53.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.23
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:54.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3994.78
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4169.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11916.52
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:33.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11836.54
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:32.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.61
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999931562

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.54
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999884141

Normal statistic for number of bits   :   -0.92
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    1.10
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.79
p-value of test                       :    0.96

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:40.97

 All tests were passed




Server wird beendet - Lösche Semaphor 176422941.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5533
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:58.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:43.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:00.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:01.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:10.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:10.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7456
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:06.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:04:10.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.86
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     325
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    5.43
p-value of test                       :  1.8e-3

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:12.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    2.14
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:41.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.61
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.08
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.84
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.17
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.22
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.81
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.85
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:32.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.27
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:01.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1472.19
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:04.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7004.96
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:57.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.25
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.53
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:15.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.11
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.26
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:42.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4913.92
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:05.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45856
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869856
  j =  1                              :        399908291
  j =  2                              :            45850
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45907
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869907
  j =  1                              :        399908188
  j =  2                              :            45903
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:32.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:53.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:08.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:56.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:38.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.08e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 2.65e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:24.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.53
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:24.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:50.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:50.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.76
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.44
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.97
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.00
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.09
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.16
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:51.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.26
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.12
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.01
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17564.67
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.67
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.21
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.97
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.86
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.12
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.28
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.78
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.88
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.28
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.80
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:36.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.27
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.65
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.12
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.37
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.85
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.96
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  195.58
p-value of test                       :  3.9e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.50
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.07
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.44
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.59
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  447.70
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4924.52
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.63
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.02
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.84
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.80
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4902.64
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  332.01
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.08
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:36.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.65
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:27.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.37
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:27.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 8.70e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.51
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.57
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.36
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:07.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.59
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:07.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9769.44
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10011.63
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.081
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:04:39.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4752.89
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:52.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  8.2e-3

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5043.71
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:55.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.84
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4174.49
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11641.27
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:32.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12089.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:34.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.34
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000062821

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.50
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999939464

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:11:22.37

 All tests were passed




Server wird beendet - Lösche Semaphor 177504285.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5424
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:52.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:38.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:38.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:55.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:03.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7496
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:04.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:54.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:59.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     861
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    2.11
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    2.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    2.23
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:15.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:41.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.58
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.43
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.60
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.93
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.74
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.41
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.45
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.05
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:42.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:59.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6936.44
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:42.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.74
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.89
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:01.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.06
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.80
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:34.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5064.05
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:02.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45714
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869714
  j =  1                              :        399908575
  j =  2                              :            45708
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46316
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870316
  j =  1                              :        399907370
  j =  2                              :            46312
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:29.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:17.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:44.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 5.89e-3
p-value of test                       :    0.9934

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.40
p-value of test                       :  5.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  1.4e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:00.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:55.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-3
p-value of test                       :    0.9987

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:35.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.52e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.09e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.025
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.027
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:36.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.77
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:38.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.08
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.13
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.35
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.80
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:48.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.66
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.37
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.15
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.26
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.98
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.60
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17538.32
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.85
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.21
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   48.31
p-value of test                       :  3.4e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.99
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.69
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.83
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.01
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.95
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.83
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.14
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.77
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.83
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.13
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.06
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.91
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.51
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.34
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.78
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.15
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.42
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.82
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.56
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.58
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.62
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  237.41
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.76
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.89
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5123.11
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.90
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.77
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.05
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:27.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.25
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:27.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.20
p-value of test                       :    0.01

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.24e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 8.26e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.01e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.13
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.05
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.92
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:06.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.14
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:06.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10021.13
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9867.81
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:49.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5097.54
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:48.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.49
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:50.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.87
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.74
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11960.57
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12062.01
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:30.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.60
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000223006

Normal statistic for number of bits   :    1.76
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.46
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000130930

Normal statistic for number of bits   :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9947

Tests on the sum of all N observations
Standardized normal statistic         :   0.091
p-value of test                       :    0.46

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   0.015
p-value of test                       :    0.49

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:53.20

 All tests were passed




Server wird beendet - Lösche Semaphor 178815005.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1463
p-value of test                       :  4.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334583
  j =  1                              :        599997074
  j =  2                              :             1463
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:51.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:39.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:38.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:56.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:57.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7123
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:04.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:04.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:54.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:59.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:14.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    3.21
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     120
p-value of test                       :    0.9934

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:45.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.80
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.34
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.43
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.19
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.75
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:10.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.30
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.23
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.04
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  192.35
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1320.04
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:02.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6820.77
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:40.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.44
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.85
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:02.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.85
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.18
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:34.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4957.14
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:04.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46014
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870014
  j =  1                              :        399907976
  j =  2                              :            46006
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46016
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870016
  j =  1                              :        399907971
  j =  2                              :            46010
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :  5.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    3.46
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:28.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:17.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:44.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:58.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:16.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:35.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.93e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 3.61e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:21.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:33.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:33.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.23
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:48.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.94
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.95
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.92
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.99
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.59
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:41.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.40
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.36
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.086
p-value of test                       :    0.9934

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17397.63
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.93
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.86
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.11
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.11
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.84
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.69
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.79
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.34
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.23
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.50
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.24
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.90
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.01
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.02
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.62
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.74
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.93
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.42
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.60
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.26
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.55
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.88
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4957.93
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.93
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.62
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.74
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.84
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5076.79
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.57
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  150.81
p-value of test                       :    0.9961


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.83
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :    1.71
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:24.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.15
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :   -1.47
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:24.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.28e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 9.67e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9907

-----------------------------------------------
CPU time used                    :  00:00:46.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.77e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.87
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.65
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.55e-3
p-value of test                       :    0.9919

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  239.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:06.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:08.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.80e-3
p-value of test                       :    0.9982

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9667.54
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9960.53
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:49.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.73
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:48.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.85
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:50.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.48
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4316.33
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11346.23
p-value of test                       :    0.9992    *****

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11877.61
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:30.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.63
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999933959

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.94
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999985493

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:05.94
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 99  HammingIndep, L=1200, r=0       0.9992 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 179863581.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:40.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5549
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:52.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:40.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:39.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:56.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:58.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:06.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:05.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:59.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:02.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.89
p-value of test                       :  1.0e-2

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.94
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:15.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:43.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.02
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.99
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.16
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.66
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:33.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:31.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.65
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:31.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.65
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:31.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.06
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.90
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1504.80
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:04.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6962.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:51.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.14
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.21
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:09.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.56
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  150.34
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:37.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5149.44
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:01.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45611
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869611
  j =  1                              :        399908782
  j =  2                              :            45603
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46031
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870031
  j =  1                              :        399907940
  j =  2                              :            46027
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:30.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:18.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:47.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:04.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:56.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:36.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.14e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 3.76e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.39e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.98
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:39.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.58
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.80
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.74
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.31
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.52
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.62
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.90
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.16
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.73
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.41
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17271.80
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.09
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.20
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.00
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.97
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.01
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.75
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.94
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.54
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.13
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.28
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.78
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.68
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.78
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.17
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.29
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.30
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.13
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.01
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.99
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.89
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.26
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.46
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.46
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.22
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.43
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.01
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.44
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4912.45
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.17
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.78
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:36.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.78
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :   -1.37
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:27.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.76
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:24.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.31e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.76e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.19
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.83
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.48
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:08.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.52
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:08.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10076.06
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9803.63
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:04:24.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.39
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:54.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5010.78
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:54.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4020.41
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3994.00
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11589.44
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:33.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11730.88
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:32.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.54
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999975344

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.15
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000096466

Normal statistic for number of bits   :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.86
p-value of test                       :    0.03

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:15.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    1.92
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:12.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:14.11

 All tests were passed




Server wird beendet - Lösche Semaphor 180879389.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:42.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:53.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:39.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:55.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:57.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:04.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:04.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:55.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:01.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    2.74
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:14.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.42
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    3.08
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     129
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:44.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.68
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.93
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.82
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.81
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.84
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.46
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.92
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  202.22
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  353.34
p-value of test                       :    0.9982

-----------------------------------------------
CPU time used                    :  00:01:43.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1501.59
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:00.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6984.30
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:42.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.78
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.83
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:02.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.29
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.12
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:35.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4894.16
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:01.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46134
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870134
  j =  1                              :        399907734
  j =  2                              :            46130
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45952
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869952
  j =  1                              :        399908102
  j =  2                              :            45940
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:28.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:18.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:45.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:00.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:54.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.83e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 3.11e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:37.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:37.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.87
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.15
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.53
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.81
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.03
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.12
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:44.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9916

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.31
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.75
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:29.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.40
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.61
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.78e-3
p-value of test                       :    0.9982

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17041.34
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:55.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.77
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.43
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.89
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.08
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.05
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.92
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.85
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.29
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.64
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.25
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.59
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.18
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.44
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.44
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.65
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.19
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.88
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.07
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  171.06
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.35
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.66
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.65
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.89
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.95
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.27
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.91
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.61
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4867.10
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.31
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.40
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.49
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:24.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.90
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   -1.42
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:24.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.45
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.87
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:06.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.44
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:07.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10083.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9778.98
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:50.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.88
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:48.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4832.15
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:51.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.61
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.27
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11509.75
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:29.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11731.70
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:30.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.27
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000087760

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.31
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  7999919892

Normal statistic for number of bits   :   -0.63
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.88

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:46.84

 All tests were passed




Server wird beendet - Lösche Semaphor 182157341.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5424
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:55.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:39.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:40.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:03.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:04.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:55.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:04:00.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    2.82
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     348
p-value of test                       :  3.6e-3

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:12.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:42.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.20
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.00
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.81
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.95
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.31
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.91
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.45
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.58
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.71
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  470.52
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:43.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1434.81
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:00.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7078.78
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:42.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.58
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.88
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.90
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:03.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.85
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  142.13
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:34.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4990.41
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:13.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46042
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870042
  j =  1                              :        399907920
  j =  2                              :            46034
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46035
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870035
  j =  1                              :        399907932
  j =  2                              :            46031
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:28.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:18.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:45.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:00.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:54.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:34.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 6.65e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:35.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.057
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:37.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   37.72
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:00:47.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.94
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.92
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.47
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.64
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.77
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:38.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.22
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.47
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.03
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.52
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17322.39
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.72
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.14
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.83
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.28
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.50
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.46
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.31
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.09
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.82
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.87
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.48
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.68
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.64
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.11
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  109.99
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.71
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.83
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.93
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.06
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.75
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.05
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4894.82
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.92
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.28
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.41
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.12
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4942.84
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.54
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.82
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.29
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :   -0.86
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:24.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.42
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  :   -1.75
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:26.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.34e-3
p-value of test                       :    0.9922

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.96
p-value of test                       :    0.02

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.67e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.44
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.66
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:08.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:07.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10059.26
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10087.59
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:45.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4918.52
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:49.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5046.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:51.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4206.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.93
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11897.18
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12076.39
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:29.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.64
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999956507

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.80
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999930194

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.67
p-value of test                       :    0.05

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:37.44

 All tests were passed




Server wird beendet - Lösche Semaphor 183074845.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1470
p-value of test                       :  2.4e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334590
  j =  1                              :        599997060
  j =  2                              :             1470
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5483
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:57.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:39.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:39.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:56.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:57.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7186
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:04.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:54.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:59.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.06
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     929
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     565
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    3.76
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.08
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.14
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:13.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.64
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:43.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.63
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.82
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.15
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:11.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.42
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.78
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.16
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.63
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.25
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:44.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.82
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:03.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6997.67
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.22
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.67
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:02.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.49
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.86
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5092.40
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:57.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45967
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869967
  j =  1                              :        399908072
  j =  2                              :            45955
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45692
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869692
  j =  1                              :        399908617
  j =  2                              :            45690
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:28.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:20.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:46.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:59.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :  2.7e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    5.42
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:36.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 5.39e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:38.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:40.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.93
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.97
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.90
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.87
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.24
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:43.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.86
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.44
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:30.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.93
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17149.41
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.02
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.63
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.12
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.63
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.82
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.14
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.71
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.83
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.77
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.24
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.27
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.54
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.82
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.36
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.86
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.70
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.39
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.96
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.78
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.18
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.60
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.58
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.88
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  331.79
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.08
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.44
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.98
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5082.03
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.88
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.60
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.13
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:24.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.13
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :   -2.29
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:02:22.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.55
p-value of test                       :  1.0e-3

Anderson-Darling statistic = A2       :    4.29
p-value of test                       :  6.6e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.53
p-value of test                       :  5.7e-3

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 5.92e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.33e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.11
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.01
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.45
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:06.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.63
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:06.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10062.00
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10047.28
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:04:06.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4897.06
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.59
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:51.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11850.25
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:29.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11874.21
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:30.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.67
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000118363

Normal statistic for number of bits   :    0.94
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.85
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000034570

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :  -0.085
p-value of test                       :    0.53

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:14.62

 All tests were passed




Server wird beendet - Lösche Semaphor 184025117.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:50.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5436
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:55.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4236
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:41.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:56.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:58.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:05.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:04.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:55.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:04:01.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:48.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.61
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.76
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:17.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:43.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.96
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.74
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.01
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.22
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.15
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.55
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.06
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  478.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:44.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1460.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:00.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7055.34
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:41.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.14
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.69
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:03.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.15
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:33.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5138.54
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:02.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45820
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869820
  j =  1                              :        399908363
  j =  2                              :            45814
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46012
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870012
  j =  1                              :        399907977
  j =  2                              :            46010
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:28.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:20.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:55.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:34.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.54e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.74e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 8.36e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:21.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.99
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.22
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.34
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.24
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.76
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.56
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.56
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:41.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.75
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.49
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.49
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.2e-3

Anderson-Darling statistic = A2       :    3.23
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17837.55
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.25
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.89
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.10
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.76
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.87
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.31
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.02
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.86
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.63
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.56
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.10
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.34
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.69
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.77
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.90
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.17
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.57
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.83
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.52
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.14
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.35
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.49
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.20
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.44
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.16
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  440.82
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.98
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.55
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.39
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.89
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -5.96e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:23.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.55
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :    1.30
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:23.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :  -0.049
p-value of test                       :    0.52

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    2.32
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.68e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 7.19e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9948

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 3.39e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.93
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.93
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.28
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:09.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.36
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:08.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10136.81
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9933.61
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.047
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:55.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:42.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.42
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:48.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4969.47
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:51.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.98
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12045.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12018.67
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.38
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999921203

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.01
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999864092

Normal statistic for number of bits   :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:51.46

 All tests were passed




Server wird beendet - Lösche Semaphor 185171997.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:50.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5346
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:56.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:41.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:42.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:57.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4477
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:58.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:06.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:05.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:55.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:04:02.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.99
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    3.02
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     840
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.63
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.75
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     637
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:15.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:45.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.86
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.88
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   37.59
p-value of test                       :  4.4e-3

-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.65
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.45
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.55
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.04
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.75
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:44.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.56
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:00.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7092.79
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.59
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.59
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.59
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:03.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.13
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.03
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:50.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5182.83
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:32.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:17.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45563
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869563
  j =  1                              :        399908879
  j =  2                              :            45553
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45828
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869828
  j =  1                              :        399908350
  j =  2                              :            45816
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:27.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:18.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.62e-3
p-value of test                       :    0.9972

Anderson-Darling statistic = A2       :    3.45
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9957


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.9e-3

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:45.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:01.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:34.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 8.06e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.089
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:34.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.67
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.69
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.23
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.39
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.24
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.42
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.56
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:38.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.27
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.93
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.27
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.92
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17754.31
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.98
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.60
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.10
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.14
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.52
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.88
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.79
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.50
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.18
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.68
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.31
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.22
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.34
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.32
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.14
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.95
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.65
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.58
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.03
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.98
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.00
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.49
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5079.19
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.82
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  239.47
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.29
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.64
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4862.17
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.53
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.84
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.52
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :   -1.34
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:22.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.05
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :    1.13
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:23.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.33
p-value of test                       :    0.9901

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.89e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 9.43e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.14
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.42
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.04
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:05.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.30
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:08.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9890.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10146.11
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:42.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4996.40
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4905.11
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:50.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4035.22
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.79
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11877.18
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12029.18
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.32
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999895004

Normal statistic for number of bits   :   -0.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.78
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000100036

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:32.53

 All tests were passed




Server wird beendet - Lösche Semaphor 186220573.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5429
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:56.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:42.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4223
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:58.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:05.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:06.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:55.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:01.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    2.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.16
p-value of test                       :    0.9974

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:14.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.17
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:44.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.52
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.74
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.05
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.91
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.16
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.22
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  202.08
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.63
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:43.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1328.88
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:00.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7007.70
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:42.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.85
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.26
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:03.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.86
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.70
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:34.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5031.77
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:57.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46013
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870013
  j =  1                              :        399907976
  j =  2                              :            46009
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45657
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869657
  j =  1                              :        399908689
  j =  2                              :            45651
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:28.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:20.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:46.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:01.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:34.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 7.56e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.69e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:34.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:35.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.74
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.64
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.49
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.86
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.94
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.37
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:44.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.25
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.02
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.05
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17685.83
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.24
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.63
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.36
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.95
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.24
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:38.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.60
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.81
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.71
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.06
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.60
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.57
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.14
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.94
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.79
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.69
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.05
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.22
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.12
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.14
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.92
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.02
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.18
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5125.22
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.38
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.97
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.20
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.47
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4996.90
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.41
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.18
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.99
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :   0.034
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:22.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.41
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:23.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.88e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 9.61e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 7.15e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.49
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.99
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:06.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.13
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:07.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10027.92
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9959.63
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:40.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4933.76
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.97
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:50.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.00
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3979.91
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12046.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:28.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11565.70
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:30.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.15
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000116260

Normal statistic for number of bits   :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.77
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000187801

Normal statistic for number of bits   :    1.48
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         : 7.18e-3
p-value of test                       :    0.50

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.09

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:14.88

 All tests were passed




Server wird beendet - Lösche Semaphor 187236381.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5461
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:55.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:41.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:43.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:58.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4224
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:59.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:10.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:08.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:04:01.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:04:05.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    2.53
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:49.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.95
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    3.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.75
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     335
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:14.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:42.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.64
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.64
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.70
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.51
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.74
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.12
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   30.01
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.34
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:48.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1485.05
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:04.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7160.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:50.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.00
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.91
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:10.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.52
p-value of test                       :    0.9913


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.48
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:37.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5207.38
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:01.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45983
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869983
  j =  1                              :        399908036
  j =  2                              :            45979
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45870
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869870
  j =  1                              :        399908263
  j =  2                              :            45864
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:30.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:20.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:46.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:04.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:36.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.81e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.085
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:43.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.31
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.82
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.38
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.28
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.53
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.25
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.39
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.86
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.99
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.29
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.48
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17325.47
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.65
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.63
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.40
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.70
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.63
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.32
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.13
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.45
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.36
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.90
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.16
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.12
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.25
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.38
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.50
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.11
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.00
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.95
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.14
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.02
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:43.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.35
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.47
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4916.06
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.83
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.74
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.02
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.04
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4880.55
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.53
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  152.54
p-value of test                       :    0.9947


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.77
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:22.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.07
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:22.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.10
p-value of test                       :    0.98

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.86e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.74
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.13
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.08
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:05.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.58
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:05.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10199.45
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9995.01
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:04:15.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4760.68
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:52.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5033.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:53.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4123.66
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11654.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11892.63
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:29.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.85
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000047911

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.17
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999906296

Normal statistic for number of bits   :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.72
p-value of test                       :    0.04

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.92

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:02.61

 All tests were passed




Server wird beendet - Lösche Semaphor 188252189.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:50.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1266
p-value of test                       :    0.9963

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334386
  j =  1                              :        599997468
  j =  2                              :             1266
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5480
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:42.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:36.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:35.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4217
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:55.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:02.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:02.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:54.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:00.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:53.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.84
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.13
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    2.16
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:11.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.74
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:38.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.84
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.68
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   44.04
p-value of test                       :  5.7e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.79
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.40
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.74
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.49
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.59
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.50
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:49.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.51
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:59.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7137.73
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:48.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.65
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:02.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.40
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.41
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:37.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4893.70
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:15.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:13.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45862
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869862
  j =  1                              :        399908278
  j =  2                              :            45858
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45773
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869773
  j =  1                              :        399908459
  j =  2                              :            45763
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:28.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:17.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:44.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:00.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:52.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:33.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.72e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.35e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:37.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:38.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.03
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.38
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.83
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:50.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.39
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.48
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:44.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.93
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.97
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.05
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:31.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.54
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:29.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.95
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17259.61
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.58
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   59.30
p-value of test                       :  6.3e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.28
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.98
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.07
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.01
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.18
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.77
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.85
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.57
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.52
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.11
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.11
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.47
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.30
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:47.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.16
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.16
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.60
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.54
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.97
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.28
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.73
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4978.37
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.44
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.90
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.76
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.09
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.36
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.98
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.28
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:34.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.95
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :   -1.92
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:13.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.89
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :   -1.54
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:13.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.97e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 7.81e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.47
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.29
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.11
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:12.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.81
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:10.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9900.02
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10057.45
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:04:02.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.43
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:49.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4902.55
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:49.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4247.55
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11847.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11775.68
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.37
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999902468

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.66
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  7999878399

Normal statistic for number of bits   :   -0.96
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :  -0.097
p-value of test                       :    0.54

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:29.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:17:07.88
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 28  SimpPoker, r = 0                5.7e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 168886302.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  5.3e-3


-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5434
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:44.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:37.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:36.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4433
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:54.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4447
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:02.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:02.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:54.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7186
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:00.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.04
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.87
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     859
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.46
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     559
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.63
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.65
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    7.07
p-value of test                       :  3.2e-4    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     231
p-value of test                       : 1 -  2.0e-5    *****

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:14.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.53
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:40.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.85
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.30
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.56
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.90
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.50
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.16
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.32
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.94
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.46
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:43.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.44
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:59.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7073.71
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.11
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.28
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:02.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.55
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.82
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:35.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5105.34
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:02.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45773
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869773
  j =  1                              :        399908457
  j =  2                              :            45767
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45931
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869931
  j =  1                              :        399908143
  j =  2                              :            45921
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:30.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.29
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:17.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-3
p-value of test                       :    0.9985

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:00.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:53.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:33.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.37e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 4.91e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 7.89e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:34.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:34.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.96
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:47.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.82
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.14
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.44
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:38.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.11
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.71
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.02
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:29.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.15
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.35
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17434.31
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.36
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.80
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.43
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.47
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.87
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.45
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.55
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.69
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.80
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.84
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.19
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.10
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.97
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.55
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:46.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.43
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.15
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.86
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.36
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.75
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.10
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.03
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4901.88
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.88
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.57
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.45
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.05
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4922.81
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.72
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.80
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.57
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :    1.33
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:19.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.95
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:17.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    2.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.16e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:47.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.28e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 7.48e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.47
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.04
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.81
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:07.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    3.58
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.52
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:12.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10012.85
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  2.9e-3

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10271.42
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.056
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:04:06.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4812.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:49.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4729.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:49.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4059.75
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4192.98
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11740.26
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12174.88
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:29.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.10
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000077392

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.20
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999967028

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:09.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.5e-3

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.89
p-value of test                       :    0.03

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:47.65
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP1, t = 9          3.2e-4
 24  ClosePairs NJumps, t = 9       1 -  2.0e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 169574430.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:05.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:05.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1499
p-value of test                       :  1.7e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334619
  j =  1                              :        599997002
  j =  2                              :             1499
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5395
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:47.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4427
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:38.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:37.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4463
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:06.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:07.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:04:03.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:06.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:48.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:16.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.37
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     126
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:51.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.42
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.55
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.04
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.31
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.43
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.10
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.13
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.13
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  196.51
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:55.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1478.18
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:02.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7050.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:51.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.79
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.94
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:14.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.70
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.30
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4889.35
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:19.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45866
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869866
  j =  1                              :        399908269
  j =  2                              :            45864
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45739
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869739
  j =  1                              :        399908524
  j =  2                              :            45735
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:32.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:19.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:46.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:03.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9941

-----------------------------------------------
CPU time used                    :  00:01:38.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.42e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:24.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:24.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:24.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.065
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:50.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.43
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.92
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.86
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.24
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.05
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:51.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.49
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 8.64e-3
p-value of test                       :    0.9907

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.21
p-value of test                       :    0.9936

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.13
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:30.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.82
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:31.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  103.63
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17574.48
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   56.54
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.05
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.67
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.60
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   55.04
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.02
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.13
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.01
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.85
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.23
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.47
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.53
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.94
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.51
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.19
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.99
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.94
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.11
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.16
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.52
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.11
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4876.62
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.92
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.46
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.07
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.35
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.36
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.12
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.37
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.18
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:27.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.91
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :    1.77
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:24.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 6.92e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.82e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 4.53e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   22.97
p-value of test                       :  3.4e-3

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.94
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.36
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:09.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.21
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:08.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9983.24
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10185.25
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.099
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:04:29.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4913.01
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:55.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4777.19
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:59.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4000.85
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4260.68
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11567.80
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:35.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11624.11
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:37.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.02
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000060886

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.27
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000009820

Normal statistic for number of bits   :   0.078
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.27

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:15.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 8.85e-3
p-value of test                       :    0.9904

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.83
p-value of test                       :    0.03

Sample variance                       :    2.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:17:40.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  6  CollisionOver, t = 3            1.7e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 170393630.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5428
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:49.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4471
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:39.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:38.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4159
p-value of test                       :    0.9966


-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7173
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:03.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:03.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:55.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:00.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     942
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:47.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.9916


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9955

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:14.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:42.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.61
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.49
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.00
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.72
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.29
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:10.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.30
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.02
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.92
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:43.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1486.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:01.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6983.29
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.20e-3
p-value of test                       :    0.9956

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.56
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:04.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.74
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.51
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:35.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4994.26
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:02.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46487
p-value of test                       :  2.3e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870487
  j =  1                              :        399907028
  j =  2                              :            46483
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46055
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870055
  j =  1                              :        399907896
  j =  2                              :            46043
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:27.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:17.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:44.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:01.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9937

-----------------------------------------------
CPU time used                    :  00:01:54.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:32.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.91e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 7.63e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:34.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:33.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.57
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.84
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.53
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.94
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.50
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.96
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   12.34
p-value of test                       :    0.9971

-----------------------------------------------
CPU time used                    :  00:01:45.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.65
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.09
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.94
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:29.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.33
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17301.96
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:54.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.06
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.02
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.67
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.55
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.28
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.93
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.74
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.47
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.18
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.04
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.31
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.72
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  568.45
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.99
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.93
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.85
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.92
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.55
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.43
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.20
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.07
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.68
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.88
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.22
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.53
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.01
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.32
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5140.58
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.06
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.56
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.88
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :    1.23
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:28.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.48
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :   -1.27
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:29.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.49e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 8.19e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.42
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.09
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.08
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:08.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.47
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:06.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10003.85
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9908.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.035
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:53.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.59
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:50.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.02
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:50.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.04
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4006.86
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11656.00
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11974.63
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:30.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.44
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999917426

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.16
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  8000116392

Normal statistic for number of bits   :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    1.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    2.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:38.62

 All tests were passed




Server wird beendet - Lösche Semaphor 171933726.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5349
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:49.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:39.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:38.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:56.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:03.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:05.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:59.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:04:03.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.84
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    2.12
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     642
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.97
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.80
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:15.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.31
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    3.16
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:43.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.27
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.72
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.40
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.30
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:12.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.03
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.75
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.68
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.26
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.78
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:50.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1491.26
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:00.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7057.80
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:52.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.26
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.53
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:12.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.59
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.27
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:37.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5036.54
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:05.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46143
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870143
  j =  1                              :        399907719
  j =  2                              :            46133
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45810
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869810
  j =  1                              :        399908383
  j =  2                              :            45804
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:31.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :  6.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.59
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:18.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:03.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:55.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :  1.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    5.31
p-value of test                       :  2.1e-3

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:49.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:48.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.10
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.23
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.65
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.34
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.16
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.22
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:47.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.07
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.86
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.62
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17484.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.31
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.65
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.60
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.68
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.99
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.71
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.61
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.84
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.48
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.65
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.25
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.03
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.57
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.35
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.99
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.82
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.25
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.16
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.29
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.77
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.53
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.54
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5039.14
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.67
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.97
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.31
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.74
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4881.29
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.30
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.72
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.39
p-value of test                       :    0.9921


-----------------------------------------------
Normal statistic for number of jumps  :    0.69
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:27.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.00
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:29.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.70e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 6.38e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.08
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.09
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.56
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:07.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.84
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:06.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9864.73
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.31
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:10.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:04:26.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.52
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:55.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4774.45
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4162.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4198.15
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11774.83
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:33.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11790.63
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:31.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.00
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000060115

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.49
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000003931

Normal statistic for number of bits   :   0.031
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:11.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:07.63

 All tests were passed




Server wird beendet - Lösche Semaphor 172752926.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:42.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5574
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:50.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:39.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7175
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:37.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4215
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:57.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:05.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:07.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:59.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:04.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.18
p-value of test                       :    0.9956

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:47.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:13.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:43.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.27
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.20
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.08
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.98
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.47
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.50
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.99
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.30
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  485.28
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:51.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1495.47
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:00.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7074.22
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:50.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.11
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.58
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:09.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.91
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.68
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:37.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5009.92
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:00.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45620
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869620
  j =  1                              :        399908766
  j =  2                              :            45608
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46240
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870240
  j =  1                              :        399907524
  j =  2                              :            46232
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:29.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:17.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:01.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:55.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:35.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 4.24e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:43.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:41.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.61
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.69
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.87
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.14
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.09
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:45.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.06
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 9.08e-3
p-value of test                       :    0.9901

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.25
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.58
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:29.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.03
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9916

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17420.63
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.12
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.60
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.50
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.21
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.11
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.40
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.00
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.89
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.38
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.88
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.40
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.27
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.66
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.89
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.05
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.42
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.11
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.83
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.18
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.07
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.88
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.46
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.55
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.81
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.61
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:36.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.68
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.12
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5072.54
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.05
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.63
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.71
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:27.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.14
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:26.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :  -0.076
p-value of test                       :    0.53

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:46.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.31e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 7.73e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.66
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.11
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.67
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:09.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.42
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:07.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10012.66
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10018.96
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:04:22.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4794.08
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:54.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4775.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:54.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4003.75
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3901.84
p-value of test                       :    0.9919

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11631.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11938.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:29.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.14
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000061570

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.56
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999936251

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.61
p-value of test                       :    0.95

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:19.82

 All tests were passed




Server wird beendet - Lösche Semaphor 173867038.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5318
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:53.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:57.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:05.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:05.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:54.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:00.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     847
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.17
p-value of test                       :    0.9958

Stat. AD after spacings (mNP2-S)      :    3.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    2.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     337
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    2.12
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:14.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:46.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.54
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.45
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.93
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.60
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:11.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.28
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.97
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.59
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.56
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  389.83
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:47.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1519.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:01.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7055.85
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.49
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.69
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:01.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   13.18
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.69
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:34.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5217.34
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:00.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45783
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869783
  j =  1                              :        399908437
  j =  2                              :            45777
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45920
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869920
  j =  1                              :        399908165
  j =  2                              :            45910
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:28.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:18.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:00.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:54.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:34.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 5.63e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.01
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   97.01
p-value of test                       :  9.7e-3

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.53
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.19
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   13.93
p-value of test                       :    0.9917

-----------------------------------------------
CPU time used                    :  00:01:44.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.58
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.24
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:29.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.54
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17498.73
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.42
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.95
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.74
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.69
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.36
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.85
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.07
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   50.73
p-value of test                       :  1.1e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.56
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.96
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.39
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.80
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.79
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.52
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.79
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.03
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.98
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.77
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.79
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.49
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.76
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5286.82
p-value of test                       :  2.4e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.21
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.08
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.39
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.34
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.42
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.10
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.59
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.81
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :   -1.46
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:25.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.28
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :  -0.015
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:26.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.03e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 6.68e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:46.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 7.99e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.55
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.98
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.06
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:06.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.51
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:08.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10098.05
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10011.87
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:55.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4975.24
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5028.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:50.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4040.13
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.86
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11812.32
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11786.99
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:29.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.31
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000061663

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.79
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999905561

Normal statistic for number of bits   :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.23

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:23.79

 All tests were passed




Server wird beendet - Lösche Semaphor 174948382.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5420
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:52.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:40.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:39.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:57.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7502
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:04.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:05.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:56.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:04:01.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.47
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     641
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    3.94
p-value of test                       :  9.4e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     340
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:13.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:43.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.53
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.41
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.87
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.55
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.00
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.17
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.13
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.70
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1461.82
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:02.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7022.46
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:44.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.89
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.75
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   91.89
p-value of test                       :  5.1e-3

-----------------------------------------------
CPU time used                    :  00:03:02.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.26
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.42
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:35.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5021.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:05.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45945
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869945
  j =  1                              :        399908113
  j =  2                              :            45939
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45982
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869982
  j =  1                              :        399908040
  j =  2                              :            45974
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:28.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:19.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:46.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:01.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:00.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:40.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:35.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.040
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:36.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.19
p-value of test                       :    0.9924

-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.64
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.14
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.11
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.97
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.61
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   14.93
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:42.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.41
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.31
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.37
p-value of test                       :  9.9e-3

-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:17.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.85
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17608.42
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:54.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.72
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.94
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.97
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.06
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.00
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.92
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.38
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.21
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.52
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.11
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.90
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.45
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  562.13
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.28
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.03
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:46.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.68
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.55
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.18
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.76
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.56
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.00
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.98
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4972.44
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.05
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  238.66
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.75
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.24
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.13
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.33
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.63
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.23
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:23.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.09
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:23.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.58e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.82e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.42
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.83
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.78
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:07.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:08.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9932.21
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9882.13
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.076
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:51.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4910.69
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:49.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.68
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:50.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.09
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4178.94
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12065.99
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11737.60
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:29.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.40
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999880691

Normal statistic for number of bits   :   -0.94
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.55
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999937850

Normal statistic for number of bits   :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.79
p-value of test                       :    0.04

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.75
p-value of test                       :    0.96

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:21.82

 All tests were passed




Server wird beendet - Lösche Semaphor 175964190.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:51.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5407
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:53.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:40.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:38.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:57.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:06.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:05.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:59.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:04:03.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    5.14
p-value of test                       :  2.5e-3

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.77
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.68
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:13.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.88
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:40.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.45
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.47
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.97
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.22
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.76
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:11.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.05
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.73
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.45
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.04
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.17
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:52.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1541.73
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:00.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6947.08
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:50.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.88
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.23
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:09.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.73
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.81
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:37.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5020.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:59.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46036
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870036
  j =  1                              :        399907932
  j =  2                              :            46028
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45958
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869958
  j =  1                              :        399908085
  j =  2                              :            45956
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:29.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  6.4e-3

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:17.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:46.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:02.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.41e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:39.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:40.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.96
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.63
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.65
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.87
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.42
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:48.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.35
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.86
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.12
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.68
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:29.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  156.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17320.12
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.09
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.68
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.04
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.84
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.71
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.46
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.37
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.04
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.01
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.81
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.79
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.05
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.26
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.43
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.44
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.46
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.86
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.74
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.44
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.11
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.61
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5023.56
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.57
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.62
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.31
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.13
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.69
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.49
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.46
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.17
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -1.33
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:25.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.36
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :    1.65
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:25.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.40e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 7.13e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.42e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.54
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.41
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.51
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:07.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.91
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:06.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10048.58
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 7.59e-3
p-value of test                       :    0.9919

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9761.08
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:04:20.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9953

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.30
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:53.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.93
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.09
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4196.54
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11790.88
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:32.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11810.75
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:31.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.82
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000139114

Normal statistic for number of bits   :    1.10
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.09
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000080443

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.43

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   0.073
p-value of test                       :    0.47

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:34.87

 All tests were passed




Server wird beendet - Lösche Semaphor 176914462.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1470
p-value of test                       :  2.4e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334590
  j =  1                              :        599997060
  j =  2                              :             1470
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5410
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:51.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:39.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:40.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4220
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4442
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:57.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:04.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:05.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:54.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:04:00.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.17
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.02
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:47.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.06
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:14.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.95
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:42.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.68
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.57
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.52
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.48
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.03
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.83
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.32
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.82
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  482.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1465.92
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:00.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7283.60
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:44.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.15
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:02.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.90
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.90
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4947.55
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:00.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45926
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869926
  j =  1                              :        399908152
  j =  2                              :            45918
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45703
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869703
  j =  1                              :        399908599
  j =  2                              :            45693
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9916

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:27.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:17.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:45.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:58.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:55.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:35.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 8.05e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.71e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:21.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:21.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:33.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.96
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:48.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.44
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.13
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.80
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.74
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.10
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:44.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.48
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.85
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.47
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:30.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.13
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:29.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   11.73
p-value of test                       :  2.8e-3

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.39
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17586.87
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   17.61
p-value of test                       :    0.9957


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.19
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.26
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.76
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.23
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.86
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.27
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.94
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.41
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.15
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.79
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.17
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.11
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.16
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.29
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  192.85
p-value of test                       :  5.7e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.72
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.66
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.38
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.24
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.89
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4874.95
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.62
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  154.79
p-value of test                       :    0.9923


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.02
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.01
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.88
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.64
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.33
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.99
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:24.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.69
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:27.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   0.027
p-value of test                       :    0.49

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.27e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:46.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.07e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 7.17e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.04
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:29.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.23
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.93
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:09.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.20
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:07.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9939.38
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9926.67
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:47.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4837.74
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:48.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.05
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:50.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.83
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.81
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11707.22
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12045.65
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.69
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999899540

Normal statistic for number of bits   :   -0.79
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.30
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000050587

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.12

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:18.57

 All tests were passed




Server wird beendet - Lösche Semaphor 178159646.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  3.6e-3


-----------------------------------------------
CPU time used                    :  00:00:55.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5401
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:52.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:40.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:39.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4484
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:57.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7193
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:04.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:04.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:55.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:00.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.21
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     944
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:15.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:46.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.18
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.55
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.44
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.46
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.23
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.62
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.45
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.37
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  471.87
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:44.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1358.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:59.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7159.08
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:45.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.87
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.32
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:01.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.69
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.46
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5061.19
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:01.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45713
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869713
  j =  1                              :        399908578
  j =  2                              :            45705
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45644
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869644
  j =  1                              :        399908716
  j =  2                              :            45636
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:27.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.78e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    4.08
p-value of test                       :  8.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  2.3e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  9.9e-3

Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
p-value of test                       :    0.9998    *****

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:17.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:44.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:57.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:32.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 5.43e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:22.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:34.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:34.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.08
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.86
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.85
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.78
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.66
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.80
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:45.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.73
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.33
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.81
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.03
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17397.21
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.94
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.76
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.75
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.15
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.64
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.80
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.02
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.08
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.65
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.24
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.08
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.87
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.45
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  167.33
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.87
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:46.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.21
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.02
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.89
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.72
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.26
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.98
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.54
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.65
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.35
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:36.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.04
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.05
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4945.17
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.85
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.27
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.19
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :    2.29
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:02:24.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.14
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :   -1.20
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:24.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.79
p-value of test                       :    0.96

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.43
p-value of test                       :    0.08

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.44e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:47.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 6.29e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.87
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.40
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.62
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:07.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:07.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10110.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9716.01
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:52.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.20
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:49.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5015.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:50.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.19
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4059.12
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12106.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11794.06
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:29.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.36
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999897437

Normal statistic for number of bits   :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.52
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999944870

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:45.55

 All tests were passed




Server wird beendet - Lösche Semaphor 179208222.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5372
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:53.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7145
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4168
p-value of test                       :    0.9949


-----------------------------------------------
CPU time used                    :  00:01:59.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:00.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7522
p-value of test                       :  9.0e-3


-----------------------------------------------
CPU time used                    :  00:03:08.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:09.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7166
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:04:05.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:10.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    2.75
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:49.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:16.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.59
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:43.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.54
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.51
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.42
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.48
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.32
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.00
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:53.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1550.78
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:01.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6891.17
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:55.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.96
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   37.40
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:03:18.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.30
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.12
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:38.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5067.25
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:05.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45550
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869550
  j =  1                              :        399908902
  j =  2                              :            45546
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45541
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869541
  j =  1                              :        399908921
  j =  2                              :            45535
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:32.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:20.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:50.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:06.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:56.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:37.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.13e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 3.65e-4
p-value of test                       :  4.9e-3

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.35e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 7.69e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:24.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:45.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.83
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.52
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:50.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.20
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.32
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.15
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:50.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.59
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.03
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.56
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.50
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.24
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17080.47
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   60.10
p-value of test                       :  7.1e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.24
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.45
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.84
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.54
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:39.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.28
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.62
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.43
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.34
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.53
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.62
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.74
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.81
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.29
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.52
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.39
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.40
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.09
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.37
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.61
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.43
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5163.39
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.04
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.69
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.34
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.06
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5178.31
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.87
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.96
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.73
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:28.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.48
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :    1.21
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:28.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.80
p-value of test                       :    0.96

Sample variance                       :    0.23
p-value of test                       :    0.9906

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 4.97e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:46.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 6.30e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.75
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.77
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.22
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:07.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.7e-3

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:07.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10000.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10042.94
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:11.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:04:28.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4763.91
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.31
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:58.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4260.27
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4040.30
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11770.17
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:34.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11636.87
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:34.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.54
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999973229

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.03
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999977846

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-3
p-value of test                       :    0.9979

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.25
p-value of test                       :    0.01

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :  -0.069
p-value of test                       :    0.53

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:07.90

 All tests were passed




Server wird beendet - Lösche Semaphor 180158494.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5398
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:53.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:40.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7498
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:40.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:57.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:05.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:05.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:55.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7192
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:04:00.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.9904

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    2.68
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     567
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    2.91
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     339
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:12.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.91
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.90
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:41.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.69
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.23
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.45
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.75
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.06
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.82
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.25
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.69
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.67
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:44.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1429.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:00.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7377.16
p-value of test                       :  3.0e-3

-----------------------------------------------
CPU time used                    :  00:01:44.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.92
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.92
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:02.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.49
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  144.07
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:34.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5164.76
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:58.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45700
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869700
  j =  1                              :        399908603
  j =  2                              :            45694
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45881
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869881
  j =  1                              :        399908240
  j =  2                              :            45877
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:27.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:17.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:43.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:59.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:32.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 4.17e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.72e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.082
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:39.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:39.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.73
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.22
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.28
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.75
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.32
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.92
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:40.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.25
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.088
p-value of test                       :    0.9933

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.71
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 8.59e-3
p-value of test                       :    0.9907

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   95.38
p-value of test                       :    0.9902

-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17407.85
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.57
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.50
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.09
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.91
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.63
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.22
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.68
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.27
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.75
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.93
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.37
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.75
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.46
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.35
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.19
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.93
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.14
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  555.76
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   98.64
p-value of test                       :    0.9933


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.23
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.95
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.11
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.37
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.58
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.00
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.96
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.06
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4743.52
p-value of test                       :    0.9954


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.50
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.86
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.99
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:25.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.08
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -1.71
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:25.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 6.01e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.32e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.17
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.23
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.28
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:07.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.35
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:05.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10032.57
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9911.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:52.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4723.70
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:49.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4993.92
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:50.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3930.82
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4175.50
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11720.14
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11826.37
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.47
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000080071

Normal statistic for number of bits   :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.28
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000131230

Normal statistic for number of bits   :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.50
p-value of test                       :    0.07

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:38.35

 All tests were passed




Server wird beendet - Lösche Semaphor 181338142.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5379
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:52.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4521
p-value of test                       :  2.8e-3


-----------------------------------------------
CPU time used                    :  00:01:40.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:40.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:56.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:04.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:06.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:56.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:01.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    3.97
p-value of test                       :  9.0e-3

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    3.31
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:14.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:45.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.99
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.24
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.42
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.78
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.93
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.08
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  197.35
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.51
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:43.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1459.01
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:59.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7082.28
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:44.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.28
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.20
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:02.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.74
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  142.87
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:34.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4818.64
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:57.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45825
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869825
  j =  1                              :        399908352
  j =  2                              :            45821
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45613
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869613
  j =  1                              :        399908777
  j =  2                              :            45607
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:26.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :  7.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:17.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:44.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:57.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.05e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:35.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:35.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.99
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:48.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.47
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.96
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.34
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.92
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.98
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.20
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:42.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.21
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.93
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.12
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.62
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.58
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17397.69
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.00
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.05
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.98
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.03
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.14
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.59
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.60
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.99
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.79
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.66
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.10
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.09
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.07
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.05
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.82
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.64
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.28
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.54
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.83
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.52
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  328.17
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.49
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.77
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.31
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.17
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.63
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.46
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5111.72
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.49
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.71
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.42
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :   -1.48
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:24.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.21
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:25.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :  -0.076
p-value of test                       :    0.53

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.17e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 3.83e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.58
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.55
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.26
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:08.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:06.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.23
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10057.67
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:46.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4978.31
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:48.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4913.85
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:50.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4031.65
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11804.23
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11898.61
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:29.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.28
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999935966

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.88
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999870242

Normal statistic for number of bits   :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :  -0.082
p-value of test                       :    0.53

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:36.77

 All tests were passed




Server wird beendet - Lösche Semaphor 182353950.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5389
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:52.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4489
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:39.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7460
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:40.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:56.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:57.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:05.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:05.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:56.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:04:01.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     940
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.89
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.93
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:16.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:46.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.48
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.76
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.27
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.28
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.73
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.57
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.40
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.11
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.06
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.67
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:43.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1412.03
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:00.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6879.70
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:41.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.36
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.89
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:01.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.90
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.40
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:32.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5051.19
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:12.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:03.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45754
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869754
  j =  1                              :        399908495
  j =  2                              :            45748
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46125
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870125
  j =  1                              :        399907754
  j =  2                              :            46117
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:27.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:18.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:45.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:59.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:33.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.016
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:37.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:37.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.34
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.16
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:49.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.38
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.81
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.89
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:44.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9991    *****

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.45
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.45
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.32
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.84
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.03
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17478.19
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.86
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.26
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.25
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.14
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.86
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.90
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.31
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.17
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.62
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.22
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.98
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.67
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.90
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.74
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.34
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.61
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.49
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.50
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.72
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.58
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.88
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.30
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5137.47
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.10
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.05
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.10
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.17
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4894.42
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.56
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.47
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.87
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    0.57
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:25.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.86
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   -0.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:24.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 7.30e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.00e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 9.77e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.86
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.19
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:05.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.95
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:06.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.87e-3
p-value of test                       :    0.9971

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10382.95
p-value of test                       :  3.7e-3

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10187.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.043
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:44.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9942

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:48.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4868.25
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:51.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.12
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.04
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11741.65
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11949.26
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:29.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.82
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000014113

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.79
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000085312

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    2.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:35.01

 All tests were passed




Server wird beendet - Lösche Semaphor 183369758.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1460
p-value of test                       :  5.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334580
  j =  1                              :        599997080
  j =  2                              :             1460
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1259
p-value of test                       :    0.9979

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334379
  j =  1                              :        599997482
  j =  2                              :             1259
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:55.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:41.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:41.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4235
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:57.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:58.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:07.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:07.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:01.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7530
p-value of test                       :  7.0e-3


-----------------------------------------------
CPU time used                    :  00:04:06.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.36
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.9907

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:49.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     267
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:16.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    2.18
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:43.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.11
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.00
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.17
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.59
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.79
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.87
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.05
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.96
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.58
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:50.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1402.22
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:01.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6973.89
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:50.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.89
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.79
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:09.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.35
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.25
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:37.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5060.05
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:02.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45804
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869804
  j =  1                              :        399908395
  j =  2                              :            45798
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45770
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869770
  j =  1                              :        399908463
  j =  2                              :            45764
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:30.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:19.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:49.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:05.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:36.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 2.79e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:42.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:42.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.96
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.82
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.18
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.95
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.44
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.87
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.87
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:46.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.01
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.87
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.30
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.60
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:29.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.92
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.61
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:39.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17579.50
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.06
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.50
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.46
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.94
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.84
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.47
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.75
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.36
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.17
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.52
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.54
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.40
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.27
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.08
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.61
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.28
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.08
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.71
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.67
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.47
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.33
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.43
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4987.25
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.17
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.56
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.29
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.73
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4857.95
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.85
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.77
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.44
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:23.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.30
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    2.58
p-value of test                       :  4.9e-3



-----------------------------------------------
CPU time used                    :  00:02:24.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.49e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.64e-4
p-value of test                       :    0.9960

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.57
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.67
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.93
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:06.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.46
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:07.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10007.88
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9799.23
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:04:21.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4788.58
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4771.38
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:55.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4236.51
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4282.35
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11854.68
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:31.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12064.45
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:31.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.10
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999968540

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.02
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000006538

Normal statistic for number of bits   :   0.052
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:11.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:07:28.54

 All tests were passed




Server wird beendet - Lösche Semaphor 184320030.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5478
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:54.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4475
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:40.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:57.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:06.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:05.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:56.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:04:01.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     867
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    2.19
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:15.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.12
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:41.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.98
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.21
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.09
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.02
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.33
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.51
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.61
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  471.60
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:44.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1471.55
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:00.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7039.42
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.00
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   39.40
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:03.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.48
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.02
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:32.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4944.90
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:03.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46334
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870334
  j =  1                              :        399907337
  j =  2                              :            46324
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45966
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869966
  j =  1                              :        399908071
  j =  2                              :            45960
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:28.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:18.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:45.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:59.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:56.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:36.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:24.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:34.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:35.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.70
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.66
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.53
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.69
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.20
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.34
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.21
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:42.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.10
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.22
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.61
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.51
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17617.18
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.43
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.13
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.50
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.61
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.83
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.13
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.07
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.54
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   44.82
p-value of test                       :  6.1e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.06
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.92
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  205.68
p-value of test                       :  8.4e-4    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.23
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.04
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.73
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.70
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.06
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  433.36
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.05
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.72
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.84
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.01
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5096.03
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.82
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.84
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  453.38
p-value of test                       :  8.4e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.34
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5155.63
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  318.87
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.52
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.62
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   -1.22
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:23.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.20
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :    0.51
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:24.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 6.30e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 6.75e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.24
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.65
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.92
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:06.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.50
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:08.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9697.52
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10144.74
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.078
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:46.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4776.05
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.67e-4
p-value of test                       :    0.9992    *****

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.65
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5170.49
p-value of test                       :  2.6e-3

-----------------------------------------------
CPU time used                    :  00:01:50.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.17
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11896.99
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11901.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.80
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000058843

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.07
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000072061

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    2.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   0.082
p-value of test                       :    0.47

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:46.05
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 M (L=1000, r=0)     8.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 185303070.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1460
p-value of test                       :  5.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334580
  j =  1                              :        599997080
  j =  2                              :             1460
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1264
p-value of test                       :    0.9968

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334384
  j =  1                              :        599997472
  j =  2                              :             1264
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5487
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:55.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7128
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:45.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:00.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:01.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:12.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:11.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:10.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:11.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     964
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    2.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.08
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.66
p-value of test                       :  1.5e-3

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    2.25
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:12.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:40.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.61
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.76
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.96
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:11.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.21
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.70
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.24
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.68
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.13
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.34
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1446.25
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:02.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7292.01
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:56.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.92
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.53
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:16.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.91
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:46.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.59
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:40.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5130.86
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:02.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45706
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869706
  j =  1                              :        399908593
  j =  2                              :            45696
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45926
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869926
  j =  1                              :        399908155
  j =  2                              :            45912
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:32.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:19.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:51.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:07.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:56.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:37.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.08e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.81e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.94e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.82e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.71
p-value of test                       :  3.4e-3

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:42.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:45.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.43
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.46
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.79
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.90
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.92
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:50.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.83
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.84
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.83
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.74
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17488.22
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.34
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.50
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.70
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.83
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.80
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.16
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.95
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.46
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.93
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.20
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.42
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.79
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.71
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.24
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.53
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.96
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.21
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.56
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.03
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.63
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.84
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.85
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4868.81
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.09
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.79
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.04
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.05
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5058.91
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.48
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.03
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.71
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:24.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.09
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:25.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.54e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 7.46e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:46.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.38e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.95
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.72
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.15
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:08.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.46
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:07.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10045.54
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9854.75
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:04:24.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.65
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:56.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4955.72
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:59.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4015.78
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4258.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11789.92
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:36.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11849.78
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:35.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.33
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000020173

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.47
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999920066

Normal statistic for number of bits   :   -0.63
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.38

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.93
p-value of test                       :    0.97

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:01.50

 All tests were passed




Server wird beendet - Lösche Semaphor 186351646.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5348
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:54.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:42.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:57.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:58.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:05.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:05.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:55.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7185
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:01.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:51.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    2.24
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:15.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:43.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.75
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.05
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.22
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.19
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.21
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.62
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.70
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  484.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:44.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.81
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:01.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6988.29
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:43.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.90
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  6.9e-3

Anderson-Darling statistic = A2       :    4.08
p-value of test                       :  8.4e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   91.21
p-value of test                       :  5.8e-3

-----------------------------------------------
CPU time used                    :  00:03:03.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.49
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:46.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.25
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5059.87
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:56.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45883
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869883
  j =  1                              :        399908240
  j =  2                              :            45871
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45599
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869599
  j =  1                              :        399908804
  j =  2                              :            45595
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:29.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:18.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:46.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:00.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:56.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 5.81e-3
p-value of test                       :    0.9935

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.58e-4
p-value of test                       :    0.9997    *****

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:33.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:22.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:40.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.27
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:36.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.75
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:49.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.16
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.76
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.05
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.88
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.42
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:43.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.99
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.84
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.79
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.72
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:37.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.6e-3

Kolmogorov-Smirnov- statistic = D-    : 2.83e-3
p-value of test                       :    0.9971

Anderson-Darling statistic = A2       :    4.44
p-value of test                       :  5.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16870.16
p-value of test                       :    0.9988



-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.38
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.65
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.41
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.00
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.93
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.81
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   62.88
p-value of test                       :  2.6e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.13
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.13
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.52
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.04
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.30
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  441.75
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.39
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.97
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:46.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.65
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.53
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.09
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.67
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.93
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.19
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.19
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.01
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.62
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.53
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.39
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.96
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5124.26
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.14
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.30
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.76
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:25.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.36
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:25.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.79e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:46.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.91e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.45
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.11
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.24
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:07.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.78
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:06.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10156.78
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9979.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : 1.86e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:53.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4913.47
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.60
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:49.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.08
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3914.11
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11739.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11953.31
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.19
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999802361

Normal statistic for number of bits   :   -1.56
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.44
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999915461

Normal statistic for number of bits   :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :  -0.083
p-value of test                       :    0.53

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    2.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:29.04

 All tests were passed




Server wird beendet - Lösche Semaphor 187432990.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:49.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5422
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:57.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4454
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:42.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:57.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:04.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:04.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:55.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:00.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     853
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    3.29
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     331
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    2.08
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:13.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:43.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.30
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.55
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.62
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.81
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.32
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.82
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.64
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.05
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:43.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1450.70
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:01.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6880.69
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.71
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.75
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:03.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.95
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:46.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.43
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:33.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5044.88
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:59.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45991
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869991
  j =  1                              :        399908026
  j =  2                              :            45975
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45882
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869882
  j =  1                              :        399908240
  j =  2                              :            45874
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:27.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:19.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:59.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:57.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:32.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:22.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:36.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.46
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.75
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.70
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.77
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.12
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:38.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.10
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.44
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.86
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.56
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17656.47
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:52.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.90
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.74
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.66
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.47
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.69
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.31
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.08
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.26
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.98
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.79
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.73
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.76
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.71
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.16
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.84
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.81
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.60
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.69
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.43
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.86
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.93
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.56
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4877.61
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  449.35
p-value of test                       :  6.7e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.50
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.76
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.09
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4986.50
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.60
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.65
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.51
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :   -1.06
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:21.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.61
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :   -1.04
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:20.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.95e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 7.27e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.88
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.30
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  239.70
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.15
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:56.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9850.24
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9692.47
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:51.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.73
p-value of test                       :    0.9969

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:24.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:35.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.80
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:35.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4229.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:11.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4221.32
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:10.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11597.89
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11917.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.66
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999903011

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.34
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000053632

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.43
p-value of test                       :    0.08

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   02:59:54.35

 All tests were passed




Server wird beendet - Lösche Semaphor 188481566.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1464
p-value of test                       :  3.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334584
  j =  1                              :        599997072
  j =  2                              :             1464
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5374
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:42.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:36.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:35.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:54.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:55.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:02.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:02.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:54.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:59.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:53.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.03
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.57
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:10.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.18
p-value of test                       :    0.9940

-----------------------------------------------
CPU time used                    :  00:02:38.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.64
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.47
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.91
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.58
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.58
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.33
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.98
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.14
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:49.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1488.40
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:59.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7209.83
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.61
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.42
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:02.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.15
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.02
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:37.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4927.99
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:14.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45611
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869611
  j =  1                              :        399908783
  j =  2                              :            45601
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46047
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870047
  j =  1                              :        399907913
  j =  2                              :            46033
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:13.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:28.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:17.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:44.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:00.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:52.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:33.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 8.77e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.61e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 8.65e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9978

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.016
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:48.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.82
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.00
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.82
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:50.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.66
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.72
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:44.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.62
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.54
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:31.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:29.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.01
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17673.38
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.88
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.33
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.45
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.45
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.97
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.68
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.12
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.66
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.34
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.46
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.27
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.08
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.75
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.76
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:47.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.01
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.81
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.84
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.65
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.75
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.00
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.95
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5122.10
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.99
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.29
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.67
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.56
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.91
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.45
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.16
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:34.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.60
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:13.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.37
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :  -0.037
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:14.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:14.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.55e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:46.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.94e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 9.69e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.48
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.00
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.46
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  155.32
p-value of test                       :    0.9916

-----------------------------------------------
CPU time used                    :  00:02:13.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.00
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:10.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9798.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9988.10
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.075
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:59.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4931.51
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:48.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.60
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:49.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.25
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11932.30
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:28.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11991.58
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.71
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999980645

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.38
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000019711

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   0.015
p-value of test                       :    0.49

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:29.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:17:13.75

 All tests were passed




Server wird beendet - Lösche Semaphor 168919071.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5362
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:46.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:38.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7165
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:36.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4222
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:54.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7462
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:02.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:03.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:56.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:00.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.61
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    4.15
p-value of test                       :  7.4e-3

Stat. AD after spacings (mNP2-S)      :    3.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:48.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    4.14
p-value of test                       :  7.4e-3

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:11.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.04
p-value of test                       :  9.1e-3

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:44.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.89
p-value of test                       :    0.9964

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.17
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.65
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.00
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.70
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.67
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.11
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.66
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.38
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.37
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:07.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7084.96
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.33
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.01
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:08.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.30
p-value of test                       :    0.9976


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.79
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:39.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5030.07
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:20.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45974
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869974
  j =  1                              :        399908055
  j =  2                              :            45968
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45944
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869944
  j =  1                              :        399908116
  j =  2                              :            45936
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:29.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:17.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:44.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:00.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:54.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:35.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.30e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 7.26e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.56e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:40.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:41.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.25
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.50
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.39
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.38
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.70
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.79
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:55.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.10
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.40
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:33.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:34.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.98
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17244.71
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:51.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.24
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.27
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.24
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.25
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.86
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.23
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.63
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.25
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.24
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.57
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.75
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.81
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.85
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.77
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.40
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.69
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.98
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.38
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.78
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.96
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.34
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5091.03
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  330.32
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.39
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.41
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.63
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4897.20
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.84
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.31
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:36.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.35
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:30.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.95
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :    0.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:26.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.55
p-value of test                       :    0.06

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.80e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 8.45e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:46.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 3.48e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.72
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.70
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.97
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:10.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.53
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:08.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9974.59
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9904

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9959.94
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.079
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:04:22.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4916.15
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:51.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.36
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:53.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4068.57
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.65
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11794.69
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:33.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11798.83
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:33.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.45
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000013015

Normal statistic for number of bits   :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.30
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999968969

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :  -0.087
p-value of test                       :    0.53

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.51
p-value of test                       :    0.07

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    2.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.57

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:11.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:13:09.57

 All tests were passed




Server wird beendet - Lösche Semaphor 169541663.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1260
p-value of test                       :    0.9978

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334380
  j =  1                              :        599997480
  j =  2                              :             1260
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1460
p-value of test                       :  5.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334580
  j =  1                              :        599997080
  j =  2                              :             1460
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5405
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:49.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:38.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:38.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4220
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:54.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:03.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7159
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:04.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:53.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7478
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:59.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:44.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.64
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     552
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    3.31
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9955


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:08.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:35.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.60
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.05
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.71
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.64
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.07
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.62
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.01
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.76
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.89
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.20
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:42.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1446.04
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:59.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7104.87
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:42.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.40
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.80
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:02.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.62
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.15
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:36.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4874.73
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:05.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46311
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870311
  j =  1                              :        399907380
  j =  2                              :            46307
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46080
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870080
  j =  1                              :        399907841
  j =  2                              :            46078
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:29.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:18.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:44.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:53.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:32.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.54e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 5.99e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.99e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:35.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.44
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.58
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.99
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.73
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.71
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.17
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:43.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.8e-3

Anderson-Darling statistic = A2       :    3.27
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.10
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.15
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.31
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.68
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:38.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17622.87
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:55.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.29
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.58
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.92
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.28
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.02
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.16
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.46
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.16
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.48
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.95
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.80
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.30
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.14
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.83
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.78
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.12
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.06
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.41
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.54
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.84
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.90
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.72
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5096.16
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.97
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.40
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.24
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.27
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4908.30
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.36
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.95
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:26.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.88
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    1.98
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:26.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.90e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:47.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 3.16e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.87
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.57
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  239.51
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:06.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:09.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10079.81
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9692.00
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:54.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.73
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:49.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4916.19
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:49.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4216.20
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11982.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:29.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11787.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.95
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  7999967427

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.64
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000032323

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.84

Sample variance                       :    2.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:08:18.95

 All tests were passed




Server wird beendet - Lösche Semaphor 170688543.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1252
p-value of test                       :    0.9989

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334372
  j =  1                              :        599997496
  j =  2                              :             1252
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5495
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:49.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:39.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:37.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:55.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:02.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:03.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:54.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:00.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    2.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.80
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     654
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    4.94
p-value of test                       :  3.1e-3

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:11.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:35.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.20
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.52
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.09
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.01
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.93
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.47
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.18
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:44.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1421.99
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:01.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7151.78
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:43.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   41.91
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:03.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.08
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  144.34
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:35.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5063.07
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:57.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46028
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870028
  j =  1                              :        399907949
  j =  2                              :            46018
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45624
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869624
  j =  1                              :        399908756
  j =  2                              :            45616
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:30.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:18.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:45.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:01.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:55.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:33.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 9.38e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:22.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:33.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.092
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:32.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.98
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:48.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.74
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.06
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.98
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.18
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.34
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:39.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.10
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.50
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.55
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  3.8e-3

Kolmogorov-Smirnov- statistic = D-    : 9.00e-3
p-value of test                       :    0.9902

Anderson-Darling statistic = A2       :    4.33
p-value of test                       :  6.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16890.88
p-value of test                       :    0.9982



-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.58
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.96
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.35
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.83
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.59
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.54
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.08
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.95
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.26
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.27
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.02
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.59
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.92
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.42
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.54
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.17
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.93
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  436.06
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.59
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.60
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.88
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.83
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5160.02
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.29
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.31
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.68
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.32
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.49
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.06
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  265.59
p-value of test                       :  1.3e-3


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.54
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:25.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.25
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:25.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :  1.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    3.55
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.12
p-value of test                       :    0.98

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 4.77e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:46.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.51e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.24
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.44
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.16
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:06.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.38
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:10.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10169.01
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10141.71
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.59
p-value of test                       :  4.8e-3

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:46.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.55
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:49.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4832.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:51.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.10
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3919.27
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11876.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11819.96
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:31.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.58
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999889451

Normal statistic for number of bits   :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.06
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999852134

Normal statistic for number of bits   :   -1.17
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :  -0.065
p-value of test                       :    0.53

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:06:18.67

 All tests were passed




Server wird beendet - Lösche Semaphor 171507743.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1264
p-value of test                       :    0.9968

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334384
  j =  1                              :        599997472
  j =  2                              :             1264
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5357
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:48.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:37.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:35.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4484
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:54.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:55.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:02.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:02.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:53.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7132
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:59.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    4.85
p-value of test                       :  3.4e-3

Stat. AD after spacings (mNP2-S)      :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9921


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     273
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    2.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:14.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:41.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.28
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.40
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.72
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.17
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.27
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.64
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.01
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.92
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.20
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  554.83
p-value of test                       :  7.4e-5    *****

-----------------------------------------------
CPU time used                    :  00:01:42.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1568.49
p-value of test                       :  8.3e-3

-----------------------------------------------
CPU time used                    :  00:02:02.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6995.92
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:42.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.12
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.14
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:02.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.17
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  152.66
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:35.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4926.02
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:01.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45884
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869884
  j =  1                              :        399908234
  j =  2                              :            45880
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46261
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870261
  j =  1                              :        399907485
  j =  2                              :            46247
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:30.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:18.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:44.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:00.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:56.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:35.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.36
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:35.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.63
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.33
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.66
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.33
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.09
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:38.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.08
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.85
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.33
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.41
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17503.71
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.19
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.73
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.77
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.48
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.74
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.34
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.46
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.01
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.65
p-value of test                       :    0.9913


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.15
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.48
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.28
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.38
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.44
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.88
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.23
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.89
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.39
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.28
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.23
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  453.94
p-value of test                       :  8.0e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.00
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4923.02
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  318.37
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.09
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.38
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.12
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5122.93
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.39
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.18
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.56
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :    1.42
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:25.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.70
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:24.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.55e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 7.73e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.08e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 4.28e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.52
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.69
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 7.93e-3
p-value of test                       :    0.9915

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  154.62
p-value of test                       :    0.9925

-----------------------------------------------
CPU time used                    :  00:02:08.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:10.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10052.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9995.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:59.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.94
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:51.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.25
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:50.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4148.55
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4341.56
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11724.99
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:29.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11877.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:30.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.52
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999826865

Normal statistic for number of bits   :   -1.37
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.85
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999938267

Normal statistic for number of bits   :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:05:09.50
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 35  Gap, r = 25                     7.4e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 172326943.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5471
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:53.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:39.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:38.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4196
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:55.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4240
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:55.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:02.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7078
p-value of test                       :    0.9976


-----------------------------------------------
CPU time used                    :  00:03:02.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:53.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:59.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     865
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:47.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.70
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    2.64
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     646
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:13.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.84
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:43.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.76
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.54
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.69
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.91
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.28
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.81
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.55
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:45.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1403.91
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:00.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7190.69
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:41.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.60
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:02.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.06
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.01
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:35.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4954.92
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:00.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46124
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870124
  j =  1                              :        399907755
  j =  2                              :            46118
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45888
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869888
  j =  1                              :        399908228
  j =  2                              :            45880
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:29.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:18.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:44.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :  1.1e-3

Anderson-Darling statistic = A2       :    4.62
p-value of test                       :  4.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  4.0e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:58.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:56.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:36.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.76e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.28e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 2.90e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:35.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:35.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:48.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.79
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.66
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.24
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.17
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:51.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.52
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.48
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:38.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.26
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.08
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17274.25
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.25
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.75
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.94
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.78
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.75
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   58.56
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.29
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.10
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.79
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.78
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.48
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.73
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.91
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.50
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.96
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.57
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.97
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.75
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.07
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.87
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.90
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.80
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5104.85
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.81
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.08
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.23
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.14
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.91
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.64
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.70
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.07
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:25.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.85
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :    0.69
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:23.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :  -0.043
p-value of test                       :    0.52

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.29e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 6.03e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.73e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.63
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.54
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.62
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:05.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.78
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:06.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10201.19
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10015.70
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:51.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5049.71
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.50
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:50.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.12
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4253.11
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11882.06
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:29.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11771.97
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:30.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.48
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000121339

Normal statistic for number of bits   :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.67
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000039703

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:47.30

 All tests were passed




Server wird beendet - Lösche Semaphor 173342751.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5330
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:57.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:41.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:57.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:03.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:03.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:52.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:58.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:49.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.18
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.08
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:14.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:43.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.00
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.69
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.62
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.83
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.85
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.01
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.44
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.44
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.15
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.57
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:43.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.01
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:01.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7081.68
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:40.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.05
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.53
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:01.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.36
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.40
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:35.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5208.66
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:01.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46020
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870020
  j =  1                              :        399907961
  j =  2                              :            46018
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45847
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869847
  j =  1                              :        399908308
  j =  2                              :            45843
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:29.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:17.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:43.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:58.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:55.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:35.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.76e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:34.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:34.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.47
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:49.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.42
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.00
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:51.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.89
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.95
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.76
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.57
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:38.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.58
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.25
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  151.19
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17572.23
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:52.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.63
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.04
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.32
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.19
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.01
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.31
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.52
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.92
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.11
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.06
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.66
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.28
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  442.01
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.04
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.65
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.48
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.87
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.63
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.76
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   45.76
p-value of test                       :    0.9960


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.87
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.99
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4900.18
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.97
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.18
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.26
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.38
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.70
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.80
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.44
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.13
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:23.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.08
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:24.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.95
p-value of test                       :    0.03

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.72e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.07
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.54
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.42
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:05.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.80
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:06.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10038.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9864.11
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    3.08
p-value of test                       :  1.0e-3

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:46.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4707.34
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:49.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4913.52
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:52.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3907.98
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.81
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11828.13
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11871.68
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:30.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.88
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999865151

Normal statistic for number of bits   :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.45
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000039070

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   0.015
p-value of test                       :    0.49

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.9998    *****

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.50
p-value of test                       :  6.1e-3

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:06.18

 All tests were passed




Server wird beendet - Lösche Semaphor 174325791.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:39.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5518
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:00.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:43.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:45.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4222
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:00.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:01.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:10.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:09.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:04:06.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:11.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:48.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     556
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    2.94
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:11.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.03
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.58
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.97
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.46
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.83
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.68
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.52
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  193.77
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:30.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  393.88
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:58.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.64
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:19.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6955.70
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:58.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.13
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.25
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:13.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.13
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.32
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4967.05
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:55.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45916
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869916
  j =  1                              :        399908171
  j =  2                              :            45910
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45681
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869681
  j =  1                              :        399908639
  j =  2                              :            45679
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:30.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:21.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:52.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  6.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    4.32
p-value of test                       :  6.2e-3


-----------------------------------------------
CPU time used                    :  00:02:07.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:57.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 1.68e-3
p-value of test                       :    0.9983

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:37.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.46e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 2.62e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:24.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:43.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.84
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.81
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.48
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.03
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:52.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.11
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.18
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.81
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17517.15
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.08
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.88
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.77
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.12
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.04
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.19
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.15
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.22
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.35
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.65
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.14
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.21
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.87
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.27
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.16
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.30
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.60
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  563.86
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.83
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.91
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.79
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.00
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5140.56
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.63
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.14
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:36.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.18
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.87
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4921.43
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.46
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.63
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.73
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :   -0.51
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:23.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.21
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :    1.13
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:23.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.25e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 2.04e-3
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.70
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.34
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.85
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:08.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.50
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:07.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10069.19
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10014.20
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:04:35.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4907.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:53.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.13
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:56.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3916.40
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.24
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11887.00
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:33.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11841.65
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:36.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.83
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999930272

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.37
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000092206

Normal statistic for number of bits   :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9966

Tests on the sum of all N observations
Standardized normal statistic         :   0.047
p-value of test                       :    0.48

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:10:09.23

 All tests were passed




Server wird beendet - Lösche Semaphor 175341599.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5425
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:53.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:39.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:38.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:04.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:03.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:54.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7450
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:00.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:45.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:13.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.49
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:39.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.92
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.25
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.58
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.68
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.95
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.33
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.42
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.42
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:45.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1421.99
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:01.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7136.28
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.25
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:03.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.70
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.86
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:35.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4841.30
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:55.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45838
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869838
  j =  1                              :        399908328
  j =  2                              :            45830
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45530
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869530
  j =  1                              :        399908943
  j =  2                              :            45524
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:33.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:28.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:54.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:11.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:56.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:34.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:32.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:33.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.96
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.71
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.57
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:49.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.22
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.04
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.16
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.15
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.11
p-value of test                       :    0.9900

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.65
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.57
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17306.56
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.08
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.46
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.61
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.58
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.94
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.16
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.07
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.99
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.74
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.25
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.42
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.00
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.49
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.08
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.24
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.12
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.89
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  442.77
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.72
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.48
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  457.36
p-value of test                       :  5.9e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.14
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4982.11
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.42
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.07
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.14
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.57
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5034.47
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.13
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.71
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.23
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:24.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.15
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:24.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.20e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 4.95e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.04
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.42
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:06.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.03
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:08.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10172.40
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10240.95
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:50.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4849.73
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:50.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4775.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:51.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4278.24
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4187.92
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11696.31
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:29.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11648.87
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.61
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000047719

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.61
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000011824

Normal statistic for number of bits   :   0.093
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    2.55
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :  -0.013
p-value of test                       :    0.51

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:12.30

 All tests were passed




Server wird beendet - Lösche Semaphor 176652319.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5504
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:54.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:39.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:39.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4441
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:56.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:03.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:02.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:53.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:58.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.19
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:45.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     560
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.96
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:06.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:34.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.45
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.73
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.09
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.48
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.96
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.94
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.09
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.20
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.15
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:45.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.05
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:03.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7081.74
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:46.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.53
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.83
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:03.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.40
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  148.92
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:35.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5033.61
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:56.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46005
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870005
  j =  1                              :        399907996
  j =  2                              :            45993
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45925
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869925
  j =  1                              :        399908152
  j =  2                              :            45921
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:29.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:15.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:01.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:56.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:35.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.22e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:37.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:37.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.52
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.13
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.13
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.03
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:48.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.58
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.62
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.64
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:43.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.50
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.35
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.88
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.30
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17267.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.79
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.86
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.87
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.91
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.22
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.95
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.52
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.99
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.02
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.64
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.46
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.57
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.14
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.29
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.43
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.96
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.32
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.54
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.66
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.42
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.87
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.84
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.04
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.89
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.99
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.64
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.78
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4945.05
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.13
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.78
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.66
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :    2.93
p-value of test                       :  1.7e-3



-----------------------------------------------
CPU time used                    :  00:02:24.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.89
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -1.61
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:24.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.75e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.04
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.26
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.82
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:08.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:09.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10015.43
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10136.46
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:04:16.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4916.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:52.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4692.42
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:51.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.01
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.60
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11707.89
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11906.48
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.67
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000042430

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.61
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000086089

Normal statistic for number of bits   :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:29.37

 All tests were passed




Server wird beendet - Lösche Semaphor 177668127.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:50.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5492
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:52.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4474
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:39.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:55.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:02.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:02.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:53.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:59.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.59
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.16
p-value of test                       :    0.9979

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    2.20
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:13.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:41.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.54
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.26
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.41
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.15
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.42
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.07
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.28
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1469.64
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:58.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7207.45
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:41.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.71
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:01.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.75
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.37
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:32.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5006.21
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:00.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45568
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869568
  j =  1                              :        399908868
  j =  2                              :            45560
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45800
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869800
  j =  1                              :        399908403
  j =  2                              :            45794
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:29.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:18.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:44.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.11e-3
p-value of test                       :    0.9967

Anderson-Darling statistic = A2       :    4.61
p-value of test                       :  4.5e-3


-----------------------------------------------
CPU time used                    :  00:01:59.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:56.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:35.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.21e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:21.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:21.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:33.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:33.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.77
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.15
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.03
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:51.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.99
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.89
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.03
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:39.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.68
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  3.9e-3

Kolmogorov-Smirnov- statistic = D-    : 1.11e-3
p-value of test                       :    0.9989

Anderson-Darling statistic = A2       :    6.25
p-value of test                       :  8.0e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   79.81
p-value of test                       :    0.9998    *****

-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17682.47
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.73
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.29
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.07
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.17
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.62
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.17
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.29
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.93
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.63
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.41
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.97
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.11
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.36
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.28
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.94
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.89
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.84
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.05
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.10
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.35
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.65
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.08
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4928.48
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  314.57
p-value of test                       :    0.9924


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.01
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.07
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.71
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.98
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.33
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.12
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.24
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :    1.48
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:24.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.71
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:25.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.12
p-value of test                       :    0.98

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.09e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.76e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 8.59e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.36
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.17
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.98
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:08.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.75
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:07.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10106.61
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9810.82
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:45.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5010.32
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:50.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5021.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:51.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4252.64
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.11
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11820.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11911.26
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:29.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.62
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000036418

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.69
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000033784

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.70
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.40e-3
p-value of test                       :    0.9965

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.95
p-value of test                       :    0.03

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:49.17
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 72  Savir2                          0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 178618399.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5400
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:57.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:42.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:53.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:02.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:11.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:29.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:30.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:12.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:04:48.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:48.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.50
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     568
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:13.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.09
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    2.20
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:41.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.43
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.96
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.45
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.35
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.87
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.74
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.55
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  396.73
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:39.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.47
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:04.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6939.29
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:44.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.07
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:13.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.88
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.91
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:37.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4929.31
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:56.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45829
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869829
  j =  1                              :        399908348
  j =  2                              :            45817
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45734
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869734
  j =  1                              :        399908537
  j =  2                              :            45724
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:37.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:28.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  6.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    4.27
p-value of test                       :  6.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:18.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:57.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:37.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.24e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 2.36e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.55e-4
p-value of test                       :  6.5e-3

Kolmogorov-Smirnov- statistic = D-    : 7.65e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    5.00
p-value of test                       :  2.8e-3

-----------------------------------------------
CPU time used                    :  00:00:24.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:43.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:44.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.18
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.05
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.01
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.00
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.65
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.00
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:13.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.89
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.11
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.62
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.69
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   94.14
p-value of test                       :    0.9924

-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17361.12
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.55
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.83
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.79
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.17
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.79
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.65
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.18
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.02
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.46
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.72
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.05
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.17
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.92
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.24
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.88
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.14
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.73
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.03
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.61
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.33
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:48.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.42
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.69
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5068.27
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.15
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.05
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:51.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  310.82
p-value of test                       :    0.9975


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.73
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5071.27
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.43
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.46
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:51.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.59
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :    0.82
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:24.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.11
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:24.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.65
p-value of test                       :    0.05

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 3.57e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.71
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.70
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.61
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:06.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.22
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:07.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9833.79
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9757.10
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:12.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.014
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:04:31.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.44
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:54.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.70e-3
p-value of test                       :    0.9929

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5109.63
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:57.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4249.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4025.94
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11650.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:34.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11599.18
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:35.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.34
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000055429

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.53
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000134245

Normal statistic for number of bits   :    1.06
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:15:24.10

 All tests were passed




Server wird beendet - Lösche Semaphor 179634207.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:51.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5339
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:52.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:40.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7153
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:40.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:03.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7478
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:03.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:55.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:00.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:13.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:40.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.17
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.53
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.08
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.67
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.84
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.99
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.74
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.13
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.79
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.48
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:44.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1525.03
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:02.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7036.69
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:42.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.43
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.74
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:02.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.44
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   84.52
p-value of test                       :    0.9929


-----------------------------------------------
CPU time used                    :  00:01:35.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5007.32
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:56.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46210
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870210
  j =  1                              :        399907586
  j =  2                              :            46198
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45706
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869706
  j =  1                              :        399908589
  j =  2                              :            45704
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:28.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:17.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:44.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:55.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:34.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 2.53e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.026
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:35.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.21
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.68
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.82
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:49.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.46
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.04
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.30
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:44.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.28
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.11
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.26
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.09
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.99
p-value of test                       :  6.8e-3

-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.02
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:37.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17432.08
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.16
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.33
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.01
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.58
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.68
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.84
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.73
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.16
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.79
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.89
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.84
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.04
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.93
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.85
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.05
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.83
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  188.54
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.56
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.22
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.24
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.05
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.54
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.40
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.27
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.61
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.62
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.12
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5025.31
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.08
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.48
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.58
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:23.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.94
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :    1.63
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:26.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.07e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 4.88e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 7.40e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.08
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.83
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.48
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:08.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.85
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:07.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9892.37
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10135.15
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.23
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:44.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4962.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:49.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4715.13
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:51.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.46
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.21
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11928.15
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11872.56
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.93
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999914444

Normal statistic for number of bits   :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.15
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999972155

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         : 5.04e-3
p-value of test                       :    0.50

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.23
p-value of test                       :    0.01

Sample variance                       :    1.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.72
p-value of test                       :    0.96

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:02.35

 All tests were passed




Server wird beendet - Lösche Semaphor 180977695.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5354
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:54.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:40.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:57.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:05.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:06.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:58.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:04:02.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.07
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    4.27
p-value of test                       :  6.5e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     270
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:08.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:42.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.10
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.64
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:12.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.97
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.87
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.48
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  480.94
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1411.76
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:05.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6906.70
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:49.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.75
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 7.01e-3
p-value of test                       :    0.9925

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.18
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:08.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.24
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.40
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:37.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4968.55
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:56.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45730
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869730
  j =  1                              :        399908543
  j =  2                              :            45724
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45782
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869782
  j =  1                              :        399908441
  j =  2                              :            45772
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:31.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:18.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.2e-3

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:03.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:36.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.15e-4
p-value of test                       :  1.0e-3

Kolmogorov-Smirnov- statistic = D-    : 6.15e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    4.59
p-value of test                       :  4.5e-3

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 7.72e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:37.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:39.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.73
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.10
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.96
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:17.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.26
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.90
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.22
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.82
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.09
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.71
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:30.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.18
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:29.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.36
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16996.49
p-value of test                       :    0.9903



-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.34
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.16
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.83
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.22
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.96
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:39.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.09
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.03
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.71
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.83
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.88
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.15
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.84
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  450.68
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   99.76
p-value of test                       :    0.9915


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.77
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.87
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.23
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.56
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  102.33
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.93
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  305.59
p-value of test                       :    0.9988


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.97
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4941.67
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.18
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.05
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.79
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.36
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.83
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.08
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.84
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:37.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.42
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:24.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.21
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :   -0.63
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:24.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 8.82e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 7.47e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   21.16
p-value of test                       :  6.7e-3

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.40
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.40
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:05.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.96
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:07.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10016.34
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.50e-3
p-value of test                       :    0.9931

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10224.24
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:04:25.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.23e-4
p-value of test                       :    0.9996    *****

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4657.56
p-value of test                       :    0.9914

-----------------------------------------------
CPU time used                    :  00:01:52.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4926.96
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:54.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.24
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3880.32
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11761.63
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:32.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11800.91
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:31.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.80
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000185656

Normal statistic for number of bits   :    1.47
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.75
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999999164

Normal statistic for number of bits   : -6.61e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:09:29.47

 All tests were passed




Server wird beendet - Lösche Semaphor 181960708.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:39.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:50.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5544
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:54.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:40.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7461
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:03.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:04.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:55.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7510
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:04:01.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:46.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.31
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:13.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.98
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     126
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:45.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.21
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.72
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   34.58
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.06
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.65
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.28
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.21
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  466.80
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:43.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1407.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:00.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6929.92
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:41.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.50
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:02.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.20
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.72
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:33.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4962.96
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:57.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45759
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869759
  j =  1                              :        399908488
  j =  2                              :            45747
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46192
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870192
  j =  1                              :        399907621
  j =  2                              :            46182
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:28.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 4.45e-3
p-value of test                       :    0.9949

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.43
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  4.8e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:19.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:47.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:01.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:54.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:34.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 2.78e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 9.45e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:21.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:33.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:34.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.65
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:48.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:51.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.34
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.05
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.56
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.24
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.11
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:38.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9920

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.26
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.42
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.63
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.49
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17291.53
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.90
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.23
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.80
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.32
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.13
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.35
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.60
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.20
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.89
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.10
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.13
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.97
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.86
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.68
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.11
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.80
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.30
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.08
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.95
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.87
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.32
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4911.80
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.43
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.42
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.79
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.11
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5104.03
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.81
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.59
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.81
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :    0.69
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:25.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.03
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :    1.36
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:27.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.41e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 9.93e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.69e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.78
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.91
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.68
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:09.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9941

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.64
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:07.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9992.38
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10150.36
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:44.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4961.97
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4729.91
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:50.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.55
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4264.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11767.26
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:28.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11749.41
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:29.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.87
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999914636

Normal statistic for number of bits   :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.92
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999936452

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.65
p-value of test                       :    0.95

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:15.20

 All tests were passed




Server wird beendet - Lösche Semaphor 183107588.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5443
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:56.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:40.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:57.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:05.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:05.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:55.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:04:00.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.55
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:15.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:41.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.30
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.59
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.23
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.89
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.00
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.71
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.96
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.96
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.02
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:44.05

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1572.02
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:02:01.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7117.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.37
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:01.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.45
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.00
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:32.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4999.44
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:59.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45722
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869722
  j =  1                              :        399908560
  j =  2                              :            45714
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45598
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869598
  j =  1                              :        399908809
  j =  2                              :            45588
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:28.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:18.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:45.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:35.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.23e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 5.96e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:26.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:21.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:34.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.083
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:35.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.53
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.15
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.63
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.28
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   14.94
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:40.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.91
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.87
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.94
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17461.59
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.66
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.55
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.44
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.07
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.38
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.68
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.97
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.41
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.14
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.59
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.55
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.18
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.86
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.83
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.45
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.10
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.01
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.21
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.00
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.39
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.59
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5122.36
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.88
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.01
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.68
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.63
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.34
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.48
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.38
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.48
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:25.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.03
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :  -0.010
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:26.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   0.082
p-value of test                       :    0.47

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.05e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 8.34e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 8.70e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.34
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.99
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 5.37e-3
p-value of test                       :    0.9944

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.11
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:08.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.50
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:07.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10166.03
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9920.37
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:42.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4962.77
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:49.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.38
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:50.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4174.89
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4013.05
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11774.76
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:28.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11763.55
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:29.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.87
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000133102

Normal statistic for number of bits   :    1.05
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.22
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000109342

Normal statistic for number of bits   :    0.86
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.96
p-value of test                       :    0.97

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:46.92

 All tests were passed




Server wird beendet - Lösche Semaphor 184057860.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5524
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:57.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4440
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:40.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:57.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:58.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:06.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:05.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:55.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:00.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.85
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:48.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.19
p-value of test                       :    0.9922

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:15.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:43.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.87
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.61
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.91
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.97
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.26
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.31
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.24
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.15
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.62
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  395.46
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:44.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1461.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:00.48

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6868.99
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.80
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.36
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:03.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.20
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  146.66
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:35.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5088.32
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:00.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45728
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869728
  j =  1                              :        399908547
  j =  2                              :            45722
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46111
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870111
  j =  1                              :        399907780
  j =  2                              :            46107
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:28.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:18.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:00.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:55.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:35.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.77e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 5.45e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 6.72e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:21.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.028
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:34.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:35.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.20
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.91
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.41
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   16.41
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.70
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.88
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:43.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.01
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.21
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17342.89
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.65
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.16
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.18
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.90
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.07
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.97
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.47
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.51
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.57
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  107.65
p-value of test                       :    0.9926


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.00
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.71
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.69
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.54
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.07
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.86
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.00
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.68
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.20
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.88
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5089.75
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.16
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.96
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.92
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.88
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5149.78
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.46
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.23
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.84
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   -2.39
p-value of test                       :    0.9916



-----------------------------------------------
CPU time used                    :  00:02:24.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.39
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:25.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.38

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 4.55e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 9.45e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.75
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.21
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.71
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:06.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.72
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:08.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10103.44
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9883.64
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:43.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4814.57
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:49.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4715.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:50.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3960.88
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4244.26
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11896.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11769.66
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:30.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.97
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000110356

Normal statistic for number of bits   :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   97.68
p-value of test                       :  2.5e-4    *****


-----------------------------------------------
Total number of bits:  8000068074

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9981

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :  -0.038
p-value of test                       :    0.52

Sample variance                       :    2.36
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:28.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:03:23.71
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 102  Run of bits, r = 27             2.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 185073668.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1262
p-value of test                       :    0.9973

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334382
  j =  1                              :        599997476
  j =  2                              :             1262
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5476
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:58.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:41.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:59.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:06.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:05.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:55.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:00.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    3.25
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:05.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    2.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    2.61
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     260
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:17.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:43.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.15
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.67
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.91
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.91
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:10.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.11
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.77
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.28
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:45.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1508.59
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:01.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6992.04
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:41.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.84
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.32
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:02.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.92
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.81
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:35.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5192.48
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:56.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45693
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869693
  j =  1                              :        399908617
  j =  2                              :            45687
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45450
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869450
  j =  1                              :        399909104
  j =  2                              :            45442
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:28.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:18.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:45.23

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:00.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:55.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:34.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.16e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 9.20e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 8.49e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:21.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:33.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:34.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.64
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.55
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.34
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.48
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.70
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.79
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:43.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.25
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.62
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.92
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.29
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17426.17
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.55
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.65
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.07
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.56
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.16
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.97
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.83
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.57
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.91
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.05
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.71
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.69
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.17
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.78
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.33
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.54
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.86
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.72
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.51
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.44
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.03
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.15
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5062.39
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.80
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.08
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.85
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.64
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4867.35
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.74
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.61
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:36.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.00
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :    1.26
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:26.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.04
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:25.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.78
p-value of test                       :    0.04

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 3.21e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:46.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 8.52e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.64
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.35
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.07
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:05.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.48
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:06.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9936.81
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10184.00
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:04:23.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.32
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4792.53
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:50.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3929.56
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4097.08
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11775.36
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11697.11
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:30.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.73
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999955097

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.84
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000084316

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.0e-3

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.57
p-value of test                       :    0.94

Sample variance                       :    0.15
p-value of test                       :    0.9983

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:28.12

 All tests were passed




Server wird beendet - Lösche Semaphor 186122244.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:49.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5405
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:56.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4452
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:41.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:42.46

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4247
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:57.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4217
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:58.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:07.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:05.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:56.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:01.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.80
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:52.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.17
p-value of test                       :    0.9962


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:18.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:43.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.28
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.60
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.51
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.63
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.93
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:17.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  466.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:43.25

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1529.26
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:01.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7087.38
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:43.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 8.60e-3
p-value of test                       :    0.9911

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.52
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.05
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:02.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.74
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.48
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:35.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5015.76
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:00.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45809
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869809
  j =  1                              :        399908385
  j =  2                              :            45803
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46015
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870015
  j =  1                              :        399907977
  j =  2                              :            46001
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:29.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:19.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:01.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:55.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:34.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.13e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 6.32e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.21
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:36.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.021
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:35.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.49
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:50.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.38
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.69
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.65
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.38
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.10
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.82
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:45.72

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.72
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.19
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.44
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.11
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.75
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17325.86
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:52.54

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.17
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.06
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.04
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.25
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.16
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.24
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.51
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.65
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.38
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.60
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.93
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.13
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.90
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.26
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.82
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.51
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.58
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.07
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.43
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.88
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.44
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.10
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4959.69
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  457.81
p-value of test                       :  3.0e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.36
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.18
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.76
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.30
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.39
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  162.73
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.41
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :   -2.35
p-value of test                       :    0.9907



-----------------------------------------------
CPU time used                    :  00:02:25.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.04
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :   -1.02
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:24.29

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 6.52e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.12e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 6.60e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.13
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   22.67
p-value of test                       :  3.8e-3

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.32
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:06.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.71
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:05.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10129.00
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10223.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:44.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4957.64
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:48.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5047.67
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:50.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.13
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4318.70
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11774.37
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11592.96
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:30.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.79
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999940985

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.40
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000013990

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.25
p-value of test                       :    0.99

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:04:51.72

 All tests were passed




Server wird beendet - Lösche Semaphor 187138052.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5337
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:54.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:41.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4481
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:58.55

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:06.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:06.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:54.98

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7174
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:00.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.05
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.07
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.66
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:51.63

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.84
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.18
p-value of test                       :    0.9956

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.85
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    2.84
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:15.36

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.72
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:45.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.76
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.59
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.03
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.94
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.52
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.62
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.60
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  394.43
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:44.44

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1372.92
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:01.60

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6908.08
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:42.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.28
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:03.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.48
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.53
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:34.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5085.98
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:56.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46197
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870197
  j =  1                              :        399907610
  j =  2                              :            46189
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45849
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869849
  j =  1                              :        399908304
  j =  2                              :            45845
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:28.65

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:18.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 6.96e-3
p-value of test                       :    0.9921

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:46.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:01.76

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:55.32

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:35.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 4.05e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.53e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 9.63e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:37.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:36.68

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.12
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.43
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.72
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.39
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.00
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.86
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:44.97

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.26
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.36
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.73
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.48
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.85
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:39.56

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17308.62
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.28
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.30
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.31
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.65
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.64
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.83
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.91
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.41
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.00
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.91
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.33
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.82
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.95
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.69
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.53
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.88
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.04
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.38
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.40
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.51
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.00
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.00
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5082.38
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.88
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.73
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.76
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.93
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4902.97
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.71
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.39
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.70
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:25.01

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.56
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:25.22

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 8.19e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 4.75e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.37
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.37
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.49
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:05.31

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.98
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:06.53

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9906.18
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9973.22
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.070
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:37.87

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4762.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:50.59

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4181.38
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3964.03
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11720.12
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:29.45

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11658.72
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.04
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999858383

Normal statistic for number of bits   :   -1.12
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.59
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999888758

Normal statistic for number of bits   :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n96, Linux

AHSrandom-TR 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-TR 
 Number of statistics:  160
 Total CPU time:   03:02:42.29

 All tests were passed




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